question stringlengths 33 165 | answer stringlengths 6 35 |
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b'Let w(g) be the third derivative of -g**6/180 - 4*g**5/45 - 5*g**4/9 - 16*g**3/9 - 92*g**2. Factor w(u).\n' | b'-2*(u + 2)**2*(u + 4)/3\n' |
b'Let q(f) be the third derivative of 0*f**6 + 0*f**4 + 0*f**3 - 1/420*f**7 + 0 + 0*f - 5/1344*f**8 + 0*f**5 + 3*f**2. Factor q(s).\n' | b'-s**4*(5*s + 2)/4\n' |
b'Let u(t) be the third derivative of 0*t + 0 - 1/2*t**3 - 1/80*t**5 + 5/32*t**4 - 11*t**2. Suppose u(c) = 0. Calculate c.\n' | b'1, 4\n' |
b'Let v be (-3)/(-42) + (-123)/(-42). Find f such that 4/5*f - 6/5*f**2 + 2/5*f**v + 0 = 0.\n' | b'0, 1, 2\n' |
b'Determine i so that 20/7*i**2 - 144/7 - 352/7*i = 0.\n' | b'-2/5, 18\n' |
b'Factor 3/5*f**4 + 0*f + 0 - 18/5*f**3 + 3*f**2.\n' | b'3*f**2*(f - 5)*(f - 1)/5\n' |
b'Let g(q) = 2*q**2 + 12*q + 8. Let c(b) = -2. Let z(p) = -4*c(p) - g(p). Factor z(r).\n' | b'-2*r*(r + 6)\n' |
b'Suppose -122 = -2*n + 5*z, -4*z = n + n - 158. Factor -300 + 2*a**2 + n*a - 6*a**2 - 11*a + a**2.\n' | b'-3*(a - 10)**2\n' |
b'Let x(n) = n**2 - n. Let m(s) = 25*s**2 - 15*s - 10. Let u be (2/(-3))/(6/(-9)). Let q(t) = u*m(t) - 20*x(t). What is l in q(l) = 0?\n' | b'-2, 1\n' |
b'Let j be 4/3*(84/8)/7. Factor -21 + 34 - 17 + 4*b**j.\n' | b'4*(b - 1)*(b + 1)\n' |
b'Solve 1/8*c**2 + 7/8*c + 0 = 0.\n' | b'-7, 0\n' |
b'Let m(h) = h - 5. Let a be m(9). Find n such that 176/5*n**3 + 56*n**a + 20*n**5 + 0 + 32/5*n**2 + 0*n = 0.\n' | b'-2, -2/5, 0\n' |
b'Let g(i) be the third derivative of -i**6/540 + i**5/270 + i**4/54 - 94*i**2. Let g(p) = 0. Calculate p.\n' | b'-1, 0, 2\n' |
b'Suppose -5*y + 40 = 5*s, 788*y - 785*y - 20 = -2*s. Determine t so that -2/5*t**s - 6/5 + 8/5*t**2 - 4/5*t + 4/5*t**3 = 0.\n' | b'-1, 1, 3\n' |
b'Let t be -18*(-24)/660*10/4. Factor 10/11*u**2 + 6/11*u - t + 2/11*u**3.\n' | b'2*(u - 1)*(u + 3)**2/11\n' |
b'Let t = 8392 + -8389. Factor 17/2*i**3 - 10*i + 5/2*i**4 + t*i**2 - 4.\n' | b'(i - 1)*(i + 2)**2*(5*i + 2)/2\n' |
b'Suppose 0 = -2*q + 2*q - 3*q. Let o(b) be the second derivative of q*b**4 + 1/6*b**3 + b - 1/20*b**5 + 0 + 0*b**2. Solve o(n) = 0 for n.\n' | b'-1, 0, 1\n' |
b'Suppose 4*h + 5 - 5 + 275*h**4 - 276*h**4 - 3*h**3 = 0. What is h?\n' | b'-2, 0, 1\n' |
b'Let v be (4/4)/((-4)/(-16)). Solve -11*a**3 + 5*a**v - 45*a**2 + 47*a - 72*a - 4*a**3 = 0.\n' | b'-1, 0, 5\n' |
b'Factor 0 + 6/5*y**3 + 0*y**2 + 0*y + 3/5*y**4.\n' | b'3*y**3*(y + 2)/5\n' |
b'Let v(w) be the second derivative of -w**7/280 - w**6/24 - 7*w**5/40 - 3*w**4/8 - w**3/3 + 9*w. Let m(i) be the second derivative of v(i). Factor m(q).\n' | b'-3*(q + 1)**2*(q + 3)\n' |
b'Suppose -13*v + 448 = v. Suppose -q = 28 - v. Factor 0*t + 1/2*t**2 + 0 + 1/4*t**3 - 1/4*t**q.\n' | b'-t**2*(t - 2)*(t + 1)/4\n' |
b'Let p(a) be the first derivative of -4*a**3/3 - 8*a**2 - 12*a + 368. Suppose p(h) = 0. What is h?\n' | b'-3, -1\n' |
b'Let t(y) = -y**2 + 8*y - 2. Let i be t(6). Let n = 10 - i. Factor -v**3 - 2/5*v + 7/5*v**2 + n.\n' | b'-v*(v - 1)*(5*v - 2)/5\n' |
b'Let v(o) = -o**2 + 8*o + 2. Let x(f) = f**2 - 2*f + 1. Let u(j) = -v(j) - 2*x(j). Factor u(k).\n' | b'-(k + 2)**2\n' |
b'Let l be (2 + (-3)/(-6))*48. Suppose 32 - 10*f**3 + l*f + 30*f**3 + 4*f**2 + 104*f**2 = 0. Calculate f.\n' | b'-4, -1, -2/5\n' |
b'Let n(r) = -33*r - 162. Let l be n(-5). Let q(m) be the first derivative of -1/24*m**4 - 3 - 1/18*m**l + 0*m**2 + 0*m. Factor q(k).\n' | b'-k**2*(k + 1)/6\n' |
b'Let a be 2 - 282/(-36)*-1. Let g = -103/30 - a. Factor 0*o + 0 + g*o**3 - 8/5*o**2 + 4*o**4.\n' | b'4*o**2*(o + 1)*(5*o - 2)/5\n' |
b'Let h(u) be the second derivative of u**5/65 - u**4/78 + 55*u. Determine w, given that h(w) = 0.\n' | b'0, 1/2\n' |
b'Let s(p) = -3*p**2 + 48*p + 39. Let d(y) = -2*y**2 + 47*y + 39. Let z(i) = 6*d(i) - 5*s(i). Factor z(h).\n' | b'3*(h + 1)*(h + 13)\n' |
b'Let d(u) = 3*u**2 + 45*u - 1089. Let b be d(13). Determine t, given that 4/3*t**4 - 4/3*t**2 + 0 + 0*t**b + 2/3*t - 2/3*t**5 = 0.\n' | b'-1, 0, 1\n' |
b'Factor -400 + 0*d**2 - 120*d - d**2 - 4*d**2 + 0*d**2.\n' | b'-5*(d + 4)*(d + 20)\n' |
b'Determine o so that -84*o**3 - 377/4*o**2 + 441/4 - 16*o**4 + 84*o = 0.\n' | b'-21/8, -1, 1\n' |
b'Let k(b) be the second derivative of b**5/90 - 2*b**4/27 + 4*b**3/27 - 10*b. Determine i, given that k(i) = 0.\n' | b'0, 2\n' |
b'Suppose 0*n + 3*n = 2*h - 27, -2*n + 8 = 3*h. Suppose 3*c + 3*x - 6 = 0, 0 = 3*c - h*c - 4*x + 6. Solve c*r + 6 + r**3 + 7*r - 3*r**3 - r**3 = 0 for r.\n' | b'-1, 2\n' |
b'Let f(s) be the first derivative of -3*s**4/2 + 23*s**3/3 - 10*s**2 - 4*s - 5. Factor f(r).\n' | b'-(r - 2)**2*(6*r + 1)\n' |
b'Suppose -4*d + 4*x = -76, 0 = d + 24*x - 21*x + 9. Find b, given that 0 - 3*b + d*b**2 - 51/4*b**3 + 15/4*b**4 = 0.\n' | b'0, 2/5, 1, 2\n' |
b'Suppose 0 = 20*b - 24*b. Let u(v) be the second derivative of b - 7*v + 1/5*v**3 - 1/5*v**2 + 1/50*v**5 - 1/10*v**4. Solve u(t) = 0.\n' | b'1\n' |
b'Let l = -46 + 33. Let p = l - -16. Let 2*s**3 - 2*s**2 - 11 - s**p + 11 = 0. Calculate s.\n' | b'0, 2\n' |
b'Let b(y) be the first derivative of -2*y**3/39 + 2*y/13 + 516. Determine x so that b(x) = 0.\n' | b'-1, 1\n' |
b'Let k be (-23)/(-5) + (-102)/(-255). Let f(y) be the third derivative of -1/240*y**k + 0 + 1/24*y**3 + 6*y**2 + 1/480*y**6 + 0*y - 1/96*y**4. Factor f(o).\n' | b'(o - 1)**2*(o + 1)/4\n' |
b'Suppose 9*h - 5*k + 20 = 10*h, -h = 4*k - 15. Let d be -3 - (-3 + 0/h). Find f such that 0*f + d - 1/3*f**2 = 0.\n' | b'0\n' |
b'Let v be 8/(((-16)/(-10))/4). Let x = 22 - v. Suppose 4 - 57*s**3 - 5*s**2 + 21*s - 33*s**x + 21*s**4 + 11*s**2 + 2 + 36*s**5 = 0. What is s?\n' | b'-1, -1/4, 2/3, 1\n' |
b'Let -45*k - 11*k**2 + 9*k**2 + 70 + 7*k**2 = 0. What is k?\n' | b'2, 7\n' |
b'Let b(p) be the second derivative of 5*p**4/12 - 65*p**3/3 + 845*p**2/2 - 287*p. Factor b(i).\n' | b'5*(i - 13)**2\n' |
b'Let h be (4176/(-192) - -21)/((-6)/32). Factor -4/7*b**h + 0*b - 24/7*b**3 + 0 - 36/7*b**2.\n' | b'-4*b**2*(b + 3)**2/7\n' |
b'Let u(z) be the first derivative of -z**4/18 + 14*z**3/9 - 13*z**2/3 + 38*z/9 + 42. Factor u(g).\n' | b'-2*(g - 19)*(g - 1)**2/9\n' |
b'Let v(d) = 2*d**2 + 3*d + 1. Let h be v(-2). Suppose -5*x = r + 17, -3*r + 1 = h*x + 4. Factor 0*j**3 - j**2 + 0*j**3 - 3*j**4 - r*j**3 - j**5.\n' | b'-j**2*(j + 1)**3\n' |
b'Let p(z) = 4*z**3 + 2*z**2 + 16*z - 17. Let u be p(1). Let s(m) be the first derivative of -3/2*m**2 - u + 0*m + 1/3*m**3. Suppose s(a) = 0. What is a?\n' | b'0, 3\n' |
b'Factor -138 - 4*q**3 + 286 + 61 + 203 - 828*q + 420*q**2.\n' | b'-4*(q - 103)*(q - 1)**2\n' |
b'Let b be 4/(-6) - (-876)/18. Suppose -4*s - r = -b, 2*r - 48 = -4*s - 0*r. Factor -5 + 2*m**2 + s*m + 9 + 14.\n' | b'2*(m + 3)**2\n' |
b'Let w(f) = 5*f**2 + 8*f - 90. Let h(l) = -4*l**2 - 9*l + 79. Let q(z) = 6*h(z) + 5*w(z). Factor q(g).\n' | b'(g - 12)*(g - 2)\n' |
b'Let i = 2994/19 - 5893/38. Factor -i*w - 1/8*w**2 - 25/2.\n' | b'-(w + 10)**2/8\n' |
b'Let a(m) = -m**2 + 10*m - 1. Let b be a(11). Let r = 16 + b. Factor u**3 + 17*u - 17*u + u**r.\n' | b'u**3*(u + 1)\n' |
b'Let y(x) be the first derivative of -x**4/16 + 2*x**3/3 + 149. Factor y(i).\n' | b'-i**2*(i - 8)/4\n' |
b'Let q(v) = 15*v**2 - 63*v + 30. Let c(l) = l**2 - 2*l - 2. Let g(b) = 18*c(b) - q(b). Factor g(r).\n' | b'3*(r - 2)*(r + 11)\n' |
b'Suppose 5*n = -4*n. Let i(z) be the third derivative of 0*z - 1/20*z**5 + n - 1/24*z**4 + 5*z**2 - 1/120*z**6 + 1/70*z**7 + 1/168*z**8 + 0*z**3. Factor i(q).\n' | b'q*(q - 1)*(q + 1)**2*(2*q + 1)\n' |
b'Suppose -11 = -7*v + 17. Solve -v*h**2 - 48*h + 1 - 5 + 40*h = 0.\n' | b'-1\n' |
b'Let p = -113 - -227/2. Let j(r) be the first derivative of 4/5*r**2 - 2/25*r**5 - 4 - p*r**4 - 4/5*r**3 + 16/5*r. Factor j(l).\n' | b'-2*(l - 1)*(l + 2)**3/5\n' |
b'Let r = 1621 + -1610. Let y(q) be the first derivative of r + 5*q - 5/2*q**4 - q**5 + 0*q**3 + 5*q**2. Solve y(n) = 0 for n.\n' | b'-1, 1\n' |
b'Let h be ((-18)/4)/(24/(-32)). Let -3*a**3 - 3*a + 2*a**5 + 2*a**2 + 1 - 3*a**4 + 5*a**3 - h*a**5 + 5*a**5 = 0. Calculate a.\n' | b'-1, 1\n' |
b'Suppose a - 25 - 17 = -2*n, -4*a + 144 = 2*n. Let -34*p + a*p - 5*p**4 - 5*p**2 + 10*p**3 = 0. What is p?\n' | b'0, 1\n' |
b'Suppose 2*z + 10 = -14. Let j be 16/96 + (-46)/z. Let -1/2*p**5 - 1/2*p**2 - 2 - j*p + 5/2*p**3 + 1/2*p**4 = 0. Calculate p.\n' | b'-1, 2\n' |
b'Let h(g) be the second derivative of g**6/2520 + g**5/280 - 11*g**3/6 - 2*g. Let o(v) be the second derivative of h(v). Suppose o(r) = 0. What is r?\n' | b'-3, 0\n' |
b'Let u(b) = 51*b**3 - 99*b**2 - 24*b + 9. Let o(n) = -13*n**3 + 25*n**2 + 6*n - 2. Let h be -27*(0 + 2/(-6)). Let p(d) = h*o(d) + 2*u(d). Factor p(f).\n' | b'-3*f*(f - 2)*(5*f + 1)\n' |
b'Let k(j) be the first derivative of -3/35*j**5 + 9/7*j - 12/7*j**2 - 12 + 6/7*j**3 + 0*j**4. Factor k(o).\n' | b'-3*(o - 1)**3*(o + 3)/7\n' |
b'Let b(h) = h**2 - 5*h + 2. Let t = 72 + -48. Suppose w = -44 + 47. Let o(c) = c. Let f(v) = t*o(v) + w*b(v). Suppose f(m) = 0. Calculate m.\n' | b'-2, -1\n' |
b'Suppose -3*i = -36 - 48. Let h = i - 24. Factor -10 + 6*p + 1 - h + 4 - p**2.\n' | b'-(p - 3)**2\n' |
b'Let i(u) be the third derivative of -u**7/42 - 7*u**6/24 + u**5/4 + 115*u**4/24 + 35*u**3/3 + 195*u**2. Factor i(f).\n' | b'-5*(f - 2)*(f + 1)**2*(f + 7)\n' |
b'Suppose -4*f - 4*l - 824 = -0*f, 5*f + 3*l + 1034 = 0. Let y = f - -210. Find b, given that -2*b**y - 4/5*b**3 - 2/5*b + 4/5 = 0.\n' | b'-2, -1, 1/2\n' |
b'Let q = 39/62 - 4/31. Let b(m) be the second derivative of -m + 0 + 1/3*m**3 + q*m**2 + 1/12*m**4. Factor b(l).\n' | b'(l + 1)**2\n' |
b'Let a(u) = u - 6. Let z be a(8). Suppose 0 = l + z*n + 8, 2*l - 2*n - 5 = 9. Factor 0 - 3/2*b**l + 3/2*b**4 - 3/2*b**3 + 0*b + 3/2*b**5.\n' | b'3*b**2*(b - 1)*(b + 1)**2/2\n' |
b'What is i in 289 + 453 + 316 - 33*i + 2*i**2 - 59*i = 0?\n' | b'23\n' |
b'Let z(x) = 15*x**2 + 1 + 0*x**2 - 1 + 3*x**4 - 29*x**3. Let j(l) = l**4 - 15*l**3 + 8*l**2. Let a(h) = -11*j(h) + 6*z(h). Suppose a(o) = 0. What is o?\n' | b'0, 2/7, 1\n' |
b'Let r(y) be the third derivative of -y**7/168 - 5*y**6/72 - y**5/8 - 5*y**4/24 - 19*y**2. Let v(g) be the second derivative of r(g). Let v(z) = 0. What is z?\n' | b'-3, -1/3\n' |
b'Find d such that 3/2*d**3 + 1/2*d + 1/2*d**4 + 3/2*d**2 + 0 = 0.\n' | b'-1, 0\n' |
b'Let z = -44 + 52. Solve 0*k**3 + z*k**2 + 4*k - 5*k - 2*k**3 - 5*k = 0 for k.\n' | b'0, 1, 3\n' |
b'Let i(w) be the third derivative of w**5/30 - 7*w**4/8 + 20*w**2. Let m(u) = -3*u**2 + 21*u. Let g(x) = 6*i(x) + 5*m(x). Determine q so that g(q) = 0.\n' | b'-7, 0\n' |
b'Let v(b) be the second derivative of b**4/6 - 16*b**3 + 47*b**2 - 449*b. Factor v(y).\n' | b'2*(y - 47)*(y - 1)\n' |
b'Let d(h) = 6*h + 1. Let p(i) = 7*i. Let k(v) = -6*d(v) + 5*p(v). Let g be k(-8). Factor -6*r**g - 27*r + 27*r + 9*r**3 - 3*r**4.\n' | b'-3*r**2*(r - 2)*(r - 1)\n' |
b'Let c(f) = -160*f**3 - 5*f**2 + 5*f. Let w(q) = 160*q**3 + 5*q**2 - 4*q. Let r(h) = 4*c(h) + 5*w(h). Factor r(o).\n' | b'5*o**2*(32*o + 1)\n' |
b'Let b(q) be the third derivative of 5/42*q**4 + 0 - 4/21*q**3 + 11/105*q**5 + 2/105*q**6 + 31*q**2 + 0*q. Factor b(v).\n' | b'4*(v + 1)*(v + 2)*(4*v - 1)/7\n' |
b'Let f(h) be the first derivative of h**7/14 + 5*h**6/12 + 3*h**5/4 + 5*h**4/12 + 11*h**2/2 - 21. Let l(p) be the second derivative of f(p). Factor l(a).\n' | b'5*a*(a + 1)*(a + 2)*(3*a + 1)\n' |
b'Let q(g) be the second derivative of g**4/18 - 20*g**3/9 + 100*g**2/3 - 87*g. Determine s, given that q(s) = 0.\n' | b'10\n' |
b'Let a(b) be the second derivative of b**5/4 - 5*b**4/6 - 5*b**3/6 + 5*b**2 - 16*b + 1. Find o such that a(o) = 0.\n' | b'-1, 1, 2\n' |
b'Let f be 2124/(-118) - 21/(-1). Let z be (-20)/(-6) - (-2)/3. Suppose 0 + 1/2*b**2 - 1/2*b**f - 1/2*b**z + 1/2*b = 0. Calculate b.\n' | b'-1, 0, 1\n' |
b'Let c = -80890/7 - -11442. Let u = 114 + c. Factor 4/7 - 6/7*i + u*i**2.\n' | b'2*(i - 2)*(i - 1)/7\n' |
b'Let w(y) = 2*y**2 + 1. Let l(s) = 12*s**2 + 416*s - 10808. Let n(i) = -l(i) + 8*w(i). Factor n(g).\n' | b'4*(g - 52)**2\n' |
b'Suppose -13*w + 0 + 4*w**3 - 7*w + 7*w**4 + 12*w**2 - 11*w**4 + 8 = 0. Calculate w.\n' | b'-2, 1\n' |
b'Let w(b) be the first derivative of -3*b**5/5 + 15*b**4/4 - 6*b**3 - 6*b**2 + 24*b - 334. Factor w(s).\n' | b'-3*(s - 2)**3*(s + 1)\n' |
b'Let m = -22 + 28. Solve 8 - m*r - 8*r**2 + 6*r**2 + 6*r = 0 for r.\n' | b'-2, 2\n' |
b'Let i(g) be the first derivative of -g**6/33 + 26*g**5/55 - 23*g**4/22 + 2*g**3/3 + 117. Solve i(s) = 0 for s.\n' | b'0, 1, 11\n' |
b'Let j(w) be the third derivative of w**6/15 - w**5/15 - 73*w**2 - 2*w. Factor j(z).\n' | b'4*z**2*(2*z - 1)\n' |
b'Let j be (0 - (0 - -4)/4)*0. Suppose -9*m + 7*m = j. Factor m + 2/5*k**2 + 4/5*k.\n' | b'2*k*(k + 2)/5\n' |
b'Let b(f) = f**2 + 9*f - 12. Let u be b(-10). Let k(o) = -8*o**2 + o. Let r(l) = -l**3 + 8*l**2 - 2*l. Let a(z) = u*k(z) - 3*r(z). What is m in a(m) = 0?\n' | b'0, 2/3, 2\n' |
b'Let l = -780 - -780. Let z(p) be the third derivative of -p**2 + 0 - 1/360*p**5 - 1/144*p**4 + l*p**3 + 0*p. Find h such that z(h) = 0.\n' | b'-1, 0\n' |
b'Let z(v) be the second derivative of v**5/20 - v**3/2 + v**2 - 3*v + 7. Factor z(p).\n' | b'(p - 1)**2*(p + 2)\n' |
b'Determine z so that -59/6*z + 25/6*z**3 - 1 - 70/3*z**2 = 0.\n' | b'-1/5, 6\n' |
b'Let w(b) = 9*b**2 + 699*b - 1581. Let x(f) = f**2 + 70*f - 158. Let t(n) = 2*w(n) - 21*x(n). Factor t(r).\n' | b'-3*(r - 2)*(r + 26)\n' |
b'Let p(a) be the third derivative of -a**6/420 - 2*a**5/15 - 25*a**4/21 - 32*a**3/7 + 105*a**2. Determine j so that p(j) = 0.\n' | b'-24, -2\n' |
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