 f(m) = m**2 + m - 2. Let z be f(-3). Suppose -p = z*p - 20. Factor -p*d**2 - d**2 + 3*d**2 + 9*d - 6 - d**2.
-3*(d - 2)*(d - 1)
Factor -8/5*z - 2/5*z**2 - 8/5.
-2*(z + 2)**2/5
Let z(q) = -96*q - 96. Let m be z(-1). Let p(b) = b**2 - 3*b. Let g be p(4). Suppose -1/4*j**5 + 1/4*j**g - 1/4*j**2 + 0 + 1/4*j**3 + m*j = 0. What is j?
-1, 0, 1
Find p, given that 32*p + 3 - 19 + 8*p**2 + 32*p - 100*p**3 + 20*p**2 - 48*p**4 = 0.
-2, -1, 1/4, 2/3
Let t(j) be the second derivative of j**7/42 - 21*j**6/5 + 1323*j**5/5 - 6174*j**4 + 3*j + 9. Factor t(x).
x**2*(x - 42)**3
Factor -64*b**4 - 5*b**2 + 2*b**2 + 67*b**4.
3*b**2*(b - 1)*(b + 1)
Let q(r) be the third derivative of -r**6/240 - r**5/60 + 7*r**4/48 - r**3/3 + 113*r**2. Determine l, given that q(l) = 0.
-4, 1
Let u(y) be the third derivative of -1/10*y**5 + 0*y + 25*y**2 + 1/60*y**6 - 1/3*y**3 + 0 + 1/4*y**4. Factor u(o).
2*(o - 1)**3
Let g(x) be the second derivative of -x**6/18 - 13*x**5/12 - 115*x**4/36 - 55*x**3/18 + 110*x + 2. Let g(v) = 0. What is v?
-11, -1, 0
Let o(b) be the second derivative of -b**4/3 + 10*b**3 + 32*b**2 - 182*b. Find p such that o(p) = 0.
-1, 16
Factor 2/13*z**3 + 0 + 17298/13*z + 372/13*z**2.
2*z*(z + 93)**2/13
Factor -195*x**2 - 6*x + 66*x**2 + 66*x**2 + 65*x**2 + 4.
2*(x - 2)*(x - 1)
Let s(q) = 14*q**2 - 13*q - 4. Let o(g) be the first derivative of 43*g**3/3 - 39*g**2/2 - 11*g + 7. Let k(r) = 6*o(r) - 17*s(r). Factor k(u).
(4*u - 1)*(5*u - 2)
Let o be ((-57)/(-190))/(1/4). Let -2/5*v**3 + 0 - 4/5*v - o*v**2 = 0. Calculate v.
-2, -1, 0
Let y(u) be the third derivative of u**6/300 + 13*u**5/150 + u**4/6 - 8*u**3/5 + 41*u**2 + 3. Factor y(o).
2*(o - 1)*(o + 2)*(o + 12)/5
Let b = 7850 - 7846. Find s, given that -18/5*s**b - 6/5*s**5 + 0*s + 0*s**2 + 0*s**3 + 0 = 0.
-3, 0
Factor 605/3 - 17/3*b**2 - 1/3*b**3 - 11/3*b.
-(b - 5)*(b + 11)**2/3
Let h(g) be the second derivative of 7*g**6/40 + 3*g**5/5 - 3*g**4/2 - 8*g**3 - 6*g**2 - 147*g. Solve h(f) = 0 for f.
-2, -2/7, 2
Let a(z) = -4*z**5 - 6*z**4 - 18*z**3 + 12*z**2 + 46*z + 4. Let p(g) = 3*g**5 + 4*g**4 + 12*g**3 - 8*g**2 - 31*g - 2. Let w(v) = 5*a(v) + 7*p(v). Factor w(b).
(b - 3)*(b - 2)*(b + 1)**3
Let t(v) be the third derivative of v**5/10 + 13*v**4/24 + v**3/3 + 70*v**2. Factor t(f).
(f + 2)*(6*f + 1)
Let s(v) = 7*v**2 + v - 3. Let x be s(1). Let i be (-4)/12 + x/9. Factor -2/9*b**2 + i + 0*b.
-2*(b - 1)*(b + 1)/9
Let s(b) be the first derivative of -b**6/30 - 7*b**5/25 - 11*b**4/20 - b**3/3 - 75. Let s(m) = 0. Calculate m.
-5, -1, 0
Suppose -2*j = -0*j + 4*r - 250, 500 = 4*j + 4*r. Let c = -249/2 + j. Factor -5/6*i + 1/3 - c*i**2.
-(i + 2)*(3*i - 1)/6
Let b be 11 - (-3 - -8 - -4). What is m in -4*m**b + 1/3*m**3 - 64/3 + 16*m = 0?
4
Let 2/15*f**4 + 2/15*f**3 - 14/15*f**2 - 2/15*f + 4/5 = 0. What is f?
-3, -1, 1, 2
Suppose -90*t = -94*t + 16. Let p(b) be the second derivative of 1/70*b**5 - 5/21*b**3 + 0 - 1/14*b**t - 2/7*b**2 - 5*b + 1/105*b**6. Factor p(a).
2*(a - 2)*(a + 1)**3/7
Let g(f) = -f**3 - 12*f**2 + 11*f - 26. Let p(w) = -w**3 - 5*w**2 - 3*w - 9. Let o be p(-4). Let d be g(o). Factor d*k + 0*k**2 + 0 + 3/4*k**3.
3*k**3/4
Let z(y) be the second derivative of y**5/120 + y**4/24 + y**3/12 + 17*y**2/2 - 7*y. Let m(s) be the first derivative of z(s). Factor m(d).
(d + 1)**2/2
Let g(c) = 2*c**3 - 2*c**2 + 1. Let p(u) = 11*u**3 - 16*u**2 + 28*u - 26. Let n(t) = 6*g(t) - p(t). Factor n(k).
(k - 2)**2*(k + 8)
Let r(i) be the first derivative of 7*i + 1/10*i**6 - 1/2*i**3 + 8 - 3/4*i**4 + 3*i**2 + 3/20*i**5. Let t(a) be the first derivative of r(a). Factor t(x).
3*(x - 1)**2*(x + 1)*(x + 2)
Factor -38*v**4 - 58*v**2 + 25*v**3 + 53*v**2 + 43*v**4 - 25*v.
5*v*(v - 1)*(v + 1)*(v + 5)
Let a(w) be the third derivative of -2*w**5/3 + 7*w**4/6 + 2*w**3 - 84*w**2 - 1. Let a(z) = 0. Calculate z.
-3/10, 1
Let l be (273/52)/((-3)/(-88)). Let i be (1 - 5) + 728/l. Determine o so that 6/11 + 2/11*o**2 + i*o = 0.
-3, -1
Let j = 83 - 79. Let z(a) be the second derivative of 5*a + 2/27*a**3 + 1/135*a**6 + 0*a**j - 1/45*a**5 - 1/9*a**2 + 0. Factor z(d).
2*(d - 1)**3*(d + 1)/9
Let r(k) be the first derivative of 2*k**3/69 + 17*k**2/23 + 144*k/23 + 96. Factor r(x).
2*(x + 8)*(x + 9)/23
Let v(i) be the second derivative of 7/78*i**4 + 1/39*i**6 - 1/273*i**7 + 0 - 30*i + 0*i**2 - 2/39*i**3 - 9/130*i**5. Factor v(k).
-2*k*(k - 2)*(k - 1)**3/13
Factor -2637*s**4 + 39*s**3 + 2*s**5 + 33*s**3 + 2661*s**4.
2*s**3*(s + 6)**2
Let g = -21646 + 194816/9. Suppose g*x**4 + 0 + 0*x + 4/9*x**3 - 2/3*x**2 = 0. Calculate x.
-3, 0, 1
Let a(v) be the second derivative of v**7/840 - v**6/120 + 7*v**3/3 - 20*v. Let u(j) be the second derivative of a(j). Factor u(l).
l**2*(l - 3)
Suppose z = -t - 4*z - 3, 0 = t - 3*z - 13. Let s(p) be the second derivative of 8/15*p**3 - t*p + 1/30*p**4 + 0 + 16/5*p**2. Let s(l) = 0. What is l?
-4
Let g(u) be the first derivative of -4*u**5/5 + 8*u**4 + 296*u**3/3 - 720*u**2 - 8100*u + 279. Suppose g(p) = 0. Calculate p.
-5, 9
Let u(k) be the first derivative of 5/3*k**3 + 12 - 10*k - 5/2*k**2. Factor u(r).
5*(r - 2)*(r + 1)
Let z(b) be the third derivative of -b**7/84 + 7*b**6/240 + b**5/40 - 7*b**4/48 + b**3/6 - 13*b**2 - b. Determine c, given that z(c) = 0.
-1, 2/5, 1
Let k(a) = -12*a**3 - 8*a**2 + 12*a + 8. Let p be (5 - 2 - 4)/(-1). Let d(b) = -b**3 - b**2 + b + 1. Let t(r) = p*k(r) - 10*d(r). Solve t(j) = 0 for j.
-1, 1
Let i(b) be the second derivative of -23*b + 0 + 0*b**2 + 3*b**3 + 1/4*b**4. Factor i(s).
3*s*(s + 6)
Suppose -6 = -5*u - u. Let s be (-52)/(-48) + u/(-3). Factor 0 - s*y - 3/4*y**2.
-3*y*(y + 1)/4
Let q(s) be the first derivative of -s**8/1260 + s**7/315 - 4*s**3/3 - 1. Let w(m) be the third derivative of q(m). Factor w(x).
-4*x**3*(x - 2)/3
Let h(p) = p**3 - 4*p**2 + 7*p - 4. Let l be h(2). Find x such that -x**3 + 798 + 5*x**3 - 8*x**l - 838 - 52*x = 0.
-2, -1, 5
Let i(j) = 3*j**2 - 26*j - 14. Let n(z) = z**2 - 2*z - 1. Let r be (3*4/3)/((-12)/(-18)). Let s(g) = r*n(g) - i(g). Factor s(m).
(m + 4)*(3*m + 2)
Let j(q) = 49*q**3 - 24*q**2 - 11*q + 91. Let u(t) = -156*t**3 + 72*t**2 + 32*t - 272. Let g(l) = 16*j(l) + 5*u(l). Factor g(o).
4*(o - 6)*(o - 2)*(o + 2)
Let x(w) = -2*w**3 + 13*w**2 - 4*w - 31. Let g(z) = 4*z**3 - 27*z**2 + 10*z + 61. Let s(k) = 6*g(k) + 10*x(k). Find d such that s(d) = 0.
-1, 2, 7
Let v(j) = -j**2 - 38*j - 37. Let u(c) = -2*c**2 - 2*c. Let m(x) = 3*u(x) - 3*v(x). Solve m(h) = 0.
-1, 37
Suppose k + 1 = z, -2*k = -z - 2 - 1. Suppose p + 3*t - 4 = z, -5*p + 3 = t. Factor 0 + 0*s**2 - 2/7*s**5 + p*s**4 + 2/7*s**3 + 0*s.
-2*s**3*(s - 1)*(s + 1)/7
Let d = -18 - -22. Find v such that -16*v**4 + 3*v**5 + 0*v + 0*v + 13*v**d = 0.
0, 1
Factor -3*o**2 - 874*o + 634*o - 2*o**2 + o**2.
-4*o*(o + 60)
Suppose -6*n - 56 = 82. Let c(w) = -w**2 - 26*w - 67. Let y be c(n). What is g in -2*g**3 + 2/3*g**y + 4/3*g + 0 = 0?
-2/3, 0, 1
Let i = 628 + -623. What is o in 0*o + 1/3*o**4 + 0 - 1/3*o**2 - 1/3*o**3 + 1/3*o**i = 0?
-1, 0, 1
Let o be (-1)/((-25)/15) - (-194)/10. Suppose o*w = 6*w + 42. Factor 1/2*l + 0 + 3/2*l**w - 1/2*l**4 - 3/2*l**2.
-l*(l - 1)**3/2
Let c(v) be the second derivative of v**4/18 + 46*v**3/9 - 233*v. Determine f, given that c(f) = 0.
-46, 0
Let k(c) be the first derivative of 0*c**2 + 1/8*c**6 + 3/4*c**5 + 0*c + c**3 + 34 + 3/2*c**4. Let k(a) = 0. What is a?
-2, -1, 0
Suppose -5*l - 25 = -0*l. Let t = 8 + l. Factor 0*j**2 - j**t - 2*j - 2*j**2 + j.
-j*(j + 1)**2
Let y = 39 + -37. Suppose -y*d = -242 + 238. Let 0*w + 0 + 0*w**d - 2/3*w**4 + 4/3*w**3 = 0. What is w?
0, 2
Suppose -2*s + 0*s + 3 = -y, -2*s + 13 = y. Factor -4*v**2 + 30*v - 21*v - 17*v + s*v**3.
4*v*(v - 2)*(v + 1)
Let u(z) = 268*z**2 + 476*z + 816. Let q(f) = 47*f**2 + 84*f + 144. Let d(n) = 40*q(n) - 7*u(n). Suppose d(x) = 0. Calculate x.
-4, -3
Let n(y) be the third derivative of y**6/40 - y**5/20 - 3*y**4/2 + 160*y**2. Factor n(x).
3*x*(x - 4)*(x + 3)
Suppose -174 = 9*x - 183. Solve -x + 1/2*s**2 + 1/2*s = 0 for s.
-2, 1
Suppose 36*s = 3 + 69. Let 9/2*v**2 - 3/2 + 5*v - s*v**3 = 0. What is v?
-1, 1/4, 3
Let n(q) = 2*q**2 + 26*q + 85. Let k be n(-6). Let w be k + 0 + ((-16)/3)/(-2). Determine s so that 40/9*s + s**3 - 16/9 - w*s**2 = 0.
1, 4/3
Suppose 5*m - 15 = -k, 5*m + 2*k - 19 = 1. What is a in -1/3*a**4