a.
0, 3
Let v(t) = -35*t**2 + 40*t - 16. Let c(x) be the second derivative of -3*x**4/2 + 10*x**3/3 - 4*x**2 + 17*x. Let g(j) = 11*c(j) - 6*v(j). Factor g(k).
4*(k - 1)*(3*k - 2)
Let q be 8/2 - (24*-1 + 1). Let a be (-6)/q - 119/(-252). Factor 1/4*g**5 + 0 + 0*g + 1/4*g**4 - a*g**2 - 1/4*g**3.
g**2*(g - 1)*(g + 1)**2/4
Let o(m) be the first derivative of -2*m**3/15 - 3*m**2 + 68*m/5 + 180. Factor o(p).
-2*(p - 2)*(p + 17)/5
Let d(i) = -37*i**2 - 5*i + 2. Let x be d(-2). Let r = x + 412/3. Solve r*h**3 + 2/3 - 4/3*h + 0*h**2 - 2/3*h**4 = 0 for h.
-1, 1
Let p be ((-50)/6)/((-322)/21 - 1). Let v = p + 3/49. Determine l so that -2/7*l - v - 4/7*l**3 + 10/7*l**2 = 0.
-1/2, 1, 2
Let w be (-2)/6 - 64/(-3). Suppose -26*x + w*x = 0. Factor -2/5 - 1/5*t**3 + x*t**2 + 3/5*t.
-(t - 1)**2*(t + 2)/5
Let n = -42 + 28. Let q be -3 + n/(3 + -5). Find i, given that -i**3 - q*i**2 + 7*i**3 + 6*i**3 + 4 - 12*i = 0.
-1, 1/3, 1
Let z be (-3 - 9 - -12)/(-5). Factor -1/3*y**4 + 0 + 0*y + 2/3*y**3 + z*y**2.
-y**3*(y - 2)/3
Let q(w) be the second derivative of w**8/6720 - w**6/240 - w**5/60 - w**4/32 - 5*w**3/2 - 17*w. Let v(n) be the second derivative of q(n). Factor v(c).
(c - 3)*(c + 1)**3/4
Determine k so that 51*k**3 - 27*k**3 - 33*k**4 - 243*k - 81 - 162*k**3 - 145*k**2 - 3*k**5 - 125*k**2 = 0.
-3, -1
Let j be (0 + -2)*(-455)/(-5). Let m = -180 - j. What is o in 3*o + 3*o**5 - 3/2*o**4 - 3/2 - 6*o**3 + 3*o**m = 0?
-1, 1/2, 1
Let z(j) be the third derivative of 0*j + 23*j**2 + 1/40*j**6 - 1/8*j**4 + 0*j**5 + 0*j**3 + 0. Factor z(v).
3*v*(v - 1)*(v + 1)
Let m(c) be the second derivative of -37/4*c**3 - 16*c - 15/2*c**2 - 7/8*c**4 + 0. Solve m(h) = 0.
-5, -2/7
Let b = 484 - 482. Let a(i) be the first derivative of 5/6*i**4 - 4/3*i + 7/3*i**2 - b*i**3 - 2/15*i**5 + 1. Factor a(r).
-2*(r - 2)*(r - 1)**3/3
Suppose 2/5*i**3 + 98/5*i + 0 + 28/5*i**2 = 0. Calculate i.
-7, 0
Suppose -g = -8*g + 357. Let z = -46 + g. Suppose 37/5*k**3 + 9/5*k**z + 4/5*k + 4*k**2 + 6*k**4 + 0 = 0. Calculate k.
-1, -2/3, 0
Let p be 188/(-329)*((-295)/65 - -4). Determine d, given that 2/13*d**2 + 6/13*d + p = 0.
-2, -1
Let q(t) = -2*t**3 - 3*t**2 - 3*t. Let b be q(-2). Let a be (-28)/b - (-12 + 8). Let 3/5*n**2 + a*n + 3/5 = 0. Calculate n.
-1
Let i(w) be the second derivative of 7*w**5/15 + 19*w**4/9 - 4*w**3/3 - 96*w. Find j, given that i(j) = 0.
-3, 0, 2/7
Let y(f) be the first derivative of -4 + 0*f - 9/4*f**4 - 1/6*f**6 - f**2 - 7/3*f**3 - f**5. Solve y(c) = 0 for c.
-2, -1, 0
Let s(a) be the first derivative of 15*a**4 - 305*a**3/3 + 265*a**2/2 - 20*a + 790. Find g such that s(g) = 0.
1/12, 1, 4
Let f = -201 + 157. Let d = 44 + f. Determine g so that 0*g + 2/7*g**5 + d + 2/7*g**2 - 2/7*g**3 - 2/7*g**4 = 0.
-1, 0, 1
Let u be (0 + 4)*27/(-12). Let w = u + 13. Factor 7*p + 3*p - 6*p - w + 4*p**2 - 4*p**3.
-4*(p - 1)**2*(p + 1)
Let g(m) be the second derivative of 3*m**5/80 - 5*m**4/16 - m**3/8 + 15*m**2/8 - 140*m. Factor g(a).
3*(a - 5)*(a - 1)*(a + 1)/4
Let k = 38966 + -38964. Factor 3/4*s**k + 0 + 3/8*s**3 + 3/8*s.
3*s*(s + 1)**2/8
Let t(x) be the first derivative of -2*x**5/15 - 7*x**4/12 - x**3/3 + 4*x**2/3 + 4*x/3 + 3. Suppose t(g) = 0. Calculate g.
-2, -1/2, 1
Let y(o) be the first derivative of o**6/6 - o**5 + 3*o**4/4 + 3*o**3 + 70. Factor y(d).
d**2*(d - 3)**2*(d + 1)
Let t = 1768/3 + -589. Suppose -1/6*c**5 + 1/6*c**4 + t*c**3 - 1/6*c - 1/3*c**2 + 1/6 = 0. Calculate c.
-1, 1
Suppose -x + 3*q - 2*q = 137, 0 = 2*x + 4*q + 304. Let k = x - -145. Let 0*t - 4/9*t**2 + 2/9*t**4 - 2/9*t**k + 0 = 0. What is t?
-1, 0, 2
Let o(i) be the second derivative of 1/48*i**4 + 0*i**2 + 0 - 1/80*i**5 - i + 1/12*i**3. Factor o(u).
-u*(u - 2)*(u + 1)/4
Let b be (-30)/(-8)*(91/(-490) + 10/35). Factor -3/8*j**2 + 0*j + 0 - 9/8*j**3 - 9/8*j**4 - b*j**5.
-3*j**2*(j + 1)**3/8
Suppose 4*w - 23 + 7 = 0. Suppose 3*z + 6 = 5*j - 1, 2*j - 5*z = -1. Suppose w*l**2 - j - 15 - 4*l + 9 = 0. What is l?
-1, 2
Let z = -3599/6 + 600. Let c(o) be the second derivative of 5*o + 2/3*o**3 - z*o**4 + 0*o**2 + 0. Factor c(v).
-2*v*(v - 2)
Suppose -15 = 5*t, -3*t + 4 - 3 = -5*f. Let p be (-140)/(-75) + f/(-15). Solve 9*v**3 + p*v**4 - 3 - 3*v**2 + 4*v**4 - 9*v + 0*v**2 = 0.
-1, -1/2, 1
Let z(v) = 4*v**4 + 9*v**3 + v**2 - 4*v - 5. Let g(i) = i**3 + i**2 - 1. Let t = 33 - 38. Let h(q) = t*g(q) + z(q). Factor h(w).
4*w*(w - 1)*(w + 1)**2
Let s(c) = -c**3 - 6*c**2 - 3*c + 18. Let t(h) = -h**2 + 4*h + 1. Let f(z) = s(z) + 4*t(z). Factor f(y).
-(y - 2)*(y + 1)*(y + 11)
Factor -4*i**4 - i**3 - 4*i**5 + 263*i**2 - 275*i**2 + 20*i**3 + 8*i**3 - 7*i**3.
-4*i**2*(i - 1)**2*(i + 3)
Find b such that -128/3*b + 16/3*b**2 - 2/9*b**3 + 1024/9 = 0.
8
Let r be (-14)/(-28)*1*4. Solve -r*k**2 + 7*k**2 + 0*k + k + k = 0.
-2/5, 0
Let r(z) be the second derivative of -1/42*z**4 - 13*z + 0*z**3 + 0 + 4/7*z**2. What is s in r(s) = 0?
-2, 2
Let t(z) be the first derivative of 4*z + 11 - 2/5*z**5 - 3*z**2 + 3/2*z**4 - 2/3*z**3. Determine p so that t(p) = 0.
-1, 1, 2
Let v(z) be the third derivative of -z**6/32 - 13*z**5/80 - z**4/8 + z**3/2 + 17*z**2 - 2. Factor v(o).
-3*(o + 1)*(o + 2)*(5*o - 2)/4
Let p(q) = 2*q**2 - 11*q - 8. Let t be p(7). Suppose -2*l = 5*g - 25, -5*g + 12 = 4*l - t. Factor 4*r + 3*r**3 - 4*r**2 + 4*r**4 - r**3 - g*r**3 - r**3.
4*r*(r - 1)**2*(r + 1)
Let v = 4993/156 + -32. Let g = 323/1716 - v. What is t in 0 - 2/11*t**2 + 2/11*t**4 - 6/11*t**3 + g*t**5 + 4/11*t = 0?
-2, -1, 0, 1
Let w(q) = 2*q**2 + q. Let j = -7 + 13. Let f(p) = 13*p**2 + 1 - 1 - 2*p**2 + 7*p - 1. Let a(x) = j*f(x) - 34*w(x). Factor a(c).
-2*(c - 3)*(c - 1)
Let k(c) be the third derivative of -c**8/840 + c**7/140 + c**6/20 + c**5/12 + 10*c**3/3 - 45*c**2. Let x(f) be the first derivative of k(f). Factor x(t).
-2*t*(t - 5)*(t + 1)**2
Suppose -m = 4*m - 15. Determine j, given that -11*j**3 + 4*j**2 - 3*j**m + 12*j**3 + 2*j - 3 - j**4 = 0.
-3, -1, 1
Let j(h) be the second derivative of h**6/75 + h**5/25 - 7*h**4/30 + 4*h**3/15 + 93*h. Factor j(k).
2*k*(k - 1)**2*(k + 4)/5
Let n = -267 - -271. Let o be 0/(n/24 + 7/(-6)). Factor -3*z**2 + 3/2*z**3 + 3/2*z**4 + 0 + o*z.
3*z**2*(z - 1)*(z + 2)/2
Let g(s) = 1. Let u(c) be the second derivative of c**5/20 + 3*c**4/4 + 9*c**3/2 + 14*c**2 + 4*c. Let i(r) = -3*g(r) + 3*u(r). Determine b so that i(b) = 0.
-3
Let o(z) be the third derivative of 0 - 77/300*z**5 + 13*z**2 + 0*z - 2/15*z**3 + 49/600*z**6 + 4/15*z**4. Factor o(c).
(c - 1)*(7*c - 2)**2/5
Determine v, given that -1/7*v**2 + 25/7*v + 0 = 0.
0, 25
Let r(g) be the first derivative of g**6/18 - 4*g**5/15 + 5*g**4/12 - 2*g**3/9 - 86. Factor r(k).
k**2*(k - 2)*(k - 1)**2/3
Let -6/5*j**3 + 204/5*j + 57/5*j**2 + 36 - 3/5*j**4 = 0. What is j?
-3, -2, 5
Suppose -12*q - 6/5*q**3 + 144/5 - 78/5*q**2 = 0. Calculate q.
-12, -2, 1
Find q, given that 5/2*q**2 + 60*q + 360 = 0.
-12
Let f(p) be the third derivative of -1/15*p**6 + 1/21*p**7 + 0*p - 1/84*p**8 + 0*p**3 - 24*p**2 + 0*p**4 + 0 + 1/30*p**5. What is m in f(m) = 0?
0, 1/2, 1
Let h = -2150 + 10754/5. Factor h - 6/5*t**3 - 4/5*t**2 + 6/5*t.
-2*(t - 1)*(t + 1)*(3*t + 2)/5
Let x be (-861)/(-15) - 4/(-10)*-1. Factor 18*z**2 - 32 + 41*z + 4*z**4 + 7*z**2 - x*z + 20*z**3 - z**2.
4*(z - 1)*(z + 2)**3
Let z(b) be the third derivative of -b**6/30 - 8*b**5/15 - 10*b**4/3 - 32*b**3/3 + 2*b**2 - 25*b. Factor z(w).
-4*(w + 2)**2*(w + 4)
Determine q so that -5*q**4 - 227*q - 126*q - 67*q - 380*q**2 - 95*q**3 = 0.
-14, -3, -2, 0
Suppose 3 = l + 5*s + 1, 0 = -5*l - s + 10. Factor 9*z**3 + 44*z + 16 - 18*z**3 + 13*z**3 + 9*z**l + 17*z**2.
2*(z + 2)*(z + 4)*(2*z + 1)
Let k(c) be the first derivative of 7*c**6/10 - 12*c**5/5 + 11*c**4/4 - c**3 - 17*c + 16. Let l(m) be the first derivative of k(m). Factor l(q).
3*q*(q - 1)**2*(7*q - 2)
Let c(d) be the first derivative of 1/5*d**2 + 2/15*d**3 + 0*d + 14. Factor c(n).
2*n*(n + 1)/5
Factor -36*h**2 + 0*h**2 - 3*h**3 + 6*h**3 + 15*h + 18*h.
3*h*(h - 11)*(h - 1)
Let h(i) be the third derivative of i**5/90 + i**4/12 + 2*i**3/9 - 4*i**2 - 2. Solve h(t) = 0 for t.
-2, -1
Suppose 7*l + 10 - 24 = 0. Let x = 5/42 + 3/14. Factor x*v + 0 - 1/2*v**l.
-v*(3*v - 2)/6
Let o(w) be the second derivative of w**6/135 + w**5/10 - 4*w**3 + 6*w + 11. Factor o(l).
2*l*(l - 3)*(l + 6)**2/9
Let q(c) = -2*c**2 + 2*c 