b.
2*b**2*(b - 1)*(b + 1)**2/7
Let p(r) = -r**3 - 5*r**2 + 2*r + 12. Let c be p(-5). Factor -4 + 3*t**2 + 4*t - 1 - c*t**2 - t**3 + 1.
-(t - 2)*(t - 1)*(t + 2)
Let -2/3*k**2 + 8/9 + 2/9*k**3 + 0*k = 0. Calculate k.
-1, 2
Let c(x) = x**2 + 7*x + 7. Let a be c(-7). Let k(f) be the third derivative of 3/8*f**4 + 1/40*f**6 - a*f**2 + 1/2*f**3 + 0*f + 0 + 3/20*f**5. Factor k(s).
3*(s + 1)**3
Let p(t) be the second derivative of 2*t**3 + 1/2*t**4 + 1/20*t**5 + 24*t + 0 + 4*t**2. Solve p(k) = 0.
-2
Let o(v) be the third derivative of v**7/1050 + v**6/1800 - 31*v**3/6 + v**2 + 30*v. Let t(g) be the first derivative of o(g). Find k, given that t(k) = 0.
-1/4, 0
Let w(b) = 5*b**4 + 6*b**3 + 10*b**2 + 3. Let q(l) = 36*l**4 + 42*l**3 + 72*l**2 + 22. Let d(n) = 6*q(n) - 44*w(n). Factor d(s).
-4*s**2*(s + 1)*(s + 2)
Suppose 2*x = 4*x - 5*p - 84, -5*x = p - 156. Let u be 176/x - 4/1. Suppose 0 + 0*y**3 - u*y**2 + 3/8*y**5 + 9/8*y**4 + 0*y = 0. What is y?
-2, 0, 1
Factor 2/5*x**2 - 22*x - 228/5.
2*(x - 57)*(x + 2)/5
Let m(u) be the third derivative of u**6/1020 - 13*u**4/51 + 32*u**3/17 - 4*u**2 - 4*u. What is c in m(c) = 0?
-8, 2, 6
Let v = 153 + -149. Factor 0*n - n - 2*n**2 + 2 + 4*n**3 - v*n + n.
2*(n - 1)*(n + 1)*(2*n - 1)
Let x(n) = -n**3 - 6*n**2 - 6*n - 2. Let i be x(-5). Factor i*b**3 - 6*b**4 - 2*b + 5*b**2 + 4*b**2 - b - 3*b**4.
-3*b*(b - 1)*(b + 1)*(3*b - 1)
Let a(j) be the third derivative of j**8/8960 - j**7/2016 - 11*j**6/2880 - j**5/160 - j**4/8 - 19*j**2. Let k(f) be the second derivative of a(f). Factor k(v).
(v - 3)*(v + 1)*(3*v + 1)/4
Suppose 53*z - 59*z = 0. Factor 1/5*t**2 + 0 + z*t.
t**2/5
Let k(d) be the second derivative of -d**4/60 + 4*d**3/15 + 18*d - 2. Factor k(m).
-m*(m - 8)/5
Let r = -31 - -35. Find q such that 21*q**2 + 13*q**2 + 4*q - 2*q**r - 28*q**2 = 0.
-1, 0, 2
Let m(n) be the third derivative of n**5/60 - 11*n**4/8 - 17*n**3/3 - 56*n**2 - 2. Suppose m(x) = 0. What is x?
-1, 34
Factor -9/4*m + 0 + 3/8*m**3 - 3/8*m**2.
3*m*(m - 3)*(m + 2)/8
Let i(u) = u**3 + 12*u**2 + 14*u + 35. Let x be i(-11). Let z(m) be the first derivative of -6 + 1/2*m**x + 1/6*m**3 + 1/2*m. Factor z(c).
(c + 1)**2/2
Let y be (-2)/2*(-19)/1. Let -11*v + 5*v**3 - 3*v**2 - 1 + 39*v - 7 - y*v**2 = 0. What is v?
2/5, 2
Let q be (-1525)/(-990) + (-6)/27. Let y = 20/11 - q. Solve -7/2*a**2 + y - 2*a**3 - a = 0.
-1, 1/4
Let r(t) = -2*t**3 + 2*t**2 - t. Let v(b) = 5*b**3 - 5*b**2 + 3*b + 1. Let m(x) = 8*r(x) + 3*v(x). Let u be m(0). Factor -2/7*j - 1/7*j**2 + 1/7*j**u + 0.
j*(j - 2)*(j + 1)/7
Let d(j) be the first derivative of 2*j**6/5 - 17*j**5/5 + 31*j**4/3 - 46*j**3/3 + 12*j**2 - 49*j - 25. Let l(o) be the first derivative of d(o). Factor l(a).
4*(a - 3)*(a - 1)**2*(3*a - 2)
Let t(f) be the first derivative of -f**6/21 + 8*f**5/35 + f**4/7 - 16*f**3/21 - f**2/7 + 8*f/7 + 499. Solve t(h) = 0.
-1, 1, 4
Suppose -2/13*x**3 + 6/13*x**2 + 0*x - 8/13 = 0. Calculate x.
-1, 2
Let a = 922/3 - 307. Let s(v) be the third derivative of -2*v**2 - 1/8*v**4 + 0*v + 0 - 1/60*v**5 - a*v**3. Determine j so that s(j) = 0.
-2, -1
Factor -19/2 - 1/2*o**2 - 10*o.
-(o + 1)*(o + 19)/2
Suppose 8 - 2 = -2*i. Let t = i + 3. Factor 0*k + 2/3*k**5 + t - 1/3*k**2 - 5/3*k**4 + 4/3*k**3.
k**2*(k - 1)**2*(2*k - 1)/3
Let i(r) be the second derivative of r**7/14 - 2*r**6/5 - 9*r**5/10 + r**4 + 5*r**3/2 + 301*r. Determine f, given that i(f) = 0.
-1, 0, 1, 5
Factor -2/3*t**3 + 0*t + 0 - 2/3*t**4 + 0*t**2.
-2*t**3*(t + 1)/3
Let c(h) = -19*h**4 + 6*h**3 - 47*h**2 - 43*h + 59. Let g(o) = 7*o**4 - 2*o**3 + 16*o**2 + 14*o - 19. Let n(p) = -4*c(p) - 11*g(p). Factor n(d).
-(d - 3)*(d - 1)*(d + 3)**2
Let o = 338/2163 - -40/309. Factor -4/7*h**2 + 2/7 - 4/7*h**3 + o*h + 2/7*h**5 + 2/7*h**4.
2*(h - 1)**2*(h + 1)**3/7
Let h = -4 + 9. Find d such that 15*d**3 - 20*d - 18*d - h*d**4 + 18*d = 0.
-1, 0, 2
Let b be -3 + -2 + 3 + 144/24. Let w(o) be the first derivative of 4*o + 5 - b*o**2 - o**3 + 9/4*o**4. Factor w(u).
(u + 1)*(3*u - 2)**2
Factor 3*d**4 + 2700*d**2 - 9262*d - 180*d**3 + 9262*d.
3*d**2*(d - 30)**2
Let a(c) be the third derivative of -c**6/45 - c**5/18 - c**4/36 + 10*c**2 + 7*c. Suppose a(q) = 0. What is q?
-1, -1/4, 0
Factor 2/13*i**2 + 72/13*i - 152/13.
2*(i - 2)*(i + 38)/13
Let n(g) be the second derivative of 2*g**6/3 + 12*g**5/5 - 16*g**4/3 - 32*g**3 - 32*g**2 + g - 174. Factor n(r).
4*(r - 2)*(r + 2)**2*(5*r + 2)
Let z be (-1*0/(-1))/(11 - 9). Suppose q - 5*d - 25 = z, -2*q + 5*d + 28 - 3 = 0. Let 0*i**2 + 3/2*i**4 + 0*i**3 + q*i + 0 + 3/4*i**5 = 0. Calculate i.
-2, 0
Determine x so that -165*x**2 - 3*x**4 - 47*x**3 + 144 - 57*x**2 - 348*x - 14*x**2 = 0.
-6, -4, 1/3
Suppose 0 = t - 5*t - 4*p + 16, 4*t = -p + 4. Let l = -29/15 + 7/3. Factor t + l*h - 2/5*h**2.
-2*h*(h - 1)/5
Determine m, given that -9*m**3 - 16*m**3 - 16*m**2 + 48*m + 21*m**3 = 0.
-6, 0, 2
Factor -20*j**2 - 3*j**3 - 2*j**3 + 5*j**4 + 50*j - 30*j.
5*j*(j - 2)*(j - 1)*(j + 2)
Let j = 893/28 - 218/7. Solve 0 - 1/4*y**3 - 1/2*y - j*y**2 = 0 for y.
-2, -1, 0
Let u(t) be the second derivative of 1/6*t**3 + 1 + 1/6*t**4 + 0*t**5 - 10*t - 1/15*t**6 - 1/42*t**7 + 0*t**2. Find r such that u(r) = 0.
-1, 0, 1
Suppose 94*k - 102 = 43*k. Find s such that 4/19*s - 2/19*s**k - 2/19 = 0.
1
Let h(m) = -m + 9*m**3 + 7*m**3 - 17*m**3 - 6 - 13*m**2. Let j be h(-13). Factor 39 + w**2 + 3*w**2 - 40*w + 54 + j.
4*(w - 5)**2
Let 11529602/13 + 2/13*g**4 + 28812/13*g**2 - 392/13*g**3 - 941192/13*g = 0. Calculate g.
49
Let b(o) be the third derivative of o**7/2100 + o**6/300 - o**5/300 - o**4/20 + 7*o**3/2 + 22*o**2. Let m(h) be the first derivative of b(h). Factor m(t).
2*(t - 1)*(t + 1)*(t + 3)/5
Let h(m) = -2*m**3 - 3*m**2 - 7*m - 7. Let b be h(-3). Let k = -41 + b. Factor 1/2*d - 9/4*d**2 + k.
-d*(9*d - 2)/4
Let w = 193 - 193. Let g(a) = -a**2 + 5*a + 4. Let q be g(w). Factor -3*t**5 + 0*t - 20/3*t**q + 0*t**2 - 4/3*t**3 + 0.
-t**3*(t + 2)*(9*t + 2)/3
Let o(a) be the third derivative of -25/2*a**4 - 1/120*a**6 + 0 + 1/2*a**5 + 11*a**2 + 0*a + 500/3*a**3. Factor o(w).
-(w - 10)**3
Let w be ((-80)/(-1260))/(6/7). Let t(k) be the first derivative of 0*k + 2/9*k**2 - w*k**3 - 8. Factor t(o).
-2*o*(o - 2)/9
Let v be (-22)/143 + 50/(-13) + 28. Let o(u) = 4*u**5 + 4*u**4 + 16*u**3 - 24*u + 24. Let d(k) = k**3 - k + 1. Let g(a) = v*d(a) - o(a). Factor g(s).
-4*s**3*(s - 1)*(s + 2)
Let r(k) be the first derivative of k**4/4 - 7*k**3/3 + 7*k**2 - 8*k - 163. Factor r(f).
(f - 4)*(f - 2)*(f - 1)
Suppose 7 = 5*b + 2. Factor -5*t + b + 7 + 9*t - 2*t**4 - 4*t**3 - 6.
-2*(t - 1)*(t + 1)**3
Let q = 10249/2 + -5123. Factor -q*v**3 + 9/4*v + 0 - 3/4*v**2.
-3*v*(v - 1)*(2*v + 3)/4
Let f be 23 - (12 + -12 + (3 - 0)). Suppose 5*o - 25 = -2*r, 3*r - 4*o = r - f. Determine p, given that 4/5*p**4 + 4/5*p**3 - 4/5*p**5 + r + 0*p - 4/5*p**2 = 0.
-1, 0, 1
Let b(h) be the third derivative of -h**8/2184 - 2*h**7/1365 + h**6/156 + h**5/39 - h**4/39 - 8*h**3/39 + h**2 - 16*h. Determine d, given that b(d) = 0.
-2, -1, 1, 2
Let v(s) = 9*s - 15. Let h(w) = -w**2 - 20*w + 31. Let g(q) = -3*h(q) - 5*v(q). Determine c so that g(c) = 0.
-6, 1
Suppose q + 6 = 4*q. Determine w so that -3*w**2 + 16 + 6*w**q + w**2 + 20*w = 0.
-4, -1
Suppose 0 = -3*v + 2*q + 11, 0 = -3*v - 0*v + 4*q + 19. Suppose -5*l + 4 = -5*p - v, -4*p = -l - 8. Factor -1 + 4 + s - 2*s**p - 2*s**2 + s**3 - 1.
-(s - 1)*(s + 1)*(s + 2)
Let u = 7/4 - 5/3. Let k(p) be the second derivative of 1/3*p**3 + 0 - 1/2*p**2 - u*p**4 + 5*p. Solve k(h) = 0.
1
Suppose -25 = 8*p + 15. Let q be 2/10 - 14/p. Factor -1/5*w**4 - 8/5 - 18/5*w**2 - 7/5*w**q - 4*w.
-(w + 1)*(w + 2)**3/5
Let x(v) = 3*v**3 - 2*v**2 + v. Let i be x(1). Factor 0*c**4 + 9*c**4 - 3*c**i - 6*c**4.
3*c**2*(c - 1)*(c + 1)
Let q(p) be the second derivative of 0*p**5 - 39*p + 2/135*p**6 + 1/27*p**3 - 1/27*p**4 + 0 - 1/189*p**7 + 0*p**2. Factor q(y).
-2*y*(y - 1)**3*(y + 1)/9
Let q(r) = -6*r**4 - 9*r**3 + 7*r**2 - 10. Let t(u) = u**4 + u**3 + u**2 + 2. Let i(s) = -3*q(s) - 15*t(s). Factor i(j).
3*j**2*(j - 2)*(j + 6)
Let u = 6106/5 + -1221. Find s such that 0 - 1/5*s + 1/5*s**4 - u*s**2 + 1/5*s**3 = 0.
-1, 0, 1
Let q(h) = 15*h**2 + 25*h + 14. Let m(o) = 60*o**2 + 100*o + 55. Let b = 80 - 84. Let c(y) = b*m(y) + 15*q(y). Factor c(v).
-5*(v + 1)*(3*v + 2)
Let n(z) 