iven that c(m) = 0.
-1, 0, 1
Let k be (36/7)/((-2)/(-7)). Suppose -3*t = -b - k, 5*b + 53 = 4*t + 18. Factor 3*c**4 - c**4 + c**4 - t*c**4.
-2*c**4
Let v = -76 + 127. Suppose 9 = -6*q + v. Solve q*o - 3*o**3 + o - 4*o**4 + o**3 + 4*o**2 - 6*o**3 = 0 for o.
-2, -1, 0, 1
What is p in 63/2*p - 3/2*p**2 + 3/2 - 63/2*p**3 = 0?
-1, -1/21, 1
Suppose -5*t**3 + 21*t**3 - 11*t**3 - 10*t**3 + 855*t**2 - 850*t = 0. What is t?
0, 1, 170
Factor 24*u**2 + 12*u**4 + 2967*u**5 - 24*u**3 - 8*u - 2*u**3 - 2969*u**5.
-2*u*(u - 2)**2*(u - 1)**2
Let h(u) be the second derivative of -u**5/10 + u**3/3 + 14*u. Let h(l) = 0. What is l?
-1, 0, 1
Factor -67*n**4 + 342*n**2 + 1236*n - 564*n + 384 + 57*n**3 + 70*n**4.
3*(n + 1)*(n + 2)*(n + 8)**2
Find x such that 5*x + 5*x + 18*x**3 - 3*x**2 + 3*x**4 - 17*x + 3*x - x**5 - 13*x**3 = 0.
-1, 0, 1, 4
Let y(z) be the third derivative of z**6/180 + z**5/15 - 25*z**4/36 + 2*z**3 + 182*z**2. Determine h, given that y(h) = 0.
-9, 1, 2
Factor 2/15*v**2 + 5618/15 + 212/15*v.
2*(v + 53)**2/15
What is i in 0 - 153/2*i**2 + 3/2*i**3 - 78*i = 0?
-1, 0, 52
Suppose -2*t - 15 = -7*t. Factor x**4 + 14*x**3 - 4 - 18*x**3 + 5*x - x + t*x**2.
(x - 2)**2*(x - 1)*(x + 1)
Factor 1/2*x**3 - 11/2*x**2 + 0*x + 0.
x**2*(x - 11)/2
Factor 5*q - 1/2*q**2 - 12.
-(q - 6)*(q - 4)/2
Let n(m) = 10*m**4 - 20*m**3 + 90*m**2 + 252*m + 168. Let a(w) = -8*w**4 + 16*w**3 - 91*w**2 - 252*w - 167. Let q(u) = 6*a(u) + 5*n(u). Factor q(l).
2*(l - 9)*(l + 1)*(l + 3)**2
Let t = -172 + 96. Let d be -9*(6 - t/(-12)). Factor 0*o - d + 3/4*o**2.
3*(o - 2)*(o + 2)/4
Suppose 0 = -5*x - 3*q + 35, 0 = 2*x - 5*q + 2*q + 7. Suppose 3*v + 0 - 1 = -5*d, 4*v - x = -4*d. Factor -8/13*i + 2/13*i**v + 8/13.
2*(i - 2)**2/13
Let f(h) be the first derivative of h**5/15 - 2*h**3/3 + 4*h**2/3 - 18*h + 12. Let s(w) be the first derivative of f(w). Factor s(k).
4*(k - 1)**2*(k + 2)/3
Determine t so that 32*t**3 + 24*t + 198*t**2 - 422*t**2 - 4*t**4 + 172*t**2 = 0.
0, 1, 6
Let y(u) be the second derivative of -7*u**6/15 - 43*u**5/30 - 7*u**4/6 + u**3/3 + 2*u**2/3 + 34*u + 2. Let y(s) = 0. Calculate s.
-1, -1/3, 2/7
Let g(t) be the third derivative of -t**6/270 + t**4/18 + 8*t**3 + 18*t**2 - 2. Let r(v) be the first derivative of g(v). Determine j, given that r(j) = 0.
-1, 1
Let k be 5/6 - (1 - 1/3). Factor 1/6*x**4 + k*x - 1/6*x**3 - 1/6*x**2 + 0.
x*(x - 1)**2*(x + 1)/6
Let f(t) be the first derivative of -1/18*t**6 - 1/9*t**3 - 1/4*t**4 + 0*t**2 + 21 - 1/5*t**5 + 0*t. Solve f(m) = 0 for m.
-1, 0
Factor -152*z**2 - 130 + 110*z**3 - 115*z**3 - 265*z + 12*z**2.
-5*(z + 1)**2*(z + 26)
Let u(z) = 4 + 7 + 6*z**3 + 11*z + 4*z**2 - 23*z**2. Let k(n) = -n**2 + n + 1. Let m(s) = -18*k(s) + 2*u(s). Factor m(v).
4*(v - 1)**2*(3*v + 1)
Let c be (-25)/(-2)*(-402)/(-1005). Let q(g) be the third derivative of c*g**2 - 1/30*g**6 + 0 + 0*g - 1/15*g**5 + 0*g**4 + 0*g**3. Factor q(z).
-4*z**2*(z + 1)
Let f(s) = s**3 + s**2. Let r(g) = 2*g**3 + 6*g**2 - 3*g + 1. Suppose 4*i - 6*i + 3*v - 15 = 0, 4*v = -4*i. Let j(z) = i*f(z) + r(z). Factor j(d).
-(d - 1)**3
Let f(y) = y**3 - 21*y**2 - 9*y - 5. Let i(x) = 6*x**2 - x - 15*x**3 - 5*x**2 + 14*x**3. Let s(o) = f(o) + 6*i(o). Factor s(d).
-5*(d + 1)**3
Factor 33*j + 15*j**3 + j**5 - 11*j**3 + 16*j**2 + 14 - 6*j**4 - 14*j**3.
(j - 7)*(j - 2)*(j + 1)**3
Let n be (-36)/(-342) + (-178)/(-114). Solve -5*r + n*r**2 + 10/3 = 0 for r.
1, 2
Suppose 4*g + 5*f - 3 + 1 = 0, g + 3*f + 3 = 0. Let a be (-3)/(-1) - (3 - 3). Factor 1 - 6*i**2 + 4*i**a - 3*i**4 + 4*i**g - 2*i**4 + 2*i**4.
-(i - 1)**3*(3*i + 1)
Let k(y) = -1. Let v(s) = -s**3 + 21*s**2 - 56*s + 34. Let u(h) = 4*k(h) - 2*v(h). Suppose u(c) = 0. Calculate c.
1, 2, 18
Let i(o) = -o**3 + 9*o**2 + 23*o - 7. Let x be i(11). Factor 2/15*l**3 + 2/15*l**2 + 0 - 8/3*l**x + 0*l.
-2*l**2*(4*l - 1)*(5*l + 1)/15
Let j(d) be the second derivative of d**4/24 + d**3 + 11*d**2/4 - 209*d. Find a such that j(a) = 0.
-11, -1
Let n(c) = -c**3 - 12*c**2 + 29*c + 19. Let d be n(-14). Suppose 8*k + 3*k**4 - 9*k**2 - 2 - k - 3*k**4 + d*k**3 - k**4 = 0. Calculate k.
1, 2
Suppose 3*z + 10*z = -2*z. Let n(q) be the third derivative of -1/1890*q**7 + 0*q - 1/540*q**5 + z*q**3 + 0 - 3*q**2 + 0*q**4 + 1/540*q**6. Factor n(r).
-r**2*(r - 1)**2/9
Let z(p) be the second derivative of 8/5*p**2 + 26*p + 2/3*p**3 + 0 + 1/15*p**4. Factor z(k).
4*(k + 1)*(k + 4)/5
Let q(y) = 10*y**3 + 19*y**2 - 72*y + 39. Let g(d) = -9*d**3 - 21*d**2 + 72*d - 39. Let k(h) = 4*g(h) + 3*q(h). Factor k(z).
-3*(z - 1)**2*(2*z + 13)
Let f(w) be the third derivative of w**5/15 + 2*w**4 - 26*w**3/3 + 21*w**2 - 1. Factor f(j).
4*(j - 1)*(j + 13)
Suppose -5*s + 22 = 3*m, -3*m + 172 = -2*s + 164. What is c in 14/13*c**s - 22/13*c + 10/13 - 2/13*c**3 = 0?
1, 5
Let r(o) = 7*o + 3*o**3 - 1 - 4*o**3 - 8*o. Let v(x) = 3*x**3 - 3*x**2 + 21*x - 3. Let y(l) = -6*r(l) - v(l). Factor y(f).
3*(f - 1)**2*(f + 3)
Suppose k - 3*k = -4*g + 134, -k + 1 = 0. Factor 15*u + 29*u**3 + 4 + 6 - g*u**3.
-5*(u - 2)*(u + 1)**2
Let f(n) = 5*n**2 + 29*n + 28. Let z be f(-5). Let g(r) be the first derivative of 7/20*r**4 + 0*r + 1/25*r**5 + z + r**3 + 9/10*r**2. Solve g(a) = 0.
-3, -1, 0
Suppose -c - 5 = -8. Factor -4*g**2 - 3*g**2 + 0*g**3 + g**2 + 5*g + g**c.
g*(g - 5)*(g - 1)
Let n = -243673/38 + 6413. Let a(p) be the first derivative of 34/95*p**5 + 2/19*p**2 + n*p**4 + 0*p + 5/57*p**6 + 14 + 22/57*p**3. Factor a(j).
2*j*(j + 1)**3*(5*j + 2)/19
Let m(r) be the third derivative of 2*r**7/105 - 11*r**6/15 + 8*r**5 + 11*r**4/3 - 242*r**3/3 - 14*r**2 + 2. Solve m(p) = 0.
-1, 1, 11
Let q(c) be the second derivative of c**7/105 - 4*c**6/25 + c**5/5 + 2*c**4/5 - 11*c**3/15 + c - 40. Find x, given that q(x) = 0.
-1, 0, 1, 11
Let g(z) = z**3 - 8*z**2 + 11*z - 4. Let o(k) = -k**2 + k. Suppose -5*c = -c + 4. Let a(h) = c*g(h) + 3*o(h). Factor a(y).
-(y - 2)**2*(y - 1)
Let y be ((84/15)/14)/(1 - 0). Let r(b) be the first derivative of 0*b - 3 + 2*b**3 + 0*b**4 - y*b**5 - 2*b**2. Find v such that r(v) = 0.
-2, 0, 1
Let l(q) = q**3 + 8*q**2 + q - 10. Let h(f) = -3*f**3 - 24*f**2 - 4*f + 31. Let r(y) = 4*h(y) + 14*l(y). Factor r(o).
2*(o - 1)*(o + 1)*(o + 8)
Let l(q) = q**3 + q**2 - 1. Let s(o) = 12*o**3 + 9*o**2 - 3*o - 15. Suppose 7*k - 8*k - 1 = 0. Let f(h) = k*s(h) + 15*l(h). Factor f(n).
3*n*(n + 1)**2
Let o(l) be the second derivative of l**4/3 - 2*l**3 - 8*l**2 + 16*l + 1. Find g such that o(g) = 0.
-1, 4
Let p(x) be the first derivative of 0*x + 1/12*x**6 + 23 + 0*x**2 - 2/3*x**3 + 1/10*x**5 - 1/2*x**4. Find i, given that p(i) = 0.
-2, -1, 0, 2
Let f(h) be the third derivative of 0*h**5 + 1/45*h**6 + 0*h - h**2 + 0 + 1/6*h**3 + 0*h**4 - 1/70*h**7. Let b(r) be the first derivative of f(r). Factor b(o).
-4*o**2*(3*o - 2)
Determine l, given that -22/3*l**4 + 13/3*l + 5/3*l**5 - 32/3*l**2 - 2/3 + 38/3*l**3 = 0.
2/5, 1
Find q, given that -6/5*q**3 - 12/5*q**2 - 1/5*q**4 - 2*q - 3/5 = 0.
-3, -1
Let m be 14/15*(-54)/8. Let b = 39/5 + m. Factor 0*d + b*d**3 + 0 - 3/2*d**5 + 0*d**2 + 0*d**4.
-3*d**3*(d - 1)*(d + 1)/2
Let c(x) be the third derivative of x**5/12 - 5*x**4/12 - 20*x**3/3 - 115*x**2. Determine z so that c(z) = 0.
-2, 4
Let 7/5 + 43/10*q + 1/10*q**4 + 17/10*q**3 + 9/2*q**2 = 0. Calculate q.
-14, -1
Suppose 10*g - 11*g + 2 = 0. Let r(c) be the second derivative of 1/231*c**7 - 3/110*c**5 + 0*c**6 + 0*c**3 - g*c + 0 + 0*c**2 + 1/33*c**4. Factor r(o).
2*o**2*(o - 1)**2*(o + 2)/11
Let h(l) be the second derivative of -l**7/140 - l**6/20 - l**5/8 - l**4/8 + l**2 - 7*l. Let n(b) be the first derivative of h(b). Solve n(t) = 0 for t.
-2, -1, 0
Let p be 12/14*42/6. Solve 6*c**3 - 1 - 5*c**5 + 12*c**2 - 5 - 48*c + 45*c - p*c**4 + 2*c**5 = 0.
-2, -1, 1
Let x(s) = 6*s - 70. Suppose 0*c + 72 = 6*c. Let p be x(c). Factor -2/7*t**p - 8/7 - 10/7*t.
-2*(t + 1)*(t + 4)/7
Let f(r) be the third derivative of 1/360*r**5 + 11*r**2 - 1/144*r**4 + 0 - 1/36*r**3 + 0*r + 1/720*r**6. Factor f(a).
(a - 1)*(a + 1)**2/6
Find l such that 0 + 0*l - l**2 + 1/8*l**4 - 1/4*l**3 = 0.
-2, 0, 4
Let i(c) be the second derivative of -c**4/3 + 52*c**3/3 - 50*c**2 + 105*c + 1. Find r, given that i(r) = 0.
1, 25
Solve 255/7*x + 3/7*x**2 + 498/7 = 0.
-83, -2
Let c be 1 + (-6372)/(-30) + 2/(-5). Let w = c - 210. Factor j**2 + 0 + 2/3*j + 1/3*j**w.
j*(j +