*x = v + 2. Solve 3*s**3 - 8*s - 4*s**2 - 5*s**2 - 6*s**3 + x*s = 0 for s.
-2, -1, 0
Let y(l) = -7*l**2 + l**2 + 10 + l**3 - 7. Let p be y(6). Factor 13*q**2 - 4*q + 15*q**p + q**2 - 2*q**2 + 4*q**4.
q*(q + 2)**2*(4*q - 1)
Factor 72*o**2 - 35*o - 43*o - 69*o**2 - 99*o.
3*o*(o - 59)
Let m(s) be the first derivative of s**4/8 + 5*s**3/6 + s**2 - 1. Factor m(w).
w*(w + 1)*(w + 4)/2
Let o(h) be the second derivative of h**7/168 - 3*h**5/80 - h**4/24 + h - 202. Determine c so that o(c) = 0.
-1, 0, 2
Let n = 10 + -3. Let h = n + -4. Find y, given that 15*y**3 + 6*y**4 + 12*y**2 + 4*y - 2*y**4 - h*y**3 + 0*y**4 = 0.
-1, 0
Suppose -7*h = -4*h - 15. Suppose h*n + 2 = 6*n. Determine d so that -d**3 + 4*d**4 - 4*d**2 + 5*d**3 + n*d - 4*d - 2*d = 0.
-1, 0, 1
Factor -171*a**3 - 185*a**3 + 84 - 249*a + 536*a**3 + 243*a**2 - 255*a**3 - 3*a**4.
-3*(a - 1)**3*(a + 28)
Let b(c) be the third derivative of c**7/210 - 3*c**6/40 + 2*c**5/15 - 7*c**2 - 7*c. Factor b(k).
k**2*(k - 8)*(k - 1)
What is d in 4/7*d**3 - 2/7*d**5 - 2/7*d**4 + 0 + 0*d + 0*d**2 = 0?
-2, 0, 1
Suppose 3*p**3 - 79*p**2 + 272*p - 112 - 144 + p**3 - 4*p**2 + 3*p**2 = 0. What is p?
2, 16
Let t be ((-4)/(-5))/2*(1 - -9). Let u(f) be the third derivative of 0*f + 0*f**3 - f**2 + 0 + 1/18*f**t - 1/90*f**5. Let u(h) = 0. What is h?
0, 2
Suppose i = -3*i - 9*i. Let u(l) be the second derivative of 1/18*l**4 - 5*l + i + 4/3*l**2 + 4/9*l**3. Factor u(y).
2*(y + 2)**2/3
Let o(j) be the first derivative of -3*j**5/40 + j**3/4 + 3*j - 6. Let v(y) be the first derivative of o(y). Factor v(f).
-3*f*(f - 1)*(f + 1)/2
Suppose 51*b + 48 = 67*b. Let w(i) be the second derivative of 135*i**2 + 83/4*i**5 + 495/2*i**b + i + 3/2*i**6 + 435/4*i**4 + 0. Factor w(r).
5*(r + 3)**3*(9*r + 2)
Let i(k) = -k**2 + 14*k - 5. Let l(t) = 10*t**2 - 125*t + 45. Let w(r) = r**2 + 3*r + 4. Let q be w(0). Let u(h) = q*l(h) + 35*i(h). Factor u(y).
5*(y - 1)**2
Suppose -g - 3 = -2*g, -m + 5*g = 14. Suppose -2 - m = -j. Factor -2/7*i**4 + 0 + 0*i + 2/7*i**2 + 2/7*i**j - 2/7*i**5.
-2*i**2*(i - 1)*(i + 1)**2/7
Let m(u) = 24*u + 2164. Let o be m(-90). Factor -8/9*i**o + 0*i**2 + 0*i - 2/9*i**5 - 2/3*i**3 + 0.
-2*i**3*(i + 1)*(i + 3)/9
Let l(f) be the first derivative of -f**4 - 8*f**3 - 24*f**2 - 32*f + 26. Suppose l(z) = 0. What is z?
-2
Factor -771*y**2 - 1130*y**2 + 13456 - 12*y**3 - 39904*y + 513*y**2.
-4*(y + 58)**2*(3*y - 1)
Suppose 0 = 9*y - 3 - 42. Let d(s) = s**3 - s**2 + 2*s. Let b(v) = -v**2 - v. Let g(m) = y*d(m) + 5*b(m). Suppose g(w) = 0. What is w?
0, 1
Let k(f) be the third derivative of f**8/756 - 19*f**7/945 + 2*f**6/27 + 5*f**5/54 + 28*f**2 + 2. Factor k(o).
2*o**2*(o - 5)**2*(2*o + 1)/9
Let a(n) be the third derivative of 0*n**3 - 3/40*n**6 - 1/70*n**7 + 1/20*n**5 + 0*n + 1/4*n**4 + 15*n**2 + 0 + 1/112*n**8. Let a(y) = 0. What is y?
-1, 0, 1, 2
Let v(h) = -15*h**3 - 9*h**2 + 6*h. Let d(t) = t**2 - 8*t + 7. Let s be d(8). Let y(j) = 30*j**3 + 19*j**2 - 14*j. Let w(f) = s*v(f) + 3*y(f). Factor w(k).
-3*k**2*(5*k + 2)
Let c(j) be the second derivative of 0 - 1/27*j**3 + 1/135*j**6 + 1/90*j**5 - 1/54*j**4 + 0*j**2 - 32*j. Suppose c(x) = 0. What is x?
-1, 0, 1
Let w(z) = -8*z**2 - 296*z - 504. Let j(u) = -u**2 - 33*u - 56. Let m(o) = -28*j(o) + 3*w(o). Factor m(h).
4*(h + 2)*(h + 7)
Let c(g) be the second derivative of -g**4/48 + g**3/24 + g**2/4 + 29*g. Determine b so that c(b) = 0.
-1, 2
Let q(y) be the second derivative of 3*y - 1/126*y**7 - 1/15*y**5 + 2/45*y**6 + 0*y**3 + 0 + 0*y**2 + 0*y**4. Suppose q(z) = 0. What is z?
0, 2
Let o be 4/6*(-56)/(-168). Determine s, given that 2/3*s**2 - 4/9 - 2/9*s**4 - o*s + 2/9*s**3 = 0.
-1, 1, 2
Let d be (-12)/(-30)*(-25)/(-2). Let s be d/(-9)*-1*(-18)/(-15). Factor s*l + 8/3*l**2 + 0.
2*l*(4*l + 1)/3
Suppose 4 = 3*j - 4*x, 6 + 1 = -j + 3*x. Let w(i) = -2*i - 42. Let y be w(-22). Factor 3*f**2 + f**3 + 8 - j + y*f.
f*(f + 1)*(f + 2)
Let u = 153 + -147. Let h(g) be the first derivative of 16/3*g**3 + 16*g**2 - 32*g + 14/5*g**5 - 3 - 8*g**4 - 1/3*g**u. Factor h(w).
-2*(w - 2)**4*(w + 1)
Let g(c) = 7*c**3 - 3*c**2 - 49*c - 51. Let i(t) = 13*t**3 - 5*t**2 - 99*t - 101. Let d(k) = 5*g(k) - 3*i(k). Determine l so that d(l) = 0.
-3, -1, 4
Let -4*y**4 + 2/3*y**5 + 8/3*y - 8*y**2 + 26/3*y**3 + 0 = 0. Calculate y.
0, 1, 2
Let n = -31 + 33. Suppose -4*v + 2*v - 3*v + 2*v - v**n = 0. What is v?
-3, 0
Let u(s) = -3*s**3 + 6*s**2 - 30*s + 15. Let t(b) = -5*b**3 + 5*b**2 - 31*b + 15. Let z(x) = -3*t(x) + 4*u(x). Determine r, given that z(r) = 0.
-5, 1
Let a(h) be the first derivative of 7*h**5/5 + 9*h**4/4 - 18*h**3 - 50*h**2 - 24*h - 21. Factor a(k).
(k - 3)*(k + 2)**2*(7*k + 2)
Suppose -5 = 5*q + 5, 0 = 2*h - 5*q - 988. Let j = -3417/7 + h. Let 2/7*m**3 + 2/7*m**2 - 10/7*m + j = 0. What is m?
-3, 1
Let t(k) be the third derivative of k**7/21 + 23*k**6/24 + 11*k**5/12 - 4*k**2 + 21*k. Factor t(l).
5*l**2*(l + 11)*(2*l + 1)
Factor 3872/7*w**3 + 0*w**2 + 2/7*w**5 + 176/7*w**4 + 0 + 0*w.
2*w**3*(w + 44)**2/7
Let t(d) = -2*d**4 - 36*d**3 + 84*d**2 - 28*d. Let h(c) = -5*c**4 - 108*c**3 + 248*c**2 - 84*c. Let y(b) = 6*h(b) - 17*t(b). Determine p, given that y(p) = 0.
0, 1, 7
Let o be (((-14)/(-42))/((-15)/6))/(22/(-110)). Determine p, given that 2*p**4 + o*p**3 - 14/3*p**2 + 0*p + 8/3 - 2/3*p**5 = 0.
-1, 1, 2
Let j(d) be the first derivative of d**3/6 + d**2 + 3*d/2 + 58. Factor j(n).
(n + 1)*(n + 3)/2
Let j = -15248/9 - -1696. Solve -2/9*x**2 - j*x - 32/9 = 0 for x.
-4
Let r(h) be the first derivative of h**3/3 + 3*h**2 - 7*h - 24. Factor r(f).
(f - 1)*(f + 7)
Suppose 2*c = d + 70, -2*c + 4*d + 97 = 27. Let j = c - 69/2. Solve -k**2 + j + 0*k**3 + 0*k + 1/2*k**4 = 0.
-1, 1
Factor 4/5*a**2 - 29/5*a + 7/5.
(a - 7)*(4*a - 1)/5
Let m be (-152)/6*(-69)/2. Let b = m - 6983/8. Factor 1/8*a**5 - 7/8*a**2 - 5/8*a**4 + b*a**3 + 0 + 1/4*a.
a*(a - 2)*(a - 1)**3/8
Let m(p) be the second derivative of 0 + 1/120*p**5 + 0*p**3 - 4*p + p**2 + 0*p**4 + 1/240*p**6. Let f(v) be the first derivative of m(v). Factor f(y).
y**2*(y + 1)/2
Factor -2*u**4 + 56 - u**3 - 52*u**2 + 29*u + 31*u - 59*u**3 - 2*u**4.
-4*(u - 1)*(u + 1)**2*(u + 14)
Let b(k) = -k**3 - 5*k**2 + 2*k + 9. Let o be b(-6). Solve -32 - 2*p**2 - 9*p - 7 - 15*p - o = 0 for p.
-6
Suppose 22*o = -206 + 250. Suppose -4/9*c + 8/9 - 4/3*c**o = 0. Calculate c.
-1, 2/3
Let u(l) be the second derivative of l**6/60 + 3*l**5/10 - 15*l**4/8 + l**3/3 + 15*l**2 + 17*l - 2. Factor u(p).
(p - 2)**2*(p + 1)*(p + 15)/2
Factor -40/9*m**2 - 188/9*m**3 + 0*m + 0 - 4*m**4.
-4*m**2*(m + 5)*(9*m + 2)/9
Let d = -4343/5 - -869. What is y in -d*y + 1/5*y**2 + 1/5 = 0?
1
Let d(v) be the second derivative of 0*v**4 + 0*v**2 + 0*v**3 + 0 + 1/10*v**6 + 3/20*v**5 - 19*v. Suppose d(q) = 0. Calculate q.
-1, 0
Let u(w) be the second derivative of w**4/16 - 3*w**3/4 + 15*w**2/8 - 14*w. Solve u(m) = 0.
1, 5
Let i(t) be the third derivative of -t**6/180 - 2*t**5/15 - t**4 - 32*t**3/9 - 646*t**2. Determine o, given that i(o) = 0.
-8, -2
Let s = 49/2640 - 1/528. Let i(d) be the second derivative of -4*d - s*d**6 + 1/20*d**5 - 1/24*d**4 + 0*d**3 + 0*d**2 + 0. Let i(r) = 0. Calculate r.
0, 1
Let v(x) be the first derivative of x**4/36 - 31*x**3/27 - 16*x**2/9 + 418. Factor v(r).
r*(r - 32)*(r + 1)/9
Let h(t) be the second derivative of -19*t + 3/40*t**5 + 0 + 0*t**2 - 1/28*t**7 + 1/30*t**6 - 1/12*t**4 + 0*t**3. Determine c so that h(c) = 0.
-1, 0, 2/3, 1
Let 15*d**2 + 3 + 10 - 46*d**3 + 91*d**3 - 46*d**3 - 27*d = 0. What is d?
1, 13
Let g(b) be the first derivative of 5*b**3/3 - 2*b**2 - b + 242. Factor g(s).
(s - 1)*(5*s + 1)
Let o(i) = 32*i**2 - 20*i - 16. Let k(z) = 22*z**2 - 13*z - 10. Let s(g) = 8*k(g) - 5*o(g). Let s(h) = 0. Calculate h.
0, 1/4
Let g(f) be the first derivative of -f**7/280 + f**6/40 - f**4/2 + 11*f**3/3 + 11. Let a(v) be the third derivative of g(v). Solve a(c) = 0 for c.
-1, 2
Let d(n) be the third derivative of n**10/6048 - n**8/672 + n**6/144 + 9*n**4/8 - 28*n**2. Let s(b) be the second derivative of d(b). Factor s(p).
5*p*(p - 1)**2*(p + 1)**2
Let a(g) = -2*g**2 - 6*g + 24. Let p(n) = 2*n**2 + 5*n - 24. Let d(x) = -3*a(x) - 4*p(x). Factor d(v).
-2*(v - 3)*(v + 4)
Let u(j) = j**3. Let r(y) = 3*y**4 + 3*y**2. Let g be 7*(5 + 116/(-28)). Let t(z) = g*u(z) + r(z). Solve t(a