**2 + 4*r + 5. Let t = 8 + -15. Let a(l) = -6*l**2 + 6*l + 7. Let u(f) = t*v(f) + 5*a(f). Factor u(q).
-2*q*(q - 1)
Factor 0*i**2 - 1/2*i + 1/6*i**3 - 1/3.
(i - 2)*(i + 1)**2/6
Let h(d) be the third derivative of d**5/150 + 13*d**4/60 + 4*d**3/5 - 43*d**2 - 2. Determine r so that h(r) = 0.
-12, -1
Let c(n) = -11*n**3 + n. Let j be c(-1). Suppose 4*b - 5*h + 12 = 0, h + 0*h - j = -3*b. Solve 4/3*o**b - 2/3*o**3 + 0 - 2/3*o = 0.
0, 1
Let k(g) be the first derivative of g**6/42 + g**5/7 + 3*g**4/14 - 4*g**3/21 - 4*g**2/7 - 5. Factor k(q).
q*(q - 1)*(q + 2)**3/7
Let q(a) be the first derivative of 1/2*a**2 - 1/3*a**3 + 0*a - 7. Factor q(x).
-x*(x - 1)
Suppose 0 = -2*t - 2, -z = -3*z - 5*t + 1. Suppose 0 = z*y + y. What is c in 3 + 0*c**2 - c**2 + 3*c + y*c - 2*c**2 - 3*c**3 = 0?
-1, 1
Let s(i) be the third derivative of 0*i + i**2 + 1/210*i**7 + 0 - 1/24*i**4 - 1/40*i**6 + 0*i**3 + 1/20*i**5. Factor s(q).
q*(q - 1)**3
Suppose 18 = 9*m - 6*m. Let k(f) be the second derivative of 1/48*f**4 - 1/40*f**5 + 1/120*f**m + 0*f**2 - 2*f + 0*f**3 + 0. Factor k(c).
c**2*(c - 1)**2/4
Let o(c) = -2*c + 14. Let g be o(0). Let t = -14 + g. Factor t - 1/6*r - 1/6*r**2.
-r*(r + 1)/6
Let f(j) be the third derivative of 1/105*j**7 + 0*j**4 + 0*j + 0*j**3 + 0*j**6 + 0 - 1/30*j**5 - 3*j**2. Find b such that f(b) = 0.
-1, 0, 1
Let t = -679 - -18335/27. Let d(v) be the first derivative of -1 - t*v**3 + 2/9*v**2 - 2/9*v. Factor d(s).
-2*(s - 1)**2/9
Let l = 11 - 10. Let a be -4 + 1 - (-2 - l). Factor -2 + 2 + a*z - z**2 + 2*z.
-z*(z - 2)
Let 8 + s**3 - 33*s**2 + s**3 + 10*s**3 + 15*s - 2 = 0. Calculate s.
-1/4, 1, 2
Factor 3*d**2 + 28*d**3 + 2*d + 16*d**2 + 2*d + d**2 + 12*d**4.
4*d*(d + 1)**2*(3*d + 1)
Let r(m) = 3*m**3 - 3*m**2 - 15*m. Let g(d) = d. Let v be (-4)/10 + (-730)/50. Let q(t) = v*g(t) - r(t). Solve q(n) = 0.
0, 1
Let d be (7 - (18 + -11))/(-4). Factor 0*y**2 + d + 0*y - 3/2*y**3.
-3*y**3/2
Let r be 12/(-21)*(-1)/2. Suppose c - 4*c = -12. Let 0*i**3 + 0*i + r*i**2 - 2/7*i**c + 0 = 0. What is i?
-1, 0, 1
Let t be (66 - 2) + (0 - 1). Let r be t/90 + 2/(-10). Factor -1/2*x**2 + 1/2*x**4 - 1/2*x**3 + r*x + 0.
x*(x - 1)**2*(x + 1)/2
Let n = -169/2 + 86. Let 1 + n*c - 3/2*c**3 - c**2 = 0. Calculate c.
-1, -2/3, 1
Let q(x) be the third derivative of -x**5/150 - x**4/30 + 11*x**2. Factor q(v).
-2*v*(v + 2)/5
Factor 3/5*g**4 + 0*g + 12/5*g**3 + 0 + 9/5*g**2.
3*g**2*(g + 1)*(g + 3)/5
Solve 15*v + 75*v**5 - 15*v - 12*v**2 - 15*v**4 - 48*v**3 = 0 for v.
-2/5, 0, 1
Let v(y) = 2*y**3 + 36*y**2 - 80*y + 56. Let q(b) = b**3 + 24*b**2 - 53*b + 37. Let m(j) = -8*q(j) + 5*v(j). Let m(i) = 0. Calculate i.
2
Let v(c) be the first derivative of -c**6/120 - c**5/40 + 2*c**3/3 - 3. Let w(a) be the third derivative of v(a). Factor w(d).
-3*d*(d + 1)
Find p, given that -2*p**5 - 10*p**5 - 14*p**4 + 2*p**5 - 7*p**3 + 3*p**3 = 0.
-1, -2/5, 0
Let 0 + 3/4*s**2 - 3/4*s = 0. Calculate s.
0, 1
Suppose 24 = 4*q + g, g - 7 = 5*q - 28. Solve -q*p**2 + 9*p**4 + 16*p**2 + 16*p**3 - 2*p**4 + 2*p = 0.
-1, -2/7, 0
What is m in -6/7*m**3 + 0*m + 0 - 2/7*m**2 = 0?
-1/3, 0
Let s(t) be the second derivative of t**6/1980 - t**5/220 + t**4/66 - t**3/3 - 2*t. Let p(h) be the second derivative of s(h). Factor p(l).
2*(l - 2)*(l - 1)/11
Solve 0 - 8/9*s**4 - 4/9*s**3 + 0*s**2 + 0*s - 4/9*s**5 = 0 for s.
-1, 0
Let r = -215/8 + 27. Let k(j) be the first derivative of -2 + 1/3*j**3 + 0*j + 1/4*j**2 + r*j**4. Find l, given that k(l) = 0.
-1, 0
Let s(b) be the second derivative of -b**5/90 - b**4/9 - 4*b**3/9 - b**2/2 - 3*b. Let t(u) be the first derivative of s(u). Suppose t(w) = 0. What is w?
-2
Let n(i) be the second derivative of -5*i + 2/3*i**3 + 2/5*i**5 - 7/6*i**4 + 0 + i**2. Factor n(j).
2*(j - 1)**2*(4*j + 1)
Suppose -5*b - 20 = 20. Let y = 10 + b. Solve -6*g**2 - 25*g**5 + y*g - 17/2*g**3 + 75/2*g**4 + 0 = 0 for g.
-2/5, 0, 2/5, 1/2, 1
Find y, given that 48/5*y + 4/5*y**2 + 0 = 0.
-12, 0
Let u be 216/15 + 2/(-5). Let t(y) = -y**3 - y + 1. Let l(q) = -q**4 + 4*q**3 - 3*q**2 + 6*q - 7. Let w(z) = u*t(z) + 2*l(z). Determine f so that w(f) = 0.
-1, 0
Factor -1/2*u**4 + 1/2*u**2 + 1/6*u**3 - 1/3*u + 1/6*u**5 + 0.
u*(u - 2)*(u - 1)**2*(u + 1)/6
Let y(m) be the third derivative of 0 - m**2 + 1/144*m**4 - 1/360*m**5 - 1/720*m**6 + 0*m + 1/36*m**3. Suppose y(h) = 0. What is h?
-1, 1
Let f(o) be the first derivative of 1/24*o**6 + 3 - 1/12*o**3 + 0*o**2 - 1/16*o**4 + 1/20*o**5 + 0*o. Factor f(m).
m**2*(m - 1)*(m + 1)**2/4
Let p(l) = -l**2 - 13*l + 2. Let s(r) = -1 - r + 0*r - r**2 + 0*r**2. Let x(w) = p(w) - 4*s(w). Find i, given that x(i) = 0.
1, 2
What is p in -17*p**3 + 2*p**4 - 7*p**3 + 6*p**2 + 25*p**3 - 7*p**3 - 2*p = 0?
0, 1
Factor -2/11*m**2 - 6/11 - 8/11*m.
-2*(m + 1)*(m + 3)/11
Factor 15*k**4 + 0*k**4 - 102*k**5 + 114*k**5 + 3*k**3.
3*k**3*(k + 1)*(4*k + 1)
Let y(k) be the second derivative of 4*k**5/5 + 4*k**4/3 + 2*k**3/3 - 3*k. Factor y(c).
4*c*(2*c + 1)**2
Let z(y) be the first derivative of -2*y**5/55 + 2*y**4/11 - 10*y**3/33 + 2*y**2/11 - 6. Let z(o) = 0. What is o?
0, 1, 2
Suppose -3/4*r**2 + 3/4 - 3/4*r + 3/4*r**3 = 0. What is r?
-1, 1
Let b(c) = -c - 2. Let f be b(-4). Let d = -2 + f. Factor 0*p**2 + d*p**2 + 3 - 3*p**2 + 0*p**2.
-3*(p - 1)*(p + 1)
Let t be 4 + (3 - (-94)/(-12) - -1). Solve -1/6*y**4 + 1/3*y**2 - 1/6 - 1/3*y**3 + t*y**5 + 1/6*y = 0 for y.
-1, 1
Let b = -1 + 2. Let v be 2/b + -2 + 2. Factor 2*x**2 + 3 + 6*x - 3*x**v + 0*x**2 + 4*x**2.
3*(x + 1)**2
Let t(l) be the second derivative of -l**6/120 - l**5/30 - l**4/24 - 3*l**2/2 + l. Let r(b) be the first derivative of t(b). Let r(u) = 0. What is u?
-1, 0
Let o(l) be the second derivative of 2/15*l**6 + 3*l + 0 - 1/21*l**7 + 7/3*l**3 - 4/3*l**4 - 2*l**2 + 1/5*l**5. Factor o(j).
-2*(j - 1)**4*(j + 2)
Let w = 4/23 + 7/92. Let g(f) be the first derivative of -1/16*f**4 + 1/4*f**3 - 3/8*f**2 + w*f - 1. Factor g(l).
-(l - 1)**3/4
Let n = -69/13 - -449/65. Solve -n*s**2 - 8/5*s - 2/5 = 0.
-1/2
Let f(u) be the first derivative of u**5/5 + u**4/3 + 8*u + 7. Let x(c) be the first derivative of f(c). Factor x(z).
4*z**2*(z + 1)
Suppose 4*f + 4*w - 2 = f, -w = f - 1. Let i(l) be the third derivative of -l**f + 0*l**3 + 1/96*l**4 - 1/120*l**5 + 0*l + 1/480*l**6 + 0. Factor i(n).
n*(n - 1)**2/4
Let u(z) = -z**3 - 7*z**2 + 7*z. Let h be u(-8). Let y = -4 + h. Factor -3*r**y - 3*r - r + 4 + 6*r**3 - 2*r - 1.
-3*(r - 1)**3*(r + 1)
Let s = 60 + -54. Let z(y) be the first derivative of 0*y**2 + 1/18*y**s - 1/12*y**4 - 1 + 0*y + 1/9*y**3 - 1/15*y**5. Factor z(a).
a**2*(a - 1)**2*(a + 1)/3
Let a(t) = 3*t**2 + 54*t + 243. Let d(i) = 12*i**2 + 216*i + 972. Let m(h) = 9*a(h) - 2*d(h). Let m(u) = 0. What is u?
-9
Suppose 1 = c - 0. Let k be (0 + c - 1)/(-1). Factor -3/4*t**3 - 3/4*t**4 - 1/4*t**2 + k*t + 0 - 1/4*t**5.
-t**2*(t + 1)**3/4
Suppose z + 0*z = 3*w + 2, -4*z = -w - 8. Factor 1/2*x**2 - 2*x + z.
(x - 2)**2/2
Let s(q) be the first derivative of -1/15*q**6 - 3 + 1/3*q**3 + 1/6*q**4 + 2*q - 1/10*q**5 + 0*q**2. Let h(n) be the first derivative of s(n). Factor h(m).
-2*m*(m - 1)*(m + 1)**2
Let d(f) be the first derivative of -f**5/100 + f**4/15 - f**3/6 + f**2/5 - 3*f - 8. Let h(s) be the first derivative of d(s). Let h(x) = 0. What is x?
1, 2
Let x(b) = b + 9. Let l be x(-7). Let p be (-1)/(-1) - 2 - -7. Factor -l*y**3 - y**4 - 6 - y**2 + p.
-y**2*(y + 1)**2
Let c(p) = 4*p**3 - 5*p**2 + 3. Let q(o) = -11*o**3 + 14*o**2 + o - 8. Let x(y) = 8*c(y) + 3*q(y). Determine m, given that x(m) = 0.
-1, 0, 3
Let g(f) be the second derivative of f**6/120 + f**5/80 - f**4/48 - f**3/24 + 7*f. Factor g(j).
j*(j - 1)*(j + 1)**2/4
Let z(b) be the second derivative of -b**7/294 + 3*b**5/140 - b**4/42 - 12*b. Solve z(s) = 0.
-2, 0, 1
Let b(p) be the second derivative of -p**7/28 + p**6/10 - p**4/4 + p**3/4 - 6*p. Determine i so that b(i) = 0.
-1, 0, 1
Let j(y) be the second derivative of y**6/60 + y**5/5 + y**4 + 8*y**3/3 + 4*y**2 - 2*y. Factor j(m).
(m + 2)**4/2
Let j(d) be the first derivative of -2/45*d**3 + 0*d**2 - 1 + 1/30*d**4 + 0*d. Find r, given that j(r) = 0.
0, 1
Let q be (-6)/5*(-20)/6. Let r(k) be the third derivative of 0*k**3 + q*k**2 + 0*k + 0 - 1/30*k**5 + 1/12*k**4. Factor r(g).
-2*g*(g - 1)
Let x = 993 + -38729/39. Let g = 8/13 - x. Let 0 + 0*u**2 