8*a + 9/8*a**3.
3*(a - 1)*(a + 1)**2*(a + 2)/8
Let y(h) be the third derivative of h**5/60 + 4*h**4/3 - 24*h**3 - 387*h**2. What is m in y(m) = 0?
-36, 4
Let i(x) be the second derivative of -3*x**2 + 0 + x**3 - 1/8*x**4 - 23*x. What is k in i(k) = 0?
2
Let q(l) be the second derivative of l**8/23520 - l**7/8820 + l**4/6 + 2*l. Let t(o) be the third derivative of q(o). Suppose t(m) = 0. What is m?
0, 1
Let f(t) be the first derivative of -t**3 - 11*t**2/6 - 2*t/3 + 115. Factor f(g).
-(g + 1)*(9*g + 2)/3
Let m(u) be the third derivative of 0 - 5/2*u**4 + 0*u + 50*u**3 + 1/20*u**5 + 33*u**2. Determine z, given that m(z) = 0.
10
Suppose -26*c = -29*c - 150. Let x = c + 251/5. Factor 0 - 3/5*t**2 - 2/5*t + 0*t**3 + x*t**4.
t*(t - 2)*(t + 1)**2/5
Let p(l) = -l**3 - 7*l**2 - l - 5. Let y be p(-7). Let o = 2247 - 6733/3. Factor 8/3*k**4 + 0 + 4*k**3 + 2/3*k + 2/3*k**5 + o*k**y.
2*k*(k + 1)**4/3
Let -4*f**2 - 4*f**5 + 36*f**3 - 5*f**4 + 98*f**2 - 22*f**2 - 3*f**4 = 0. What is f?
-3, -2, 0, 3
Let s = 168/155 - 15/31. Factor -s*r**5 + 0*r + 3/5*r**3 - 3/5*r**2 + 0 + 3/5*r**4.
-3*r**2*(r - 1)**2*(r + 1)/5
Let m = 941/20 + -47. Let r(q) be the first derivative of m*q**4 + 1/15*q**3 - 1/30*q**6 + 0*q - 1/25*q**5 + 0*q**2 + 1. Find c such that r(c) = 0.
-1, 0, 1
Let a(y) be the first derivative of 3*y**5/5 - 15*y**4/4 + y**3 + 63*y**2/2 - 54*y - 69. Factor a(m).
3*(m - 3)**2*(m - 1)*(m + 2)
Let j = -57/2 + 29. Let d(w) be the first derivative of -3 + 1/2*w + j*w**2 + 1/6*w**3. Factor d(m).
(m + 1)**2/2
Let w(x) be the first derivative of -x**6/8 + 9*x**5/10 + 3*x**4/2 - 3*x**3/2 - 21*x**2/8 + 13. Find i such that w(i) = 0.
-1, 0, 1, 7
Let w(g) be the second derivative of -g**5/30 + g**4/18 + 4*g**3/3 + 9*g - 1. Factor w(v).
-2*v*(v - 4)*(v + 3)/3
Let d(g) be the first derivative of -2*g**3/15 + g**2/5 + 12*g/5 - 2. Factor d(t).
-2*(t - 3)*(t + 2)/5
Let n(l) be the third derivative of -1/1680*l**8 + 0*l**6 + 0*l + 0*l**4 - 16*l**2 + 0*l**5 + 0 + 0*l**3 - 1/1050*l**7. Find b, given that n(b) = 0.
-1, 0
Suppose -1458*g + 105 = -1443*g. Let w(x) be the second derivative of 0 + 0*x**4 - 1/40*x**5 + 1/84*x**g + 0*x**3 - 7*x + 0*x**6 + 0*x**2. Factor w(p).
p**3*(p - 1)*(p + 1)/2
Suppose 3*g + 5*m = 34, 5*g - 3*m = -0*g. Let y = -1180 + 5918/5. Let y*k - 2*k**g + 12/5*k**2 - 4/5 = 0. What is k?
-1, 1/5, 2
Let t(v) = 3*v**3 + 6*v**2 - 8*v - 6. Let w(z) = z**3 - 2*z. Let f(p) = -2*t(p) + 10*w(p). Let f(n) = 0. Calculate n.
-1, 1, 3
Suppose -5*z = 5*y, 4*y - 1 + 13 = -z. Let n(l) be the third derivative of 0 + 1/30*l**5 - 1/4*l**z + 0*l + 0*l**3 + 3*l**2. Solve n(v) = 0 for v.
0, 3
Suppose -5*x + 15 = 0, -2*j + 9*x = 4*x + 7. Factor -2*m + 1/4*m**2 + j.
(m - 4)**2/4
Let b be -10*-8*(-7)/(-70). Let y(f) be the first derivative of 1/14*f**4 + 8/7*f**3 + 128/7*f + 48/7*f**2 + b. Factor y(h).
2*(h + 4)**3/7
Suppose 13 = 8*n - 27. Suppose 0 = -4*c + 4*a, a - n = -3. Factor 2/11*b**4 + 4/11*b**3 + 0*b**c - 2/11 - 4/11*b.
2*(b - 1)*(b + 1)**3/11
Let f(p) be the first derivative of 12 + 1/10*p**2 + 2/5*p**4 + 0*p + 1/3*p**3 + 4/25*p**5. Factor f(w).
w*(w + 1)*(2*w + 1)**2/5
Let t = -81 + 409/5. Let b be 6 + 1/((-5)/20). Factor 4/5*r**4 + 0 - t*r**b + 0*r**3 + 2/5*r - 2/5*r**5.
-2*r*(r - 1)**3*(r + 1)/5
Suppose 3*d - 4 = d. Let o be 6655/(-363)*(0 - (-12)/(-10)). Factor 0*m**2 - 16*m - 6*m**d + 6 - o + 2*m**2.
-4*(m + 2)**2
Let x(r) = -r**2 - r + 13. Let u(g) = -1. Let f(p) = -4*u(p) - x(p). Suppose k = -3*k - 8. Let l(a) = 1. Let b(o) = k*f(o) - 14*l(o). Factor b(n).
-2*(n - 1)*(n + 2)
Let m be (-2)/4*48/(-8). Suppose -5 = m*d - 17. Determine o so that o**2 + o**2 - 2*o + 3*o**2 + 2*o**5 - 5*o**d = 0.
-1, 0, 1/2, 1, 2
Let w(b) be the third derivative of b**6/270 + b**5/30 + 2*b**3 - 3*b**2. Let f(h) be the first derivative of w(h). What is r in f(r) = 0?
-3, 0
Let y(l) be the third derivative of l**5/30 - 14*l**4/3 + 784*l**3/3 - 41*l**2 - l. Let y(f) = 0. What is f?
28
Suppose 4*l = -20*h + 18*h + 16, 0 = -2*l - 2*h + 12. Determine n, given that 9/4*n**4 + 3/4*n**5 - 3/4 - 3/2*n**l - 9/4*n + 3/2*n**3 = 0.
-1, 1
Let p = 22 - 52. Let q be (7 - (-207)/p)*4. Factor -q*f**2 - 1/5*f + 2/5 + 1/5*f**3.
(f - 2)*(f - 1)*(f + 1)/5
Let v(t) be the third derivative of 4/35*t**7 + 2*t**4 - 16/3*t**3 + 0 + 0*t - 11/30*t**6 - 1/84*t**8 + 2/15*t**5 - 21*t**2. Solve v(h) = 0 for h.
-1, 1, 2
Determine n so that 3/2*n + 0 - 5/6*n**3 - 1/2*n**2 - 1/6*n**4 = 0.
-3, 0, 1
Let w(x) be the third derivative of x**9/4536 - x**8/630 + x**7/420 - x**3 - 38*x**2. Let b(c) be the first derivative of w(c). Factor b(o).
2*o**3*(o - 3)*(o - 1)/3
Let t(h) = 10*h**3 + 61*h**2 + 80*h + 18. Let c(n) = 2*n**3 + 12*n**2 + 16*n + 4. Let f(u) = -22*c(u) + 4*t(u). Factor f(o).
-4*(o + 1)*(o + 2)**2
Let b(r) be the first derivative of -16/7*r - 8/7*r**2 - 4/21*r**3 - 26. Factor b(m).
-4*(m + 2)**2/7
Determine z, given that 31/4*z - 3/4 - 5/2*z**2 = 0.
1/10, 3
Let 33*c + 60 - 17*c**3 - 44 - 9*c + 3*c**3 - 4*c**2 + 2*c**5 = 0. What is c?
-2, -1, 2
Solve 712*a**2 - 133*a - 313*a + 444*a**2 + 19 + 81 - 234*a = 0.
5/17
Let k(t) be the second derivative of t**5/20 + 11*t**4/6 + 161*t**3/6 + 196*t**2 + 97*t. Factor k(h).
(h + 7)**2*(h + 8)
Let r = -73 - -75. Let 7 + 1 + 2*p**r + 1499*p - 1491*p = 0. What is p?
-2
Suppose -1/7*t**2 + 1/7*t**3 - 2/7*t + 0 = 0. What is t?
-1, 0, 2
Let l(v) = 3*v**2 - 5*v - 6. Let n(b) = b**2 + 4217*b - 4217*b. Let u(m) = 5*l(m) - 10*n(m). Factor u(y).
5*(y - 6)*(y + 1)
Let -3/4*a**4 - 1/4*a - 11/4*a**2 - 11/4*a**3 + 1/2 = 0. What is a?
-2, -1, 1/3
Let k = 34539 + -69075/2. Factor -9/4*l**4 + 0*l + 0*l**2 + k*l**5 + 0 + 3/4*l**3.
3*l**3*(l - 1)*(2*l - 1)/4
Let n = 2444/3 - 4885/6. Factor 0 - p**3 - 9/4*p**2 - n*p.
-p*(p + 2)*(4*p + 1)/4
Suppose 4*y + y = -5*g + 10, 2*g = -3*y + 8. Suppose s - b - 15 = y*b, 3 = s - b. Factor -6/5*k**2 - 4/5*k + 0 + 2/5*k**4 + s*k**3.
2*k*(k - 2)*(k + 1)**2/5
Solve 48/7 - 435*l**4 - 537/7*l**2 + 318/7*l - 5232/7*l**3 - 300/7*l**5 = 0.
-8, -2, -1/5, 1/4
Let n(c) = -80*c**2 - 100*c - 125. Let b = 18 + -14. Let i(a) = -9*a**2 - 11*a - 14. Let f(v) = b*n(v) - 35*i(v). Determine g, given that f(g) = 0.
-2, -1
Let h be (-91*2)/(-4 + 2). Let c be (-1)/(-2) - h/(-14). Factor -4*v + 0*v + 0*v**3 + 2*v**4 + c*v**3 - 3*v**3 - 2.
2*(v - 1)*(v + 1)**3
Let q(b) be the third derivative of b**8/336 + b**7/84 - 3*b**3 + 9*b**2. Let l(g) be the first derivative of q(g). Factor l(s).
5*s**3*(s + 2)
Let i = -411 - -416. Let g(m) be the first derivative of m**4 + 4/3*m**3 - i - 2*m**2 - 4*m. Factor g(t).
4*(t - 1)*(t + 1)**2
Let j(s) = 3*s - 3. Let g be j(1). Suppose -o - 3*o + o = g. Suppose 1/4*m**2 + o + 0*m = 0. What is m?
0
Let l(d) be the third derivative of -d**3 + 6*d**2 - 11/12*d**4 + 0*d + 1/20*d**6 + 0 - 1/6*d**5. Solve l(n) = 0 for n.
-1, -1/3, 3
Let m be 8/60 - (-84)/5*(-24)/(-216). Find z such that 8/7 - 12/7*z**3 - 32/7*z**m - 12/7*z = 0.
-2, -1, 1/3
Let o(w) be the first derivative of 1/2*w**2 - 1/20*w**5 - 4 + 1/6*w**3 - 1/12*w**4 + w. Let b(t) be the first derivative of o(t). Factor b(u).
-(u - 1)*(u + 1)**2
Let w = 2545 - 2545. Let m(r) be the second derivative of 2/15*r**6 + 1/2*r**2 + 3/2*r**3 + 97/48*r**4 - 4*r + w + 9/10*r**5. Suppose m(t) = 0. Calculate t.
-2, -1/4
Let 11*w**3 - 14*w**3 + 552*w**2 + 389344 - 25392*w - w**3 = 0. What is w?
46
Let i = -5 + 6. Let p be 0*(2 + -1) - (-1 - i). Solve 1/5*f**3 + 0 + 0*f - 2/5*f**p = 0.
0, 2
Let b(x) be the first derivative of -10*x**3/27 + 17*x**2/9 - 4*x/3 + 117. Determine l so that b(l) = 0.
2/5, 3
Let y(v) be the first derivative of 0*v**3 + 0*v**5 + 0*v + v**4 + 0*v**2 - 2/3*v**6 - 13. Suppose y(i) = 0. What is i?
-1, 0, 1
Factor 1/2*w**2 + w**4 - 3/2*w**3 + 0 + 0*w.
w**2*(w - 1)*(2*w - 1)/2
Let m(t) be the second derivative of -t**5/20 - t**4/4 - t**3/2 - t**2/2 + 245*t. Determine v, given that m(v) = 0.
-1
Let t(v) be the second derivative of v**7/168 - v**6/72 - v**5/12 + 17*v**3/6 - 4*v. Let n(w) be the second derivative of t(w). Factor n(z).
5*z*(z - 2)*(z + 1)
Let u be (-7 + 1)*(-128)/(-48). Let q = -16 - u. Factor 1/2*m**2 + q - 3/2*m.
m*(m - 3)/2
Determine h so that 0 + 3/7*h**2 + 2/7*h - 8/7*h**3 + 3/7*h**4 = 0.
-1/3, 0, 1, 2
Suppose -1 = 5*a - 31. Let l(i) = i**3 - 9*i**2 + 16*i + 14. Let d be l(a). 