t f(g) be the first derivative of -g**5/5 + 4*g**4/3 - 2*g**3 + 25*g + 29. Let k(s) be the first derivative of f(s). Find l, given that k(l) = 0.
0, 1, 3
Let y(z) = -53*z**2 - 120*z - 18. Let s(j) be the second derivative of -13*j**4/3 - 20*j**3 - 17*j**2/2 + 20*j. Let q(v) = -2*s(v) + 3*y(v). Factor q(x).
-5*(x + 2)*(11*x + 2)
Let b(g) = -3*g**2 - 6*g + 2. Let i(r) = 6*r**2 + 13*r - 5. Let z be -2 + 16/1 + -4. Let t(j) = z*b(j) + 4*i(j). Suppose t(y) = 0. What is y?
-4/3, 0
Suppose 7*g - 15*g = 8. Let n be (-3)/(78/40) - (-1 + g). Solve 2/13 + n*q**2 + 10/13*q - 18/13*q**3 = 0 for q.
-1/3, 1
Let n = -231 - -3446/15. Let b = n - -163/105. Factor -6/7*i + b*i**2 - 8/7.
2*(i - 4)*(i + 1)/7
Let i(m) be the first derivative of m**7/420 - m**6/60 + m**5/20 - m**4/12 - 22*m**3/3 + 30. Let g(w) be the third derivative of i(w). Factor g(s).
2*(s - 1)**3
Let s(o) be the second derivative of -2*o + 0 - 1/48*o**4 + 1/240*o**5 + 1/24*o**3 - 9/2*o**2. Let d(m) be the first derivative of s(m). Solve d(h) = 0 for h.
1
Suppose 2 = 3*l - 70. Let t be (-9)/l*12/(-9). Let 0*n + 0*n**3 - t*n**4 + 1/2*n**2 + 0 = 0. Calculate n.
-1, 0, 1
Let a(b) be the third derivative of 2/15*b**6 - 1/84*b**8 - 1/2*b**4 + 0 - 2/15*b**5 + 0*b**7 + 9*b**2 + 4/3*b**3 + 0*b. Solve a(s) = 0.
-2, -1, 1
Factor -3*i**4 + 288*i**2 - 1023*i**2 + 4872*i + 174*i**3 - 1956*i**2 - 2352.
-3*(i - 28)**2*(i - 1)**2
Let m(y) = 5*y - 28. Let r be m(10). Let s be (-48)/(-26) - r/(-143). Factor 1/5*z**4 - 1/5 - 2/5*z + 0*z**s + 2/5*z**3.
(z - 1)*(z + 1)**3/5
What is w in -12*w + 3/5*w**2 + 60 = 0?
10
Let u(t) be the first derivative of -7 - 9*t**4 + 28/3*t**3 + 0*t + 4*t**2. Determine h, given that u(h) = 0.
-2/9, 0, 1
Let z(i) = -3*i**5 + 4*i**4 + 3*i**3 - 3*i**2 + i + 1. Let x(c) = -c**4 - c - 1. Let v(w) = -x(w) - z(w). Determine h so that v(h) = 0.
-1, 0, 1
Suppose 4*l - 540 = 4*z, -z + 150 = l - 5*z. Let n = l + -517/4. Suppose -1/2 + 0*q**2 + n*q - 1/4*q**3 = 0. What is q?
-2, 1
Let y(o) = -14*o**3 + 70*o**2 - 138*o + 92. Let l(v) = -v**3 - v**2 + v + 2. Let z(s) = -10*l(s) + y(s). Factor z(x).
-4*(x - 18)*(x - 1)**2
Let j(m) be the third derivative of m**5/390 + m**4/78 + 78*m**2. Determine k so that j(k) = 0.
-2, 0
Let z = 217/68 + -50/17. Let a(j) be the second derivative of 0 - z*j**4 + 1/2*j**3 + 3*j + 0*j**2. Factor a(i).
-3*i*(i - 1)
Let q = -1716 - -12014/7. Let h be 516/378 - 2/9. Factor -8/7 - q*s**2 - h*s.
-2*(s + 2)**2/7
Factor -3/4*a**5 + 375/4 + 51/4*a**4 - 975/4*a - 159/2*a**3 + 435/2*a**2.
-3*(a - 5)**3*(a - 1)**2/4
Let 3/2*h**2 + 9/2*h + 3 = 0. What is h?
-2, -1
Let x(s) be the third derivative of s**5/12 + 10*s**4/3 + 25*s**3/2 - 594*s**2. Factor x(r).
5*(r + 1)*(r + 15)
Let y(z) be the first derivative of 9*z - 3*z**2 - 2 + 1/3*z**3. Factor y(n).
(n - 3)**2
Let t(d) be the third derivative of d**9/15120 + d**8/2240 + d**7/840 + d**6/720 + 5*d**4/12 + 11*d**2. Let z(g) be the second derivative of t(g). Factor z(m).
m*(m + 1)**3
Let z(k) be the second derivative of -k**7/1050 + k**6/300 - k**4/60 + k**3/30 - 22*k**2 - 18*k. Let w(t) be the first derivative of z(t). Solve w(l) = 0.
-1, 1
Let s(v) = -48*v**3 - 2028*v**2 + 4512*v + 33. Let w(y) = 3*y**3 + 127*y**2 - 282*y - 2. Let d(x) = 2*s(x) + 33*w(x). Factor d(a).
3*a*(a - 2)*(a + 47)
What is a in -2/9*a**2 - 4/3 + 10/9*a = 0?
2, 3
Factor -6/5 - 156/5*h**2 + 13*h + 9*h**3.
(h - 3)*(3*h - 1)*(15*h - 2)/5
Let y = 6976/17 + -410. Suppose -12/17*x**3 - 2/17 + 6/17*x - 2/17*x**4 + 4/17*x**2 + y*x**5 = 0. What is x?
-1, 1/3, 1
Suppose 87*j - 92*j - 295 = 0. Let s = j - -63. Find n, given that -3/4*n**5 + 1/2*n**3 + 1/4*n - 3/2*n**2 + 5/4*n**s + 1/4 = 0.
-1, -1/3, 1
Let a = -37416 + 37419. Solve 0*i**2 + 0 + 1/3*i - 1/3*i**a = 0 for i.
-1, 0, 1
Suppose 4*p - 21 = -3*s + p, p = 5*s - 29. Let j be 26/39 - 2/s. Solve -2/3*u - u**2 - j*u**3 + 0 = 0.
-2, -1, 0
Let j(k) = 2*k + 26. Suppose -12*z = -8*z + 48. Let q be j(z). Solve -q*v + 3/2*v**2 + 1/2 = 0.
1/3, 1
Let b(z) be the first derivative of -z**6/27 + 28*z**5/45 - 38*z**4/9 + 44*z**3/3 - 27*z**2 + 24*z + 215. Determine y so that b(y) = 0.
1, 3, 4
Factor -3*o**4 - 12 + 115*o - 60*o - 16*o + 21*o**3 - 45*o**2.
-3*(o - 4)*(o - 1)**3
Let i(f) be the second derivative of 5/12*f**4 + 8*f + 0 - 5/6*f**3 + 0*f**2. Factor i(n).
5*n*(n - 1)
Let f(w) be the first derivative of 38 + 1/2*w**2 + 1/10*w**5 - 1/2*w - 1/4*w**4 + 0*w**3. Factor f(y).
(y - 1)**3*(y + 1)/2
Let x(h) be the second derivative of h**6/45 + 3*h**5/10 - 711*h. Factor x(w).
2*w**3*(w + 9)/3
Let j be -13*155/2821*(-7 - -1). Let 3*c**4 - 54/7*c**2 - j*c**3 + 81/7*c + 81/7 - 3/7*c**5 = 0. Calculate c.
-1, 3
Let p(s) be the third derivative of s**6/24 - 5*s**4/8 + 5*s**3/3 - 600*s**2. Let p(j) = 0. What is j?
-2, 1
Let f(h) = -5*h + 11*h**2 + h**3 + 14 - 34*h**2 + 4*h + 11*h**2. Let z be f(12). Solve -1/3*v**z + 0 - 2/3*v = 0 for v.
-2, 0
Let u = -480 - -483. Let x(f) be the first derivative of -1 - 3*f + 1/3*f**u + f**2. Suppose x(n) = 0. Calculate n.
-3, 1
Let t(j) be the first derivative of -6*j**3/17 - 5*j**2/17 + 432. What is a in t(a) = 0?
-5/9, 0
Let b be (-10)/4*((-332)/40 + 8). Let s(o) be the first derivative of -b*o**2 + 0*o - 3/8*o**4 - 7 - o**3. Factor s(t).
-3*t*(t + 1)**2/2
Find p, given that -5083*p**4 - 56*p**3 - 60552*p**2 + 5545528 + 2341344*p - 39495016 + 5080*p**4 + 752*p**3 = 0.
58
Let b(t) be the second derivative of -t**4 + 9*t + 0*t**2 + 0 + 4/3*t**3 + 1/5*t**5. Factor b(r).
4*r*(r - 2)*(r - 1)
Suppose -10 = -p - 14. Let g be ((12/17)/p)/(9/(-6)). Solve g*j - 2/17*j**2 + 4/17 = 0 for j.
-1, 2
Let r(x) be the first derivative of -x**5/15 + 2*x**3/3 - 4*x**2/3 - 13*x + 11. Let w(d) be the first derivative of r(d). Find v, given that w(v) = 0.
-2, 1
Let n(u) = 3*u**3 + u**2 + 1. Let d(k) = -k**4 - 27*k**3 - 15*k**2 + 12*k + 6. Let l(c) = -3*d(c) - 15*n(c). Factor l(s).
3*(s - 1)*(s + 1)**2*(s + 11)
Factor -132*u - 2259*u**2 + 44*u**3 + 2134*u**2 + 3*u**3 - 4 + 49*u**3.
(u - 2)*(3*u + 2)*(32*u + 1)
Let f(c) = -c**4 - 7*c**3 + 5*c**2 - 3*c + 3. Let w(p) = -7*p**3 + 6*p**2 - 4*p + 4. Let v(x) = 4*f(x) - 3*w(x). Factor v(g).
-g**2*(g + 2)*(4*g - 1)
Factor -28/11 - 38/11*t - 8/11*t**2 + 2/11*t**3.
2*(t - 7)*(t + 1)*(t + 2)/11
Let u be 49/14 - (3/(-2) + 1). Factor -u*y**2 - 1085*y**4 - 3*y**5 + 1097*y**4 - 12 + y**5 + 4 - 16*y**3 + 18*y.
-2*(y - 4)*(y - 1)**3*(y + 1)
Factor 18*c**3 - 151*c + 13*c + 21*c**4 - 69*c - 243 - 198*c + 2*c**5 - 162*c**2 + c**5.
3*(c - 3)*(c + 1)*(c + 3)**3
Let j(w) be the second derivative of -1/16*w**3 + 0 + 1/96*w**4 - 1/8*w**2 + 6*w + 3/160*w**5 + 1/240*w**6. Factor j(p).
(p - 1)*(p + 1)**2*(p + 2)/8
Let b(y) be the third derivative of y**5/150 - y**4/60 - 2*y**3 - 3*y**2 + 69. Factor b(t).
2*(t - 6)*(t + 5)/5
Let t(j) be the second derivative of j**5/90 + 5*j**4/36 + 4*j**3/9 - 13*j**2 - 37*j. Let z(l) be the first derivative of t(l). Factor z(f).
2*(f + 1)*(f + 4)/3
Factor 244 + 12 - 2*u**2 + 4*u**2 - 2*u**2 + u**2 - 32*u.
(u - 16)**2
Let f(q) be the first derivative of q**7/168 + q**6/40 - q**5/80 - q**4/16 + 5*q + 11. Let d(p) be the first derivative of f(p). Factor d(j).
j**2*(j - 1)*(j + 1)*(j + 3)/4
Factor 2*c**2 + 1/8*c**5 - 4*c - 5/8*c**4 + 2 + 1/2*c**3.
(c - 2)**3*(c - 1)*(c + 2)/8
Let t(u) be the first derivative of -9*u**3 + 183*u**2/2 + 42*u + 336. Factor t(l).
-3*(l - 7)*(9*l + 2)
Let r(j) be the third derivative of j**5/180 - 17*j**4/72 + 178*j**2. Factor r(h).
h*(h - 17)/3
Let r(g) be the second derivative of -g**4/60 - 7*g**3/10 + g - 20. Let r(w) = 0. Calculate w.
-21, 0
Let m(u) be the second derivative of u**6/75 - u**4/30 + u - 1. Factor m(t).
2*t**2*(t - 1)*(t + 1)/5
Let 29/8*p - 1/8*p**2 - 7/2 = 0. What is p?
1, 28
Suppose -z + 3*o = -11, -3*o = -4*z + 49 - 14. Factor 5*k**2 - 6*k**3 + 4*k**3 + k**2 - z.
-2*(k - 2)**2*(k + 1)
Let l(h) = -h**3 - 3*h**2 + 5*h + 5. Let o be l(-4). Factor -2 + 7*f**2 - 4*f**2 - o.
3*(f - 1)*(f + 1)
Solve -69/2 + 1935/4*t**2 - 21*t**3 - 63/4*t = 0 for t.
-1/4, 2/7, 23
Let p(n) = -3*n**4 + 101*n**3 + 285*n**2 + 279*n + 90. Let m(h) = 10*h**4 - 405*h**3 - 1140*h**2 - 1115*h - 360. Let k(j) = 4*m(j) + 15*p(j). Factor k(y).
-5*(y + 1)**3*(y + 18)
Suppose 0 = -167*u + 513 - 179. Factor t**u + 0 + 3/4*t**3 - t.
t*(t + 2)*(3*t - 2)/4
L