4*x**4. Suppose h(w) = 0. What is w?
0, 1/3, 1
Suppose -5*x + 4*z + 7 = -1, 5*x - z = 17. Factor -a**3 + 196*a**x - 45*a**3 + 13*a**3 - 79*a**3 + 16*a**2.
4*a**2*(7*a - 2)**2
Let a be 58/36 + 0 - (-2)/(-18). Factor -a - 3/2*o**2 - 3*o.
-3*(o + 1)**2/2
Let t be (-3)/(-1)*11*6/(-9). Let s be (-2)/t*((-24)/(-8) - 1). Factor 0 - s*j**2 + 4/11*j**4 + 0*j + 2/11*j**3.
2*j**2*(j + 1)*(2*j - 1)/11
Let g = -3/764 - -1567/9932. Factor -4/13*p - g*p**2 + 0 + 2/13*p**3.
2*p*(p - 2)*(p + 1)/13
Suppose 10 = 6*k - 2. Factor -10*z**2 - 3*z - k*z + 9*z**2.
-z*(z + 5)
Factor -5*u**2 - 6*u**3 - 5*u**2 + 2*u**4 + 6*u + 0*u**2 + 6*u**4 + 2.
2*(u - 1)**2*(u + 1)*(4*u + 1)
Suppose -226 = -25*g - 176. Factor 0 - 1/4*d + 1/4*d**g.
d*(d - 1)/4
Suppose -4*k = -0*f + f + 24, -f - 23 = 5*k. Let s be (-2)/3 - f/6. Factor -1/3*v**2 - 1/3*v + 1/3*v**3 + 0 + 1/3*v**s.
v*(v - 1)*(v + 1)**2/3
Suppose 16*p + 60 = 26*p + 2*g, p + 5 = 2*g. Factor 3/5*y**4 + 3/5*y**p + 0*y**2 + 0*y**3 + 0 + 0*y.
3*y**4*(y + 1)/5
Suppose 2*k = 3*k - 5*g - 2, -k = -3*g - 6. Suppose k*r = 14*r - 4. Find h, given that 1/9*h**4 + 2/9*h**3 + 0 + 0*h**r + 0*h = 0.
-2, 0
Suppose 4*v + 3*h = 3*v + 12, -5*v + 3*h + 24 = 0. Suppose -2 + 5*w - v*w**2 - 17*w - 12*w**2 = 0. What is w?
-1/3
Let a be (1/(-2))/(11/(-8)). Let -6/11*x**3 + 10/11*x**2 + 0 - a*x = 0. What is x?
0, 2/3, 1
Suppose -34*q + 48 = -54. Let k(a) be the second derivative of -1/30*a**5 + 0*a**2 + 1/63*a**7 + 1/45*a**6 + 0 - 1/18*a**4 + 0*a**q - a. Factor k(p).
2*p**2*(p - 1)*(p + 1)**2/3
Let w = 7 + -4. Factor 9*l**w + 3*l**2 - 168*l + 6 - 4 + 10 + 144*l.
3*(l - 1)*(l + 2)*(3*l - 2)
Factor 0 + 16/9*g - 2/3*g**3 + 4/3*g**2 - 2/9*g**4.
-2*g*(g - 2)*(g + 1)*(g + 4)/9
Let z(k) = -k**3 + k**2 - 2*k + 1. Let m(n) = 7*n**3 - 15*n**2 + 20*n - 3. Let j(i) = -2*m(i) - 18*z(i). Let j(c) = 0. What is c?
-3, -1, 1
Let w(k) be the third derivative of k**6/150 + 22*k**5/75 + 16*k**4/5 - 192*k**3/5 + 45*k**2. Determine n, given that w(n) = 0.
-12, 2
Suppose 140*j - 92 = 117*j. Let y(o) be the second derivative of 4*o - 3/20*o**5 + 0 + 0*o**j + 3/2*o**3 - 3*o**2. What is u in y(u) = 0?
-2, 1
Suppose -o - 15 = -5*m - 4*o, 3 = m - o. Factor 12*l**3 - 15*l**2 + 24*l**3 - 2*l + 0*l**m + 1.
(3*l - 1)**2*(4*l + 1)
Factor -9*s - 3*s**2 + 0 + 3/4*s**3.
3*s*(s - 6)*(s + 2)/4
Let r(g) be the third derivative of g**7/105 - 3*g**6/20 + 2*g**5/3 + 97*g**2 + 1. Factor r(f).
2*f**2*(f - 5)*(f - 4)
Let m(y) be the first derivative of 2*y**6/15 + 24*y**5/25 + 4*y**4/5 - 24*y**3/5 - 2*y**2 + 48*y/5 + 101. Solve m(k) = 0.
-4, -3, -1, 1
Let r(p) be the third derivative of 0*p + 0 + 1/150*p**5 + 0*p**3 + 0*p**4 - 42*p**2. Determine y so that r(y) = 0.
0
Let s(j) be the first derivative of 2/23*j**4 + 0*j**2 + 0*j - 8/69*j**3 - 2/115*j**5 + 10. Factor s(d).
-2*d**2*(d - 2)**2/23
Let t = -53 + 117. Let a = 64 - t. What is f in a - 3/5*f - 1/5*f**2 = 0?
-3, 0
Suppose -4*h = 5*f - 249, h - 14 = -f + 36. Let y = f - 97/2. Factor 2*x**2 + y*x**3 + 1 + 5/2*x.
(x + 1)**2*(x + 2)/2
Suppose -4*y - 26 - 34 = 0. Let j = 15 + y. Factor -3*u**2 + 4*u**3 + 2*u**2 - 4*u + 7*u**2 + j*u.
2*u*(u + 2)*(2*u - 1)
Let o be 14*4/128*4*4. Factor o*x**3 - 2*x**3 - 4410*x**2 + 4405*x**2.
5*x**2*(x - 1)
Let x be 3/(-4 + 11/2). Factor w + x*w**2 - w**2 + w.
w*(w + 2)
Let g = 711 + -708. Let p(j) be the second derivative of 0*j**g - 1/42*j**7 - 1/48*j**4 - 3/40*j**5 + 0*j**2 - 3/40*j**6 + 0 - 4*j. Factor p(k).
-k**2*(k + 1)**2*(4*k + 1)/4
Let r(d) = -11*d**2 - 271*d + 70. Let q(j) = 45*j**2 + 1081*j - 282. Let h(l) = 6*q(l) + 22*r(l). Let h(a) = 0. What is a?
-19, 2/7
Let s(u) be the third derivative of -1/120*u**5 - 11/480*u**6 + 0 + 0*u + 0*u**4 + 12*u**2 - 3/280*u**7 + 0*u**3. Solve s(w) = 0.
-1, -2/9, 0
Suppose -17*g + 46 + 22 = 0. Factor -3/2 + 0*h**2 + 3/2*h**g - 3*h**3 + 3*h.
3*(h - 1)**3*(h + 1)/2
Let t(f) be the third derivative of 529*f**6/24 + 23*f**5/6 + 5*f**4/24 - 5*f**2 - 5*f. Factor t(b).
5*b*(23*b + 1)**2
Suppose 18*s = 72 - 18. Let u(g) be the first derivative of -1/20*g**5 - 11 + 2*g**2 + 9/16*g**4 + 0*g - 2*g**s. What is k in u(k) = 0?
0, 1, 4
Let q(d) be the first derivative of d**4 - 12*d**3 + 16*d**2 - 106. What is l in q(l) = 0?
0, 1, 8
Let z(p) = -p**3 + 8*p**2 + 10*p - 7. Let v = 19 - 10. Let j be z(v). Let 2*t**j + 6*t + 5*t - 15*t = 0. Calculate t.
0, 2
Let s(f) be the first derivative of 3*f**5/160 + f**4/8 + 5*f**3/16 + 3*f**2/8 + 24*f - 24. Let u(n) be the first derivative of s(n). Factor u(d).
3*(d + 1)**2*(d + 2)/8
Let f = 18859 + -18857. Factor 15/2*v**f + 5/2*v - 15/2 - 5/2*v**3.
-5*(v - 3)*(v - 1)*(v + 1)/2
Let z be (3/(-5))/((-80)/100). Find i, given that 0 + 0*i**2 + 3/4*i**3 - z*i = 0.
-1, 0, 1
Let f = -175 + 159. Let r be (-3 - (-10)/4)*f/28. Factor 0 + r*n**2 + 4/7*n**4 + 0*n - 6/7*n**3.
2*n**2*(n - 1)*(2*n - 1)/7
Let u(l) be the third derivative of l**7/350 + 3*l**6/50 + 8*l**5/25 - 6*l**4/5 - 72*l**3/5 - 238*l**2. Factor u(y).
3*(y - 2)*(y + 2)*(y + 6)**2/5
Let r(g) = -g**4 - g**3 + 2*g + 4. Let a(o) = -3*o**4 - 4*o**3 + 12*o**2 + 44*o + 40. Let t(h) = -a(h) + 2*r(h). Solve t(l) = 0 for l.
-2, 4
Let p(z) be the second derivative of -z**2 + 1/30*z**5 - 1/3*z**3 + 0 - 4*z + 0*z**4. Let j(k) be the first derivative of p(k). Let j(c) = 0. What is c?
-1, 1
Let l(z) = -24*z**4 - 12*z**3 + 20*z**2 + 26*z + 62. Let t(n) = n**4 - n**2 + n - 1. Let d(i) = 2*l(i) + 44*t(i). Solve d(g) = 0.
-5, -2, -1, 2
Let m(i) be the first derivative of 10*i**6 + 146*i**5/5 + 11*i**4/2 - 56*i**3/3 + 4*i**2 - 53. Determine h, given that m(h) = 0.
-2, -1, 0, 1/6, 2/5
Suppose -19*w + 23*w = 16. Suppose 5*r = 2*i + 17, w*r - i - 14 = 2. Factor -x**2 - 3*x**2 - 4*x**2 + r*x**2 - 3*x**3.
-3*x**2*(x + 1)
Let j(k) be the second derivative of -k**10/75600 + k**8/8400 - k**6/1800 + 5*k**4/12 + 5*k. Let y(o) be the third derivative of j(o). Factor y(l).
-2*l*(l - 1)**2*(l + 1)**2/5
Let q(f) = -9*f - 79. Let w be q(12). Let y = -185 - w. Find j, given that 0*j**y - 2/3*j**4 + 0*j + 0 + 1/3*j**3 = 0.
0, 1/2
Let l = -4017 + 76327/19. Factor -l + 10/19*u + 2/19*u**3 - 8/19*u**2.
2*(u - 2)*(u - 1)**2/19
Suppose 3*b - 6 = -5*l, b = l - 4*l + 2. Factor 15*m**b + 5*m**3 + 5*m + 18*m**3 - 13*m**3.
5*m*(m + 1)*(2*m + 1)
Suppose 0 = -2*t + 10, -4*l - 2*t = -10 - 12. Let s(c) be the first derivative of 3 + 0*c - 9/4*c**4 + 0*c**2 - l*c**5 + 2*c**3. Suppose s(r) = 0. What is r?
-1, 0, 2/5
Let d(f) = -39*f**2 - 8*f + 5. Let k = 21 + -22. Let j(i) = -i**2 - 1. Let t(g) = k*d(g) - 5*j(g). Find a, given that t(a) = 0.
-2/11, 0
Let a(t) be the first derivative of t**5/20 + t**4/4 + 6*t + 10. Let o(m) be the first derivative of a(m). Factor o(z).
z**2*(z + 3)
Suppose -69 = 2*c - 3*v, -3*c - 2*v - 220 = 2*c. Let d = c - -44. Determine q, given that 0 + 1/2*q**d + 1/2*q = 0.
-1, 0
Let x(o) = 2*o**2 - 197*o + 197*o + 7. Let f(c) = 3*c**2 + 8. Let d(q) = 3*f(q) - 4*x(q). Factor d(y).
(y - 2)*(y + 2)
Factor -12*h**2 - 18*h**2 + 8*h**2 - 13*h**2 + 10 - 25*h.
-5*(h + 1)*(7*h - 2)
Find t such that 3/4*t**3 + 1/4*t**4 - 1/2 - 3/4*t + 1/4*t**2 = 0.
-2, -1, 1
Let n(v) be the first derivative of -9*v**5/5 + 3*v**4 - v**3 + 298. Let n(w) = 0. What is w?
0, 1/3, 1
Let q = 17743/12 + -5877/4. Factor 46*z**2 - q*z**3 - 280/3*z + 2/3*z**4 + 200/3.
2*(z - 5)**2*(z - 2)**2/3
Let f(r) be the second derivative of 0 + 1/4*r**4 + 13*r + 150*r**2 - 10*r**3. Factor f(d).
3*(d - 10)**2
Let a = -59 + 62. Factor -5*r**2 + 451 + 5*r**a - 451 - 5*r + 5*r**4.
5*r*(r - 1)*(r + 1)**2
Let p(b) = -6*b**3 + 4*b**2 - 18*b - 4. Let q(x) = -2*x - x**3 + 51 + x - 50. Let j(s) = p(s) - 8*q(s). Determine a, given that j(a) = 0.
-3, -1, 2
Let y = -275 + 277. Let a(g) be the first derivative of -5 + 8/9*g**3 - 4/3*g + 7/3*g**y. Let a(p) = 0. Calculate p.
-2, 1/4
What is r in 0 + 8/9*r**4 + 0*r**2 + 0*r**3 + 2/9*r**5 + 0*r = 0?
-4, 0
Let u(y) be the second derivative of -1/10*y**6 + 4*y**3 + 6*y**2 + 1/14*y**7 - 3/4*y**5 + 8*y + 0 + 1/4*y**4. Let u(a) = 0. Calculate a.
-1, 2
Let s(t) = 77*t**2 + 349*t + 684. Let o(z) = -65*z**2 - 350*z - 685. Let u(m) = 6*o(m) + 5*s(m). Determine k, given that u(k) = 0.
-69, -2
Let q(l) be the second derivative of -l**5/20 + l**4/6 - l**3/6 + 5*l - 13. Find m such that q(m) = 0.
0, 1
Let x = -702 + 709. Let a(r) be the second der