
Suppose -4*g + 8 = 4*k, -2*k = 6*g - 2*g - 4. Factor 2*t**4 + 0*t**3 + 2*t**5 - 2*t**2 + 0*t**3 - k*t**3.
2*t**2*(t - 1)*(t + 1)**2
Let g = 2 - -1. Suppose 12 + g = 5*c. Find t such that -2*t**3 - 4*t**2 - t**3 - 7*t**c = 0.
-2/5, 0
Let x(v) be the third derivative of v**11/1496880 - v**10/226800 + v**8/22680 + v**5/30 - v**2. Let p(a) be the third derivative of x(a). Factor p(s).
2*s**2*(s - 2)**2*(s + 1)/9
Let r(g) be the second derivative of -g**6/30 + 3*g**5/20 - g**4/4 + g**3/6 + g. Find k, given that r(k) = 0.
0, 1
Let z(k) = 12*k**2 + 15*k + 9. Let v(u) = u**2 - 1. Let w(r) = -7*r**2 - r + 5. Let o(x) = 6*v(x) + w(x). Let q(m) = -9*o(m) - z(m). Solve q(h) = 0 for h.
-2, 0
Let a = 55 + -38. Factor -d - a*d**2 + 0*d + 19*d**2 + d**5 - 2*d**4 + 0*d**4.
d*(d - 1)**3*(d + 1)
Let u(m) = -m**2. Let g(j) = -2*j**3 - 10*j**2. Let w(r) = -g(r) + 4*u(r). Find l, given that w(l) = 0.
-3, 0
Let i(w) be the third derivative of w**9/17640 + w**8/11760 - w**7/8820 + w**4/8 + 3*w**2. Let s(k) be the second derivative of i(k). Factor s(p).
2*p**2*(p + 1)*(3*p - 1)/7
Let v = 14 + -10. Let k(d) = -d**2 + 0*d**3 - 2*d + d**v - 9 + 2*d**3 + 15. Let z(u) = -u**3 + u**2 - 1. Let l(c) = -k(c) - 6*z(c). Factor l(o).
-o*(o - 2)*(o - 1)**2
Let w be 9 + 460/(-52) - (-64)/91. Factor 2/7*k**2 + 4/7 + w*k.
2*(k + 1)*(k + 2)/7
Solve 0 - 2/13*g**3 - 8/13*g + 8/13*g**2 = 0.
0, 2
Factor -3*c**2 - 2*c**2 - 3 + 3*c**2 + c**2 - 4*c.
-(c + 1)*(c + 3)
Factor y**3 - 8*y**2 + 6*y**3 - 4*y + 8 - 3*y**3.
4*(y - 2)*(y - 1)*(y + 1)
Let h(s) be the third derivative of -s**8/420 + s**6/30 - s**5/15 - 5*s**3/6 - s**2. Let a(j) be the first derivative of h(j). Determine l, given that a(l) = 0.
-2, 0, 1
Let i(b) be the first derivative of -b**7/210 - b**6/60 + b**4/12 + b**3/6 - b**2 - 2. Let w(y) be the second derivative of i(y). Let w(j) = 0. Calculate j.
-1, 1
Let v be ((-52)/(-260))/((-2)/(-4)). Factor 0 - 2/5*h**4 + 0*h + v*h**2 + 0*h**3.
-2*h**2*(h - 1)*(h + 1)/5
Let s(u) = 8*u - 1. Let r be s(2). Suppose -r = -4*i - 3. Factor -21*d**i + 12*d**4 + d**5 - 3*d**3 + 16*d**2 - 3*d**5.
-2*d**2*(d - 2)**3
Let i(u) be the second derivative of 1/27*u**4 + 0 - 1/135*u**6 + 1/45*u**5 - 5*u - 1/9*u**2 - 1/189*u**7 - 1/27*u**3. What is d in i(d) = 0?
-1, 1
Suppose 3*l + 0*l = 6. Factor 0 + 2*o**2 + l*o - 2 - 3 + 3 - 2*o**3.
-2*(o - 1)**2*(o + 1)
Let b = -22 + 24. Suppose b*v + 20 = 5*v + 5*y, 3*v + 8 = 2*y. Factor -3/5*f**3 - 2/5*f**4 - 1/5*f**2 + 0*f + v.
-f**2*(f + 1)*(2*f + 1)/5
Let b be (-27)/(-4) - 1/(-4). Let u = b + -5. Factor 8*g**2 + 2 - 6*g**u - 4*g**2.
-2*(g - 1)*(g + 1)
Let d be 2/6 - (-4)/(-12). Let o(n) be the second derivative of 3*n + 0 - 1/12*n**4 - 3/10*n**5 + d*n**2 + 0*n**3 - 3/10*n**6. Factor o(x).
-x**2*(3*x + 1)**2
Let c(q) be the second derivative of q**4/72 - 5*q**3/18 + 25*q**2/12 - 8*q. Let c(a) = 0. What is a?
5
Let c(z) be the second derivative of -z**6/480 + z**5/80 - z**4/32 + 2*z**3/3 + 2*z. Let k(p) be the second derivative of c(p). Factor k(t).
-3*(t - 1)**2/4
Let p(m) be the third derivative of -m**8/1008 + m**7/210 - m**6/120 + m**5/180 - 2*m**2. Factor p(q).
-q**2*(q - 1)**3/3
Suppose -2*b + 6 = 18. Let x be -5 - -5 - 2/b. Determine u, given that -x*u**2 + 1/3*u + 0 = 0.
0, 1
Let s(m) be the first derivative of 3*m**5/5 - 3*m**4/4 + 9. Solve s(x) = 0 for x.
0, 1
Find o, given that -4*o**2 + 2 - 2*o**3 - 2 + 3*o + 3*o = 0.
-3, 0, 1
Let z(q) be the first derivative of q**4 + 8*q**3/3 + 2*q**2 - 17. Factor z(t).
4*t*(t + 1)**2
Let q(u) be the second derivative of -3*u**5/10 + 4*u**4 - 77*u**3/4 + 147*u**2/4 + u. Factor q(o).
-3*(o - 1)*(2*o - 7)**2/2
Let l(r) = -3*r + 1. Let x be l(-1). Suppose -16 - 4 = -x*f. Factor -y + 0*y + 2*y**3 - 2*y**5 + y**f.
-y*(y - 1)**2*(y + 1)**2
Suppose 4*q - 20 = -2*o, o - 2*o = 3*q - 16. Suppose -3*c + c = -q. Factor 0 - j**2 - 3/2*j**c - 1/2*j**4 + 0*j.
-j**2*(j + 1)*(j + 2)/2
Let k(a) = -a - 2. Let o be k(-7). Suppose -4*b + 11 = i, i = 3*b - 15 + o. Factor 0 - 5/2*l**b + 0*l - 7/2*l**4 + l**2.
-l**2*(l + 1)*(7*l - 2)/2
Suppose 0 = -160*h + 153*h + 21. Let -1/3*f**h - 5/3*f - 4/3*f**2 - 2/3 = 0. What is f?
-2, -1
Let v(g) be the third derivative of g**9/7560 - g**8/3360 + g**4/8 - 3*g**2. Let r(k) be the second derivative of v(k). Find d, given that r(d) = 0.
0, 1
Let c be (-2)/(-20)*-4 - (-128)/220. What is t in 4/11*t - 2/11 - c*t**2 = 0?
1
Factor 4/3*h - 38/3*h**2 + 0 + 30*h**3.
2*h*(5*h - 1)*(9*h - 2)/3
Factor 3*v**2 + 53*v**3 + 2*v**4 + 2*v**2 - 43*v**3 + 3*v**4.
5*v**2*(v + 1)**2
Suppose 20 = -7*x + 2*x. Let k be x/3*15/(-10). Factor -1/3*m**3 + 0*m + 0 + 2/3*m**k.
-m**2*(m - 2)/3
Let p(v) = 2*v**2 - 38*v + 36. Let q be p(18). Let u(j) be the second derivative of -1/60*j**5 + 1/90*j**6 + 0 + 0*j**2 + 0*j**3 + q*j**4 + j. Factor u(n).
n**3*(n - 1)/3
Let l(m) = 3*m. Let p be l(1). Let x(g) be the first derivative of -4/3*g**p - 3/2*g**2 + 4 + g. Factor x(f).
-(f + 1)*(4*f - 1)
Let z(d) be the second derivative of -1/12*d**3 + 1/4*d**2 + 1/40*d**5 + 0 - 2*d - 1/24*d**4. Factor z(c).
(c - 1)**2*(c + 1)/2
Suppose -m + 8 + 8 = 4*t, 2*m = 4*t - 16. Factor -7*k + 10*k**2 + k + m*k - 2*k**2.
2*k*(4*k - 3)
Suppose -z + 31 = 4*z - 2*w, 5*z + 4*w - 43 = 0. Let a = 10 - z. Factor 4*t**3 - t**4 - a*t**2 - 6*t**2 - t**4 + 7*t**2.
-2*t**2*(t - 1)**2
Let x = 1/45 + 1/5. Let p(u) be the first derivative of 0*u - 2 - 1/3*u**2 + x*u**3. What is y in p(y) = 0?
0, 1
Suppose -3*y - 5*v + 9 = 0, -2*y + v + 6 = -0. Suppose -12/7*f**2 - 16/7 - 2/7*f**y - 24/7*f = 0. What is f?
-2
Factor 0 + 0*r + 2/9*r**3 + 2/9*r**5 + 4/9*r**4 + 0*r**2.
2*r**3*(r + 1)**2/9
Let 39 + d**3 - 55*d + 49*d**3 - 35*d**4 + 5*d**5 - 14 + 10*d**2 = 0. What is d?
-1, 1, 5
Suppose 0*w = -4*w + 8. Let o = -1 - -4/3. What is v in o*v**w + 1/3*v + 0 = 0?
-1, 0
Let m(l) = l**2 - l - 1. Let g(b) = -3*b + b**3 - 9*b - 3*b**3 - 4 + 0*b**3 - 14*b**2. Let s(t) = g(t) + 4*m(t). Let s(r) = 0. Calculate r.
-2, -1
Suppose 265*o**2 - 2*o**4 + 4*o**3 - 265*o**2 = 0. What is o?
0, 2
Let -3/4*q + 3/4*q**4 - 3/4*q**2 + 0 + 3/4*q**3 = 0. Calculate q.
-1, 0, 1
Let v = -2 + 5. Suppose 13*u**2 - v - 4*u**2 - u + u + 6*u = 0. What is u?
-1, 1/3
Solve -21*f**4 - 38*f**3 - 6*f - 33*f**2 - 2*f**3 - 8*f**3 = 0.
-1, -2/7, 0
Let k(d) be the second derivative of 0*d**3 - d**2 + 0*d**4 + 0*d**5 + 1/480*d**6 + 1/840*d**7 + 0 + d. Let o(b) be the first derivative of k(b). Factor o(l).
l**3*(l + 1)/4
Factor -4/7*p**3 + 0*p + 2/7*p**2 + 0 + 2/7*p**4.
2*p**2*(p - 1)**2/7
Let n(a) = 9*a**3 + 6*a**2 + 6*a + 9. Let q(d) = 4*d**3 + 3*d**2 + 3*d + 4. Let o(c) = -3*n(c) + 7*q(c). Factor o(y).
(y + 1)**3
Suppose 0*r = -5*r + 20. Suppose 5*t + r*x = 83, -3 = -2*t + x + 25. Let -2 + 7*g - 3*g**4 - t*g**2 + 4*g**3 + 2*g + 7*g**3 = 0. What is g?
2/3, 1
Suppose -5*u + 27 + 13 = -5*f, 3*u + 2*f + 1 = 0. Let 0*r**u + 3*r**3 - 5*r**5 + 3*r**5 - r**3 = 0. What is r?
-1, 0, 1
Let s = 515/3 + -171. Suppose 0 + 0*q + s*q**2 = 0. Calculate q.
0
Let u(o) = 12*o**4 - 36*o**3 + 88*o**2 - 64*o + 8. Let y(g) = -g**4 + g**2 - 1. Let x(s) = -u(s) - 8*y(s). Let x(d) = 0. What is d?
0, 1, 4
Let i = 81 - 50. Let j = -92/3 + i. Determine d, given that 0 - 1/3*d**3 + j*d**4 + 1/3*d - 1/3*d**2 = 0.
-1, 0, 1
Let t be 1/1 + 63/6. Let g = 12 - t. What is o in -g*o + 1/2*o**2 + 0 = 0?
0, 1
Let o(b) be the third derivative of -b**8/560 - 3*b**7/280 - b**6/60 - b**3/6 - 2*b**2. Let h(w) be the first derivative of o(w). Factor h(s).
-3*s**2*(s + 1)*(s + 2)
Let h(i) = -8*i**3 + 25*i**2 - 4*i - 2. Let c(a) = 4*a**3 - 13*a**2 + 2*a + 1. Let t(r) = -11*c(r) - 6*h(r). Factor t(n).
(n - 1)**2*(4*n + 1)
Let x(m) be the first derivative of 1/15*m**6 + 1/5*m**2 + 8/25*m**5 + 0*m + 8/15*m**3 + 3/5*m**4 + 2. Factor x(a).
2*a*(a + 1)**4/5
Let o be (-2)/9 + 14/(-18) - -3. Factor 0*r + 0 - 2/5*r**o.
-2*r**2/5
Suppose h - 4*d = -16, -5*h + 45 = 5*d - 0*d. Suppose -z + h*z = 0. Factor 0 + 1/3*j**2 + z*j + 2/3*j**3 + 1/3*j**4.
j**2*(j + 1)**2/3
Factor -8/7*w**3 + 0*w**4 + 4/7*w**2 + 6/7*w + 2/7*w**5 - 4/7.
2*(w - 1)**3*(w + 1)*(w + 2)/7
Let a be (-3)/2*30/(-9). Suppose -3*g - 5 + 0 = -2*i, a*i + 5*g = 25. Find b, given that b + 0*b**2 - b**2 - i*b - 2 = 0.
-2, -1
Let a = -42/17 - -328/119. Determine p, given that 0*p + 0 + 0*p**2 - a*p**4 - 2/7*p**3 = 0.
-1, 