0*v**6 + 3*v. Factor r(g).
-g**2*(g - 1)**2*(g + 1)
Let q = 32 - 29. Factor q*w**2 + 5 - 3*w**2 - 5*w**2.
-5*(w - 1)*(w + 1)
Let m(l) = -l**2 + 7*l + 2. Let i be m(7). Suppose 2*u + 5*h - 5 = 0, 0*h + 2*h - 2 = i*u. Factor s**3 + u*s**3 + 5*s**2 + s**2 + 2*s**3 - 3*s**4.
-3*s**2*(s - 2)*(s + 1)
Suppose -5*j - w = -19, -2*j - 1 = 3*w - 6. Suppose 9*r**3 + 37*r**j + 3*r**4 + 26*r**3 + 10*r**2 + 15*r**5 = 0. What is r?
-1, -2/3, 0
Let j(x) be the first derivative of 2*x**5 - 49*x**4/10 + 46*x**3/15 + x**2/5 + 128. Factor j(b).
2*b*(b - 1)**2*(25*b + 1)/5
Suppose -10*x + 6 = -8*x. Factor 4*g**2 + 12*g + x*g**3 - 30*g - 4*g**4 + 14*g + g**5.
g*(g - 2)**2*(g - 1)*(g + 1)
Let y(o) be the first derivative of 5*o**3/3 - 55*o**2 - 83. Factor y(k).
5*k*(k - 22)
Let a(q) = -2*q**3 - 13*q**2 - 3*q + 26. Let d be a(-6). Let k = -1 + 5. Solve b**3 - k*b**5 - 4*b**4 - b**4 + d*b**5 = 0 for b.
0, 1/4, 1
Let s(q) be the third derivative of -q**5/20 - 17*q**4/8 - 21*q**3 + 79*q**2. Factor s(w).
-3*(w + 3)*(w + 14)
Let k(j) be the second derivative of -j**8/1848 + j**7/385 - j**6/220 + j**5/330 - 11*j**2 - 2*j. Let y(g) be the first derivative of k(g). Factor y(u).
-2*u**2*(u - 1)**3/11
Let p be 2/(-21) + (3 - (-68)/(-42)). Solve 3/7*f**2 - 12/7 + 36/7*f - p*f**3 = 0 for f.
-2, 1/3, 2
Let o = -73 + 115. Let i be (o/(-77))/((-12)/88). Determine d, given that -2*d**3 - d + 1/2*d**i + 0 + 5/2*d**2 = 0.
0, 1, 2
Let c be ((-13)/26)/((-1)/(-24)). Let m(f) = f**2 + 14*f + 28. Let x be m(c). Factor 0*s**2 + 0*s + 0 - 3/2*s**5 + 3*s**x - 3/2*s**3.
-3*s**3*(s - 1)**2/2
Let r = 16/105 + -5/42. Let q(z) be the third derivative of 0*z**3 - 6*z**2 - 1/12*z**4 + 0*z + 0 - r*z**5. Factor q(g).
-2*g*(g + 1)
Let u be (6 + 4)*(-1)/(-2). Suppose -p + 3*g = 1, -g - 13 = -4*p + u. Factor -r**p - 2*r**4 - 3*r**2 + 5*r**2 + r**5 - 2*r**3 + 2*r**5.
2*r**2*(r - 1)**2*(r + 1)
Let j be 9 + (-2)/(1*(-6)/3). Suppose -j = -2*a - 0*a - 2*d, 5*d = 5*a - 25. Factor -16/7*y**a + 2/7*y**3 + 0 + 0*y**2 - 4/7*y**4 + 0*y.
-2*y**3*(2*y + 1)*(4*y - 1)/7
Let z(t) be the third derivative of t**7/35 + 3*t**6/40 + t**5/20 - 40*t**2. Solve z(k) = 0.
-1, -1/2, 0
Let g(r) = 3*r**5 - 17*r**4 + 13*r**3 + 17*r**2 - 18*r + 2. Let o(k) = k**4 + k**3 - k**2 - 1. Let c(j) = g(j) + 2*o(j). Determine t, given that c(t) = 0.
-1, 0, 1, 2, 3
Let t(k) be the third derivative of -k**5/15 + 13*k**4/3 + 112*k**3/3 - 209*k**2. Solve t(q) = 0 for q.
-2, 28
Factor -5*o**3 + 626*o**2 + 622*o**2 - 1198*o**2.
-5*o**2*(o - 10)
Suppose 32*b - 65 - 31 = 0. Let t(r) be the first derivative of -1/4*r**4 + 0*r**2 + 1/10*r**5 + 0*r + 3 + 1/6*r**b. Factor t(g).
g**2*(g - 1)**2/2
Let y(n) be the second derivative of 0*n**2 + 1/720*n**6 - 1/24*n**4 + 1/240*n**5 + 0 - 3*n - 13/6*n**3. Let c(o) be the second derivative of y(o). Factor c(g).
(g - 1)*(g + 2)/2
Suppose 2 = 2*m - 5*z, 3*m - z + 4*z = 24. Factor 36*k**2 + 18 - 112*k + 2*k**3 + 46 - m*k**3 + 16*k.
-4*(k - 4)**2*(k - 1)
Let f(v) be the second derivative of 3*v**5/80 + v**4/8 - v**3/8 - 3*v**2/4 - v + 16. Factor f(p).
3*(p - 1)*(p + 1)*(p + 2)/4
Suppose -9*g - 63 = -12*g. Let u be 3 - (129/g - 4). What is r in 4/7 + 6/7*r - 2/7*r**2 - 2/7*r**4 - u*r**3 = 0?
-2, -1, 1
Solve -10*r**3 + 8/5*r + 69/5*r**2 - 3/5 - 24/5*r**4 = 0 for r.
-3, -1/4, 1/6, 1
Let t(r) be the third derivative of -r**8/6720 + r**7/105 - 4*r**6/15 + 11*r**5/30 - 22*r**2. Let k(c) be the third derivative of t(c). Factor k(w).
-3*(w - 8)**2
Let s = -10851/8 + 1357. Suppose s*y - 3/4 - 1/8*y**2 = 0. Calculate y.
2, 3
Let m be 1 + -3 - (18 + -10 - 14). Factor 2/3*q**2 + 2/3*q**3 + 2/9*q**m + 2/9*q + 0.
2*q*(q + 1)**3/9
Factor -1/2*v**2 + 0 - 6*v.
-v*(v + 12)/2
Suppose -12/7*f**2 + 8/7*f**4 + 2/7*f**5 + 0*f + 2/7*f**3 + 0 = 0. What is f?
-3, -2, 0, 1
Suppose 4*f + 2*c = f - 11, 2*f = 4*c + 14. Let y be f + (-4 - -3) - -13. Find t such that 2 - y*t + 12*t**2 - 8*t + 2 + 7*t - 4*t**3 = 0.
1
Let -19*c**4 - 123*c**2 - 96*c**2 + 5*c**5 - 101*c**2 + 39*c**4 - 60*c**3 - 320*c = 0. Calculate c.
-4, -2, 0, 4
Let b(u) be the third derivative of -u**6/120 + u**5/28 - 3*u**4/56 + u**3/42 - 7*u**2 + 2*u. Factor b(x).
-(x - 1)**2*(7*x - 1)/7
Let p = 279 - 249. Let g be -1*26/p - (1 + -2). Solve 10/3 + g*s**2 - 4/3*s = 0.
5
Suppose -3*y**3 + 0 + 17/3*y**2 + 4/9*y**4 - 28/9*y = 0. Calculate y.
0, 1, 7/4, 4
Let p(t) be the first derivative of -4*t**3/3 - 32*t**2 - 60*t - 150. Find s, given that p(s) = 0.
-15, -1
Let p be 1/3 + (-2)/(-3). Suppose 2*i - 3 = p. What is q in 12*q + 6*q - 17*q**i + 12*q**3 - 3 - 6*q - q**2 - 3*q**4 = 0?
1
Let y(o) be the second derivative of -16*o**6/135 + 28*o**5/45 - 11*o**4/18 - 28*o**3/27 - 4*o**2/9 + 19*o. Factor y(u).
-2*(u - 2)**2*(4*u + 1)**2/9
Factor 3/7*t**2 + 18/7*t - 48/7.
3*(t - 2)*(t + 8)/7
Let m be -5*(-30)/(-800)*(-20)/6. Factor 3/8*g - 3/8*g**3 - 1/8*g**4 + m*g**2 - 1/2.
-(g - 1)**2*(g + 1)*(g + 4)/8
Let j = -61 + 355. Let p = 294 - j. Factor -k**4 + p*k**3 + 1/2*k + k**2 - 1/2*k**5 + 0.
-k*(k - 1)*(k + 1)**3/2
Let w(n) = -n**2 - 5*n + 6. Suppose -4*y = -4*q + 32, -5*y - 16 - 9 = 0. Let p(r) = -2*r**2 - 16*r + 18. Let o(k) = q*p(k) - 8*w(k). Solve o(u) = 0.
1, 3
Let t = 3167771/9386 + 2/4693. Suppose -375/2*i**3 + t*i**2 - 405/2*i + 81/2 = 0. What is i?
3/5
Factor 40*d**3 + 35*d**3 - 51*d**3 + 3*d**4.
3*d**3*(d + 8)
Solve -152/5*n**2 - 16/5*n**4 + 52/5*n + 0 - 44*n**3 = 0 for n.
-13, -1, 0, 1/4
Let z be (-2)/7 - (-3440)/3612. Find k such that z*k**4 - 2/3*k**2 + 0 - 4/3*k + 4/3*k**3 = 0.
-2, -1, 0, 1
Let p(u) = 192*u - 11. Let s be p(-3). Let d = -2926/5 - s. Factor 3/5*i**2 - 9/5*i + d*i**3 - 3/5.
3*(i - 1)*(i + 1)*(3*i + 1)/5
Let a(i) be the second derivative of -i**4/60 + 4*i**3/15 + 2*i**2 + 3*i + 11. Factor a(r).
-(r - 10)*(r + 2)/5
Let o be (-4)/((-9)/138*4/3). Factor -5*g**4 - 14 + 16*g - 21 - o*g + 40*g**2 + 30*g**3.
-5*(g - 7)*(g - 1)*(g + 1)**2
Let i(c) = -33*c**3 + 1. Let u be i(1). Let l be 2 - -7 - u/(-8). Solve l*p**2 - p + 10 - 6*p - 8*p = 0 for p.
1, 2
Let -238/13 - 712/13*a + 6/13*a**2 = 0. Calculate a.
-1/3, 119
Let g be (-2 + 44/16)*(12 + (-8 - 0)). Solve -21/2*s**2 + 12*s + 3/2*s**g + 24 = 0 for s.
-1, 4
Let t(v) = 9 - 18*v**2 + 42*v**2 - 25*v**2 + 5*v. Let p(k) = 6*k**2 - 31*k - 54. Let a(y) = 6*p(y) + 34*t(y). Determine c so that a(c) = 0.
-1, 9
Suppose 0 = i + i + 4*u - 36, -3*u = 5*i - 97. Suppose -m = -5*v - 5 + i, 0 = 2*v + 4*m - 6. Factor -3*f**4 + f**3 - 5*f**v + 7*f**3.
-3*f**3*(f - 1)
Let y be (-3)/(3/139) - 4/4. Let f = y + 140. Suppose 2/3*h**2 - 2/3*h**4 - 2/3*h + f + 2/3*h**3 = 0. What is h?
-1, 0, 1
Factor -20/7 - 2/7*p**2 - 22/7*p.
-2*(p + 1)*(p + 10)/7
Let u(l) be the third derivative of -7*l**5/24 + 5*l**4/4 + 48*l**2. Find b such that u(b) = 0.
0, 12/7
Let i(k) = -k**2 + k - 1. Let s(w) be the second derivative of -w**5/10 - w**4/6 + w**3/3 - 3*w**2 - 3*w. Let m(h) = 8*i(h) - s(h). Let m(a) = 0. What is a?
1
Let n = 18 - 3. Let z be -2 + (3 + n)/2. Factor -3*t**4 + z*t**4 - 3*t**2 + t**3 - t**4 + t**5 - 2*t.
t*(t - 1)*(t + 1)**2*(t + 2)
Let l = -21464/7 + 3070. Let -8/7*p**5 - l*p**4 - 2*p**2 + 0 - 2/7*p - 30/7*p**3 = 0. What is p?
-1, -1/4, 0
Let f = 1265/6 - 2527/12. Factor -3/2*c + 11/4*c**2 - c**3 - f*c**4 + 0.
-c*(c - 1)**2*(c + 6)/4
Let p(t) = -3*t**3 - 3*t**2. Let w(f) = 4*f**3 + 3*f**2 - 3*f - 3. Let s(v) = v + 1. Let k(j) = 3*s(j) + w(j). Let y(o) = -4*k(o) - 5*p(o). Factor y(d).
-d**2*(d - 3)
Let b(i) be the second derivative of -13/70*i**6 + 1/49*i**7 - 9/14*i**2 - 8/7*i**4 + 6*i + 8/7*i**3 + 0 + 9/14*i**5. Find g such that b(g) = 0.
1/2, 1, 3
Let x(c) be the third derivative of c**6/780 - 4*c**5/39 + 3*c**4 - 432*c**3/13 + 8*c**2 + 2*c. Factor x(w).
2*(w - 18)**2*(w - 4)/13
Let o = -4101/10 + 2064/5. Let d(h) be the second derivative of 3/5*h**3 + o*h**2 + 0 + 6*h + 1/20*h**4. Factor d(n).
3*(n + 3)**2/5
Factor 386/3*i - 2/3*i**2 - 128.
-2*(i - 192)*(i - 1)/3
Let n(y) be the first derivative of y**3/3 - 7*y**2/2 + 6*y - 18. Factor n(c).
(c - 6)*(c - 1)
Let u = -8879 + 8891. Let -3/2*w**4 - 6*w + u*w**3 - 3/2 + 3*w**2 - 6*w**5 = 0. What is w?
-1, -1/4, 1
Let 756*g**4 + 2*g**3 - 751*g**4 + 3*g**3 - 65*g**2 - 125*g - 60 = 0. What is g?
-3, -1, 4
Let x(l) be the first derivative of 5*l**3/3 + 15*l**2 - 135*l - 598. Factor x(p).
5*(p - 3)*(p +