7/210 + x**6/240 + x**5/20 - 3*x**4/32 - 49*x**2. Factor t(v).
-v*(v - 1)**2*(v + 3)**2/4
Factor -118*t**2 + 4*t**4 - 26*t**3 - 5*t**4 - 51*t**2.
-t**2*(t + 13)**2
Let y be 15/(-74 + 14) - ((-61)/(-20))/(-1). Suppose 2*n = 9 - 3. Factor 2/5*g**n + y*g**2 + 6*g + 18/5.
2*(g + 1)*(g + 3)**2/5
Let s(k) be the second derivative of k**7/630 + k**6/360 - k**5/90 + 21*k**2/2 - 19*k. Let w(v) be the first derivative of s(v). Determine t so that w(t) = 0.
-2, 0, 1
Let g(f) be the first derivative of -f**3/9 - 73*f**2/3 - 5329*f/3 + 145. Factor g(y).
-(y + 73)**2/3
Let o(l) = -34*l**2 - 304*l + 21. Let r be o(-9). Suppose 2/7*u**r - 2/7*u + 0 + 0*u**2 = 0. What is u?
-1, 0, 1
Let h be (34/(-4) - 1/(-2)) + 8. Find r such that 0*r**3 - 2/5*r**2 + h*r + 0 + 2/5*r**4 = 0.
-1, 0, 1
Factor 4/3 - 2/3*w**2 - 2/3*w.
-2*(w - 1)*(w + 2)/3
Let z(c) be the third derivative of -c**8/224 - c**7/210 + c**6/20 + c**5/15 - 68*c**2. Find v such that z(v) = 0.
-2, -2/3, 0, 2
Let k(p) = p**3 + 23*p**2 + 22*p + 7. Let o be k(-22). Solve 3*l + o*l - 46*l**2 + 25 + 47*l**2 = 0 for l.
-5
Suppose 461 = 6*o - 10*o - 3*q, -4*o = -q + 465. Let h = o - -1046/9. Factor -2/9*n**4 + 0 - 2/3*n**2 - 2/3*n**3 - h*n.
-2*n*(n + 1)**3/9
Let q be (-3036)/(-15) - (-18)/30. Suppose q = 5*y - 2*s, -s = -y - 8 + 51. Factor -31*g + 4 + 4 + 2*g**2 + y*g.
2*(g + 2)**2
Suppose 0 = -0*i + 2*i - 28. Factor h**2 - i*h + 4*h**2 + 44*h.
5*h*(h + 6)
Determine j so that 0 - 50/3*j - 16*j**2 + 2/3*j**3 = 0.
-1, 0, 25
Let r(u) be the third derivative of -u**2 + 0*u + 0 + 16/15*u**3 + 1/300*u**6 + 2/5*u**4 + 3/50*u**5. Factor r(s).
2*(s + 1)*(s + 4)**2/5
Suppose -2*f + 15 = f. Suppose -2*h - 8 = 4*u, 0*u - 32 = -f*h + 3*u. Suppose -4/7*r**3 - 2/7*r**2 + 0*r - 2/7*r**h + 0 = 0. Calculate r.
-1, 0
Let z(j) = -5*j**5 + 6*j**4 - 5*j**3. Let a(f) = f**5 + f**3. Suppose 5*h = 2*x + x + 16, -h + 12 = -5*x. Let o(c) = h*a(c) + z(c). Factor o(g).
-3*g**3*(g - 1)**2
Let l(c) be the third derivative of c**8/672 + 3*c**7/140 - 23*c**6/120 + 37*c**5/60 - 17*c**4/16 + 13*c**3/12 + 8*c**2. Determine d so that l(d) = 0.
-13, 1
Let j(c) = -5*c**3 - 155*c**2 + 11*c + 137. Let m(u) = 70*u**3 + 2170*u**2 - 155*u - 1915. Let g(b) = -85*j(b) - 6*m(b). Factor g(y).
5*(y - 1)*(y + 1)*(y + 31)
Let o(p) be the first derivative of p**6/27 + 8*p**5/45 + p**4/9 - 8*p**3/27 - p**2/3 + 53. What is j in o(j) = 0?
-3, -1, 0, 1
Let k = -26 + 42. Let l = -13 + k. Factor -3 - 3*q**2 + q - 4*q - l*q.
-3*(q + 1)**2
What is d in 1/3*d**2 + 79/6*d - 20/3 = 0?
-40, 1/2
Let o(p) = -7*p + 110. Let w be o(16). Let g be (-2)/w - (-41 - -37). Determine r, given that -2/3*r - r**4 + 1/3*r**g + 0 + 1/3*r**3 + r**2 = 0.
-1, 0, 1, 2
Let y(f) = 2*f**5 - 12*f**4 - 3*f**3 + 16*f**2 + 3*f. Let h(k) = -2*k**5 + k**3 - k. Let m(v) = 3*h(v) + y(v). Factor m(n).
-4*n**2*(n - 1)*(n + 2)**2
Solve 5*x**2 - 32*x**2 + 125 + 75*x - 18*x**2 + 5*x**3 = 0 for x.
-1, 5
Factor -50*k**2 + 236*k - 7 - 140 - 479*k + 38*k**2 - 348*k.
-3*(k + 49)*(4*k + 1)
Let o = -4 - -7. Suppose 0 = p + o - 5. Factor -2*k**2 + k**4 + 2*k - 3*k**4 - p*k**3 + 4*k**2.
-2*k*(k - 1)*(k + 1)**2
Let h(v) = 7*v + 146. Let b be h(-20). Let r(q) be the third derivative of 0*q**5 + 0 - 1/60*q**4 + 1/300*q**b - q**2 + 0*q + 0*q**3. Factor r(o).
2*o*(o - 1)*(o + 1)/5
Let t(p) = -p**3 + p**2 + p. Let u be t(-1). Factor u + 2*f**2 - 3 + 2*f**2 - 13*f**4 + 11*f**4.
-2*(f - 1)**2*(f + 1)**2
Let v be 4 + (-90)/18 + (-5)/(-2). Factor -v*i**3 - 21/2*i + 15/2*i**2 + 9/2.
-3*(i - 3)*(i - 1)**2/2
Factor 305*o + 75 - 636*o + 291*o + 5*o**2.
5*(o - 5)*(o - 3)
Let q = 46 + -44. Determine p so that -18*p**3 - 4*p**4 - 12*p + 2*p**4 - 27*p**q - p**4 = 0.
-4, -1, 0
Let l be -2 + 0 - ((-10)/5 - 2). Factor 4*z**4 - 11*z**2 + 67*z**3 + 6 - z**l - 71*z**3 + 2 + 4*z.
4*(z - 2)*(z - 1)*(z + 1)**2
Let w = 64 - 444/7. Factor 2/7*u**4 - w*u - 2/7 + 4/7*u**3 + 0*u**2.
2*(u - 1)*(u + 1)**3/7
Let l(p) be the first derivative of 3*p**6/14 - 12*p**5/5 + 61*p**4/7 - 32*p**3/3 + 32*p**2/7 - 146. Determine q, given that l(q) = 0.
0, 2/3, 4
Let g = -59 + 187/3. Let t(y) be the second derivative of -g*y**3 - 5*y + 4*y**2 + 2/3*y**4 + 2/21*y**7 + 0 + 4/5*y**5 - 8/15*y**6. Find j, given that t(j) = 0.
-1, 1, 2
Let j(h) be the second derivative of -5/6*h**4 + 1/10*h**5 - 4*h**2 + 0 + 8/3*h**3 - 14*h. Solve j(u) = 0 for u.
1, 2
Let q(r) be the second derivative of -r**6/24 + r**5/12 - 5*r**2 + 15*r. Let v(b) be the first derivative of q(b). Solve v(z) = 0.
0, 1
Let j(q) be the second derivative of -q**4/3 + 4*q**3/3 - 18*q - 2. Factor j(c).
-4*c*(c - 2)
Let q = -10/139 - -33966/695. Solve q*i**3 - 98/5*i**5 + 16/5*i - 24*i**2 - 42/5*i**4 + 0 = 0.
-2, 0, 2/7, 1
Suppose -l + 2*l - 2*o + 5 = 0, -3*o = -4*l. Suppose 3*j = 0, -5 = l*k + j - 17. Let 1/5*n**3 + 1/5*n**2 - 1/5*n**5 + 0 + 0*n - 1/5*n**k = 0. What is n?
-1, 0, 1
Solve 45*f - 527 - 3*f**5 + 452 + 102*f**2 - 10*f**3 - 32*f**3 - 27*f**4 = 0.
-5, -1, 1
Let s(f) = -f**3 - 2*f**2 - 2*f. Let h(g) = 20*g**3 - 50*g**2 - 45*g. Let k(t) = h(t) + 25*s(t). Factor k(v).
-5*v*(v + 1)*(v + 19)
Let b(h) be the first derivative of -3*h**5/10 - 15*h**4/8 + 21*h**3/2 + 255*h**2/4 - 150*h + 137. What is z in b(z) = 0?
-5, 1, 4
Factor -289*h**2 + 192*h**3 + 4*h + 16823 - 127*h**2 - 16815 + 56*h.
4*(h - 2)*(4*h - 1)*(12*h + 1)
Let l(y) = -y**2 + 11*y - 8. Let j be l(9). Let g = -7 + j. Find k, given that 4*k - g*k**3 - 12*k - 6*k**2 + k**3 - 2*k**2 = 0.
-2, 0
Let d(j) be the third derivative of j**5/60 + 5*j**4/12 - 11*j**3/6 + 43*j**2 + 2*j. Factor d(y).
(y - 1)*(y + 11)
Let a(i) be the first derivative of i**8/336 - i**7/42 + i**6/36 + i**5/6 - 5*i**4/8 - 3*i**3 + 3. Let o(y) be the third derivative of a(y). Solve o(l) = 0.
-1, 1, 3
Factor -g**2 + 1 - 7/2*g**3 + 7/2*g.
-(g - 1)*(g + 1)*(7*g + 2)/2
Let w(g) = -4*g**2 - 18*g + 7. Let j(x) be the second derivative of 2*x**4/3 + 37*x**3/6 - 15*x**2/2 - 2*x. Let r(m) = -3*j(m) - 7*w(m). Factor r(d).
(d + 4)*(4*d - 1)
Suppose 13*m - 12 = -3*s + 17*m, -s = -3*m - 9. Factor -1/2*a**2 + 1/4*a**4 + s*a + 1/4 + 0*a**3.
(a - 1)**2*(a + 1)**2/4
Let n = 1384/791 - 4/113. Let d(b) = -b**3 + 10*b**2. Let a be d(10). What is j in -2/7*j**3 - 18/7*j - n*j**2 + a = 0?
-3, 0
Let u = -4269/221 - -331/17. Suppose -u*t + 0*t**2 + 2/13*t**3 + 0 = 0. What is t?
-1, 0, 1
Let c(v) be the third derivative of -v**6/24 + 16*v**2 - 1. Factor c(j).
-5*j**3
Let x(w) = -w**3 + 13*w**2 - 19*w - 28. Let d(h) = -h**2 - 17*h - 19. Let g be d(-15). Let t be x(g). Factor 0 + 0*j**2 - j**3 + 1/2*j**t + 0*j**4 + 1/2*j.
j*(j - 1)**2*(j + 1)**2/2
Factor -20/3*o + 4/3*o**2 + 0.
4*o*(o - 5)/3
Let 25*c**4 - 139*c**2 + 105*c**3 + 40*c + 167*c**2 + 87*c**2 - 5*c**5 = 0. What is c?
-1, 0, 8
Let h be 1 + (((-24)/(-30))/1)/(88/110). Factor 12/5*p + 12/5*p**3 + 3/5*p**4 + 18/5*p**h + 3/5.
3*(p + 1)**4/5
Let a(b) be the third derivative of -b**7/2520 + b**6/360 - b**5/120 + b**4/72 - b**3/6 + 8*b**2. Let k(z) be the first derivative of a(z). Factor k(f).
-(f - 1)**3/3
Suppose -31*q = -9*q + 11*q. Solve q - 6/11*m - 2/11*m**2 = 0 for m.
-3, 0
Let x(p) be the second derivative of p**6/45 + 17*p**5/30 + 34*p**4/9 + 100*p**3/9 + 16*p**2 - 260*p. What is q in x(q) = 0?
-12, -2, -1
Let o(t) be the third derivative of t**8/63840 - t**7/11970 - t**6/1710 + t**5/60 + 15*t**2. Let n(z) be the third derivative of o(z). Factor n(u).
2*(u - 2)*(3*u + 2)/19
Solve -29*w**3 + 9*w**2 + 38*w**3 + 0*w**2 + 3*w + 3*w**4 = 0.
-1, 0
Suppose -323 = 11*f + 623. Let g = -86 - f. Suppose 0*a**2 - 1/4*a**3 + g + 0*a = 0. What is a?
0
Suppose -w - 22 = -0*w. Let n = -19 - w. Determine p so that 13*p + 4*p**4 - 7*p + 16*p**n + 24*p**2 + 4 + 10*p = 0.
-1
Suppose 0*g - 2*g + 10 = 0. Let i be (5 - g) + 1*3. Factor -5*d**2 + i*d**2 + d**3 + 0*d**3.
d**2*(d - 2)
Suppose -21*s = 5 - 68. Let f(g) be the second derivative of 6/5*g**5 + 0 + 36*g**s - 9*g**4 - 1/15*g**6 - 81*g**2 + 2*g. What is l in f(l) = 0?
3
Let p = 463/3 - 162. Let j = p - -8. Factor -j + 1/6*q**2 + 1/6*q**4 + 1/2*q - 1/2*q**3.
(q - 2)*(q - 1)**2*(q + 1)/6
Let q(d) be the first derivative of -32 - 2/3*d + 1/30*d**5 - 1/6*d**3 + 1/12*d**4 - 2/3*d**2. Factor q(i).
(i - 2)*(i + 1)**2*(i + 2)/6
Let q(u) = 9*u**3 + 65*u**2 + 113*u + 55. Let p(v) = -20*v**3 - 130*v**2 - 225*v - 110. 