9*j**3 - 13*j**4 + 59*j**3 + 9*j**4. Let i(h) = 9*h**4 - 23*h**3 + 11*h**2. Let c(u) = 8*i(u) + 3*x(u). Factor c(t).
-4*t**2*(t - 1)*(3*t - 2)
Let w(z) be the first derivative of 27*z**5/5 - 177*z**4/4 + 138*z**3 - 198*z**2 + 120*z - 3477. Factor w(j).
3*(j - 2)**3*(9*j - 5)
Suppose -317 + 71 = -135*d + 159. Let v(k) be the first derivative of 30*k - 5/3*k**d - 25/2*k**2 + 31. Solve v(s) = 0.
-6, 1
Let r(j) be the second derivative of j**7/210 - j**6/24 + 2*j**5/15 - j**4/6 - 39*j**2/2 - 2*j - 22. Let h(g) be the first derivative of r(g). Solve h(d) = 0.
0, 1, 2
Let l be (13732/10 - 1/(-1)) + 0. Let u = l - 1373. Factor 0 - u*b + 8/5*b**3 + 22/5*b**2.
2*b*(b + 3)*(4*b - 1)/5
Let h = -6/3125 - 335619/3125. Let p = h + 1631/15. Let 4/3*o**2 - 8/9*o**3 + p*o - 8/9 = 0. Calculate o.
-1, 1/2, 2
Let y(k) be the third derivative of k**8/2016 + k**7/105 - k**6/16 + k**5/90 + 5*k**4/12 - 2*k**2 + 30*k + 13. Solve y(o) = 0 for o.
-15, -1, 0, 2
Solve -435*u**2 - 648*u + 895*u**2 + 3*u**4 - 642*u**3 - 1753*u**2 = 0 for u.
-1, 0, 216
Suppose 0 = -2*j - 5*a + 29, -12 = -4*j - 3*a + 11. Factor -19*q - 18 + 4*q**2 - 3*q - j*q + 8*q**3 - 2*q**4.
-2*(q - 3)**2*(q + 1)**2
Suppose -77*j = 83*j - 1120. Let s(v) be the third derivative of 1/165*v**5 + j*v**2 + 1/660*v**6 + 0*v**3 + 0*v + 0 + 0*v**4. What is o in s(o) = 0?
-2, 0
Suppose 0 = -16*u + 14*u + 4. Suppose 2*x - 18 - 20 = u*f, -x - 3*f = -39. Factor -x*t + 0*t**3 - 22*t - 26*t - 33*t**2 + 108 - 3*t**3.
-3*(t - 1)*(t + 6)**2
Let y be 2/3*-15*12/10. Let c be (-1)/(-2) + (30/y - -6). Let 10*v**2 + 5*v**3 - 16*v**4 + 6*v**c - 4*v - v**3 = 0. What is v?
-1, 0, 2/5, 1
Let f(s) = 13*s**3 - 1214*s**2 - 18*s - 6. Let a(i) = -3*i**3 - i**2 + 3*i + 1. Let c(q) = 6*a(q) + f(q). Factor c(x).
-5*x**2*(x + 244)
Let u be (-133764)/22365 - (-5 - 1). Let w(b) be the first derivative of 11/42*b**4 - 128/21*b + 16/21*b**2 + 5 + 8/7*b**3 + u*b**5. Factor w(i).
2*(i - 1)*(i + 4)**3/21
Find i such that 0 + 2/13*i**5 - 18/13*i**2 + 6/13*i**3 + 10/13*i**4 + 0*i = 0.
-3, 0, 1
Let q(r) be the third derivative of -11/16*r**4 + 0*r + 7/20*r**5 - 1/140*r**7 - 3/40*r**6 + 0 + 1/224*r**8 + 3/4*r**3 + 171*r**2. Solve q(u) = 0 for u.
-3, 1
Solve 256*a - 5*a**2 + 3*a**2 - 625 + 163 - 42 = 0 for a.
2, 126
Suppose -1860*u + 2351 + 520 = -849. Factor -3/2*m**4 - 3033*m**u - 138*m**3 + 6486*m - 6627/2.
-3*(m - 1)**2*(m + 47)**2/2
Let p = -1650 + 1650. Let k(a) be the second derivative of -33/14*a**4 - 1/35*a**6 + 6*a - 40/7*a**3 + p - 3/7*a**5 - 48/7*a**2. Factor k(m).
-6*(m + 1)**2*(m + 4)**2/7
Let o(q) be the first derivative of 1/24*q**6 - 9/4*q**3 + 3/20*q**5 - 20 - 5/16*q**4 - 4*q**2 - 3*q. Let o(b) = 0. Calculate b.
-2, -1, 3
Let t(a) be the second derivative of a**5/60 + 7*a**4/12 + 25*a**3/9 - 12*a**2 + 2472*a. Let t(p) = 0. Calculate p.
-18, -4, 1
Let b(k) = -390*k - 120. Let n be b(-18). What is o in 0*o**2 - 8*o**2 - 2*o**3 - 6906*o + n*o = 0?
-3, -1, 0
Suppose c - 9708 = 4*c. Let s = 5079 + c. Let s*w**2 + 8 - 28 + 24*w - 1847*w**2 = 0. Calculate w.
1, 5
Let i(r) be the first derivative of -5*r**3/3 + 195*r**2/2 - 990*r + 1806. Factor i(a).
-5*(a - 33)*(a - 6)
Let r be (-26)/(-117) - 2/9. Let m be (54/12 + -4)*r. Factor 7/4*p**4 + m - 1/2*p**3 + 1/2*p - 7/4*p**2.
p*(p - 1)*(p + 1)*(7*p - 2)/4
Let o = 8494/17661 - 4/841. Let g(t) be the first derivative of 19 + 12/7*t**2 + 8/7*t + o*t**3. Factor g(m).
2*(m + 2)*(5*m + 2)/7
Let s = 88262/26475 + -4/8825. Let c(m) be the first derivative of 15/2*m**2 + 0*m + s*m**3 - 5/4*m**4 - 22. Factor c(w).
-5*w*(w - 3)*(w + 1)
Let l(r) = -227*r - 905. Let j be l(-4). Let i(s) be the third derivative of 0*s + 1/120*s**5 + 0*s**j - 1/24*s**4 - 8*s**2 + 0. Find u such that i(u) = 0.
0, 2
Let l be (120/(-45)*(-126)/40)/((-9)/(-30)). Let r(j) be the first derivative of -l + 4/5*j**2 - 16/5*j + 4/15*j**3 - 1/10*j**4. Factor r(w).
-2*(w - 2)**2*(w + 2)/5
Let q(u) be the second derivative of 8/3*u**4 + 0*u**2 - 35 + 2/21*u**7 - 8/3*u**3 - 3/5*u**5 - 4/15*u**6 - u. Let q(o) = 0. Calculate o.
-2, 0, 1, 2
Let j = 97 + -88. Factor -11 - 7*u - j*u**2 + 33*u**2 - 3*u**3 - 13 + 10*u.
-3*(u - 8)*(u - 1)*(u + 1)
Let q(g) = -g**3 + 18*g**2 + 61*g + 49. Let i be q(21). Determine c so that -12*c + i + c**5 + 4*c**4 + 62*c**3 - 63*c**3 - 16*c**2 - 7 = 0.
-3, -2, -1, 0, 2
Let q(o) be the second derivative of 2*o**6/15 + 33*o**5/5 + 31*o**4/3 - 22*o**3 - 64*o**2 + 2119*o + 2. Factor q(k).
4*(k - 1)*(k + 1)**2*(k + 32)
Let -119*m + 53/5*m**2 + 1911/5 - 1/5*m**3 = 0. What is m?
7, 39
Let t(l) = 6*l**2 + l. Let u be t(1). Suppose -861 = -u*x - 0*x. Solve -59 - 4*z**2 - 2*z**3 + 8*z - 48 + x = 0.
-2, 2
Let t be -1 - ((-4)/(-1) - 7). Let w be (3 - t)/(9/(-6) + 2). Factor w + 5*f**3 - 4*f**3 + 14*f + 14*f - 31*f.
(f - 1)**2*(f + 2)
Factor -690*o**3 + 715*o**3 - 39*o**2 + 125 + 575*o - 206*o**2.
5*(o - 5)**2*(5*o + 1)
Let u(p) = 4*p**3 - 27*p**2 - 27*p - 5. Let s(w) = -3*w**3 + 27*w**2 + 16*w + 4. Let d(b) = -5*s(b) - 4*u(b). Let d(g) = 0. Calculate g.
-28, 0, 1
Suppose -37 = 10*x - 57. Solve 7*z**2 - 12 + 3*z**3 - 69*z - 15 - 14*z**2 - 23*z**x - 9 = 0 for z.
-1, 12
Let x be 4/8*3/(-6)*10/(-35). Let y(u) be the second derivative of 0*u**4 - 3/10*u**5 + 0 + 1/2*u**3 + 0*u**2 + x*u**7 + 0*u**6 - 2*u. Solve y(l) = 0 for l.
-1, 0, 1
Let v(a) = 5*a**2 + 56*a - 514. Let x be v(6). Determine p, given that 0*p + 0 + 3/2*p**3 + 3/2*p**x = 0.
-1, 0
Let d(n) be the second derivative of 5*n**4/12 - 85*n**3/6 - 95*n**2 - n + 2106. Determine q, given that d(q) = 0.
-2, 19
Let q(l) = -1. Let v(t) = -t**3 - 3*t**2 - 2*t - 3. Suppose -7*a - 16 = a. Let w be v(a). Let p(m) = -3*m**2 + 9*m - 3. Let s(h) = w*q(h) - p(h). Factor s(d).
3*(d - 2)*(d - 1)
Let m(p) be the first derivative of p**4/8 - 11*p**3 - 205*p**2/4 - 69*p + 2522. What is b in m(b) = 0?
-2, -1, 69
Let h = 519 - 279. Suppose 0 = 8*k + 2*k - h. Let -16 + 8*z + 4*z + 28*z**2 - k*z**2 = 0. Calculate z.
-4, 1
Let q(c) be the second derivative of -c**6/60 - c**5/20 + 7*c**4/24 + 5*c**3/3 + 3*c**2 + 83*c + 2. Factor q(y).
-(y - 3)*(y + 1)*(y + 2)**2/2
Suppose -4*q = -r - 9, 3*q + 4 = -2*r + 19. Factor -y**4 - 10*y**q + 129*y**2 + 3*y**4 - 133*y**2 + 4*y**4.
2*y**2*(y - 2)*(3*y + 1)
Factor 1/2*g**4 + g**3 + 50*g + 250 - 75/2*g**2.
(g - 5)**2*(g + 2)*(g + 10)/2
Let z(r) be the third derivative of r**10/403200 + r**9/5760 + 7*r**8/1920 - 23*r**5/12 - 109*r**2. Let u(m) be the third derivative of z(m). Factor u(b).
3*b**2*(b + 14)**2/8
Let z be (-4)/(-240)*9 - (245/28 - 9). Factor -8/5*t + 8/5*t**4 + z*t**5 + 16/5 + 2/5*t**3 - 4*t**2.
2*(t - 1)**2*(t + 2)**3/5
Let b be (-3 - -3)/(-11)*(15/2 + -7). Determine i so that 0 + b*i - 1/9*i**2 + 10/9*i**3 = 0.
0, 1/10
Suppose 115 - 709 = -121*v - 176 - 176. Find j such that 12/5 - j**3 - 31/5*j + 24/5*j**v = 0.
4/5, 1, 3
Let s(d) be the third derivative of -d**5/15 - 1018*d**4/3 - 2072648*d**3/3 - 1991*d**2 - 1. Factor s(x).
-4*(x + 1018)**2
Suppose -166*l = -139*l. Let b(a) be the third derivative of 1/50*a**6 + 1/30*a**4 + 0*a + l + 0*a**3 + 1/25*a**5 - 12*a**2 + 2/525*a**7. Factor b(d).
4*d*(d + 1)**3/5
Suppose 15*m - 33*m = -54. Let v(p) = -2*p - 10. Let s be v(-5). Factor 33/8*u**2 + 3/8*u**4 + 9/4*u + 9/4*u**m + s.
3*u*(u + 1)*(u + 2)*(u + 3)/8
Let j be 15 - 30*8/24. Suppose 4*i = -3*h + 25, -4*i - j = -3*i - 3*h. Suppose -2/5*c**3 + 0*c**2 + 0 + 0*c + 0*c**i + 2/5*c**5 = 0. Calculate c.
-1, 0, 1
Let k be 246/63 - (-4)/42. Suppose -4*x + h + k = 0, -3*h = x - 0 + 12. Factor 0 + x*u**4 - 1/2*u**5 + 0*u**2 - 1/2*u + u**3.
-u*(u - 1)**2*(u + 1)**2/2
Factor -599 - 377 + 244*s**2 - 3508*s**3 + 3512*s**3 - 3*s - 13*s.
4*(s - 2)*(s + 2)*(s + 61)
Let n = 0 + 3. Suppose 0 = -2*a + a + 2*z + 10, 10 = -n*a - 4*z. Factor -2*w**2 - 6*w + 0*w + 2*w + a*w + 4.
-2*(w - 1)*(w + 2)
Factor -3123/8 - 1563/4*q - 3/8*q**2.
-3*(q + 1)*(q + 1041)/8
Let r be (25 - 4 - 1)/(-5 + 4). Let o be r/(-70) - 48/(-21). Factor 128/7*w**4 + 0 - 96/7*w**3 + 0*w + o*w**2.
2*w**2*(8*w - 3)**2/7
Let c = -10199/6 - -1700. Let p(u) be the first derivative of -1/9*u**3 - c*u**2 + 2/3*u + 9. Determine l, given that p(l) = 0.
-2, 1
Suppose -4*x + 375 - 255 = 0. Let x*a + 64*a - 142*a**2 - 90 + 149*a - 8*a + 117*a**2 = 0. Calculate a.
2/5, 9
Suppose -108 + 138/7*q**2 + 82/7*q**3 + 10