et f(r) = 6*r**3 - 250*r**2 - 6*r + 234. Let p(o) = -f(o) + 8*l(o). Factor p(k).
2*(k - 1)*(k + 1)*(k + 129)
Let h(q) = 164*q + 11162. Let w be h(-68). Let s(x) be the first derivative of 0*x**4 + 0*x + 0*x**2 - w - 2/3*x**6 + 0*x**3 + 0*x**5. Factor s(a).
-4*a**5
Let t(b) be the first derivative of 20*b**2 + 64*b - 50 + 4/3*b**3. Factor t(v).
4*(v + 2)*(v + 8)
Let n = -114255/41 + 2787. Let b = 118/123 - n. Suppose 4/3*m**2 - 4*m**3 + 2*m - 2/3*m**4 + 2*m**5 - b = 0. What is m?
-1, 1/3, 1
Suppose 0 = 8*o - 5 - 59. Let q(b) be the second derivative of -1/5*b**5 + 0 + 0*b**3 + 0*b**2 - 7/3*b**4 - o*b. Factor q(y).
-4*y**2*(y + 7)
Let r(i) = -i**3 + 111*i**2 + 635*i - 6372. Let g be r(116). Factor 2/7*f**4 - 52/7*f**3 - 110/7*f**2 + 0 - g*f.
2*f*(f - 28)*(f + 1)**2/7
Factor -1/7*n**2 - 40*n - 2800.
-(n + 140)**2/7
Suppose -y - 4*y + 7 = -2*o, -y = 2*o + 1. Let s be o/((-2)/20*2). Factor -4*q**4 + 2*q - 14*q**2 + 5*q**5 + 18*q**2 - 7*q**s.
-2*q*(q - 1)*(q + 1)**3
Find y such that -43*y**4 + 25*y**3 - 14*y**5 + 5*y**5 + 53*y**4 + 4*y**5 - 18*y**2 - 12*y**2 = 0.
-2, 0, 1, 3
Let d be (-52)/(-14) + 18/14 + -1. Suppose 4*n + n - 45 = -2*j, 0 = -2*j + 4*n. Factor h**5 - 8*h**4 + j*h**3 + 23*h**4 + 0*h**d + 4*h**5.
5*h**3*(h + 1)*(h + 2)
Factor -2500 - 2800/3*n - 103/3*n**2 - 1/3*n**3.
-(n + 3)*(n + 50)**2/3
Factor 9*a**2 - 21*a**2 - 1176*a + 82*a + 10*a**2 - 1832 - 740*a.
-2*(a + 1)*(a + 916)
Suppose -2/11*u**2 - 439922/11 - 1876/11*u = 0. What is u?
-469
Let c(z) be the second derivative of -z**4/30 - 21*z**3/5 + 26*z**2 + 223*z - 2. What is s in c(s) = 0?
-65, 2
Let s(y) be the third derivative of -17/100*y**5 - 9 - y**2 + 0*y + 7/40*y**4 + 1/10*y**3 + 9/200*y**6. Factor s(m).
3*(m - 1)**2*(9*m + 1)/5
Let m(w) be the first derivative of -w**6/36 - 152*w**5/15 + 153*w**4/4 - 460*w**3/9 + 307*w**2/12 + 1068. Find l, given that m(l) = 0.
-307, 0, 1
Let g be (-19)/55 + 102/187 - 36/(-120). Suppose 4*u = -u. Determine x, given that -g*x**5 + 1/2*x**2 + 1/2*x**3 - 1/2*x**4 + 0 + u*x = 0.
-1, 0, 1
Let n(z) be the third derivative of z**6/60 - 7*z**5/6 + 32*z**4/3 - 124*z**3/3 + 2*z**2 - 78*z. Determine x, given that n(x) = 0.
2, 31
Let f(o) be the third derivative of -o**5/90 + 7*o**4/18 - 8*o**3/3 + 2*o**2 + 3*o + 1326. Determine l, given that f(l) = 0.
2, 12
Let o = 404904 - 2834326/7. Factor o*u**4 - 2024/7*u + 1058/7 + 876/7*u**2 + 88/7*u**3.
2*(u - 1)**2*(u + 23)**2/7
Suppose 0 = -280*n + 282*n - 2*w - 2, -3 = 4*n + 3*w. Let d(m) be the second derivative of 27/4*m**2 + 1/8*m**4 + n + 3/2*m**3 + 25*m. What is p in d(p) = 0?
-3
Let r = 169 + -164. Factor -8 - r*y + 12 + 5*y**3 - 14 + 10*y**2.
5*(y - 1)*(y + 1)*(y + 2)
Let d(h) be the second derivative of 4/33*h**3 + 1/33*h**4 - 1/110*h**5 + 0*h**2 + 0 - 1/330*h**6 - 6*h. Factor d(g).
-g*(g - 2)*(g + 2)**2/11
Suppose 0 = 3*d - 27 + 12. Suppose -2*q + d = -2*s + 1, q = 2*s - 1. Factor -12*z + 26*z**s + 16*z**3 - 27*z**3 + 3*z**2.
3*z*(z + 1)*(5*z - 4)
Let -49*l**3 + 170*l + 37*l**3 - 165*l**2 + 7*l**3 = 0. What is l?
-34, 0, 1
Let n = -1386 + 1412. Let s = n - 129/5. Factor 1/5*a - s*a**3 + 1/5 - 1/5*a**2.
-(a - 1)*(a + 1)**2/5
Suppose -5*p - 3*q - 1235 = -6281, -2*q + 2020 = 2*p. Let l = 1010 - p. What is r in 6/11*r + 2/11*r**l - 20/11 = 0?
-5, 2
Let h(q) = 8*q**5 + 10*q**4 - 6*q**3 - 4*q + 4. Let p(r) = -r**4 + r**3 + r - 1. Let i = 40 - 32. Let s be 4/10*20/i. Let x(c) = s*h(c) + 4*p(c). Factor x(z).
2*z**3*(z + 1)*(4*z - 1)
Determine a so that 2/7*a**3 + 842402/7 - 2594/7*a**2 + 839806/7*a = 0.
-1, 649
Let j(m) be the second derivative of -m**7/210 + 13*m**6/150 - 57*m**5/100 + 103*m**4/60 - 41*m**3/15 + 12*m**2/5 - 2427*m. Factor j(u).
-(u - 6)*(u - 4)*(u - 1)**3/5
Let 101*h**2 + 26 - 39*h**2 - 62 + 2*h**3 - 42*h**2 + 34*h - 20 = 0. Calculate h.
-7, -4, 1
Let n(t) = -t**3 + 2*t**2 + 5*t - 7. Let h be n(3). Let u(l) = l**2 - l + 1. Let f(p) = -3*p**2 - p + 17. Let q(d) = h*u(d) + f(d). Factor q(g).
-4*(g - 2)*(g + 2)
Let c = 540096 + -540093. Factor 8/9*s + 10/9*s**2 + 2/9*s**c + 0.
2*s*(s + 1)*(s + 4)/9
Let o(z) be the second derivative of -2*z**6/15 - 4*z**5/5 - 2*z**4/3 + 8*z**3/3 + 6*z**2 + 2022*z. Determine b, given that o(b) = 0.
-3, -1, 1
Let c(o) be the third derivative of -o**7/70 - 23*o**6/40 - 7*o**5 - 49*o**4/2 + 9069*o**2. Determine z, given that c(z) = 0.
-14, -7, -2, 0
Let w(j) be the third derivative of 1/735*j**7 + 1/42*j**4 + 0*j + 0*j**6 - 1/70*j**5 + 0 + 0*j**3 + 42*j**2. Solve w(u) = 0.
-2, 0, 1
Let o(l) be the second derivative of 127*l + 3/20*l**6 + 0 - 9/5*l**5 + 11/4*l**4 - 16/9*l**3 + 7/12*l**2. Factor o(z).
(z - 7)*(3*z - 1)**3/6
Let i = -1159 - -1172. Let z(m) be the first derivative of 0*m**4 - 3/5*m**5 - i + 0*m**2 + 0*m + m**3. Factor z(l).
-3*l**2*(l - 1)*(l + 1)
Let g(c) be the third derivative of 7*c**6/120 - 79*c**5/90 - 23*c**4/72 + 747*c**2. Determine l, given that g(l) = 0.
-1/7, 0, 23/3
Let m(l) be the first derivative of l**4/4 + 13*l**3/3 - 34*l**2 + 422. Find s such that m(s) = 0.
-17, 0, 4
Let z(i) be the third derivative of -2*i**7/105 - 98*i**6/15 - 4224*i**5/5 - 43560*i**4 + 383328*i**3 + 276*i**2 + 8. Solve z(g) = 0 for g.
-66, 2
Let r be (15 + 1610/(-105))/((-16)/300). Find s, given that 9/4*s**3 + 0 - 3/2*s - r*s**2 = 0.
-2/9, 0, 3
Solve -8*s - 935 + 8*s**2 - 929 + 0*s**3 - 909 + 2*s**3 + 2741 = 0 for s.
-4, -2, 2
Let j be 16/(-10) + 2 - (-1568)/80. Let z be (45/j)/(6/32). Factor 3 - 12*l + 9*l**2 - 45*l**2 - 4*l**3 + 5 + z*l**4.
4*(l - 2)*(l + 1)**2*(3*l - 1)
Let v(t) be the first derivative of -3*t**7/1540 + t**6/99 - 13*t**5/660 + t**4/66 - 72*t**3 + 54. Let g(n) be the third derivative of v(n). Factor g(f).
-2*(f - 1)**2*(9*f - 2)/11
Let c(h) be the third derivative of h**8/10080 - h**7/360 + h**6/36 + 53*h**5/30 + 80*h**2. Let g(l) be the third derivative of c(l). Factor g(q).
2*(q - 5)*(q - 2)
Suppose -73*y = -78*y - 180. Let i = -14 - y. What is a in a**2 + a**3 + i*a - a**2 - 2 - 25*a = 0?
-1, 2
Let a(z) = -7*z**3 - 20*z**2 + 59*z + 176. Let f(o) = -6*o**3 - 18*o**2 + 57*o + 177. Let y(h) = 3*a(h) - 4*f(h). Solve y(b) = 0.
-5, -3, 4
Let o = 147061/16495 - 381/3299. Suppose 24/5*j**4 - o*j**2 + 294/5*j + 8/5*j**5 - 36 - 102/5*j**3 = 0. What is j?
-5, -2, 1, 3/2
Suppose 16 + 24 = 10*i. Let f(s) = 4*s - 3. Let r be f(i). Determine h so that 4*h**2 - 8 - r*h + 9*h + 0*h**2 = 0.
-1, 2
Let x = -374704/7 + 53530. Factor -1/7*y**2 - 5/7*y - x.
-(y + 2)*(y + 3)/7
Let x be 1152/588 + -2 - (-88392)/4704. Factor -45/4 - x*t - 35/4*t**2 - 5/4*t**3.
-5*(t + 1)*(t + 3)**2/4
Suppose -411 - 306 = -270*b + 31*b. Solve -27/4*u**b - 105/2*u**2 - 357/4*u + 45/2 = 0.
-5, -3, 2/9
Let u(f) be the second derivative of 17/66*f**4 - 1/110*f**5 - 81/11*f**2 - 21/11*f**3 + 0 - 108*f. Factor u(h).
-2*(h - 9)**2*(h + 1)/11
Let h(n) be the third derivative of -n**7/2520 + n**6/180 + n**4/4 - 5*n**3/6 + 27*n**2. Let x(p) be the second derivative of h(p). Let x(d) = 0. Calculate d.
0, 4
Let k(a) be the first derivative of a**6/2 + 9*a**5 - 33*a**4/4 - 147*a**3 + 393*a**2 - 360*a - 912. Find j such that k(j) = 0.
-15, -4, 1, 2
Determine n so that 211/2*n + 1/2*n**2 - 106 = 0.
-212, 1
Let w(y) be the third derivative of -3*y - y**2 + 0*y**5 + 0 + 1/105*y**7 + 0*y**4 + 1/60*y**6 + 0*y**3. Solve w(x) = 0.
-1, 0
Factor 4174357/2*c**2 - 53596587/4*c + 82163961/4 + 63645/2*c**3 + 1/4*c**5 + 621/4*c**4.
(c - 3)**2*(c + 209)**3/4
Let h(d) be the third derivative of 0*d**4 - 1/357*d**7 + 2*d - 30*d**2 + 1/170*d**6 + 0 - 1/2856*d**8 + 0*d**3 + 0*d**5. What is i in h(i) = 0?
-6, 0, 1
Suppose -68 - 65 + 25 = -54*r. Let f(n) be the third derivative of -1/24*n**3 + 0 + 0*n**4 - r*n**2 + 0*n + 1/240*n**5. Let f(o) = 0. Calculate o.
-1, 1
Let k = -87316/33 + 2646. Let h(n) be the second derivative of 0 - 1/22*n**5 - 14*n + 1/33*n**3 + 0*n**2 - k*n**4. Factor h(y).
-2*y*(y + 1)*(5*y - 1)/11
Let z(p) be the first derivative of -p**5/10 - 3*p**4/4 + 8*p**2 + 1. What is f in z(f) = 0?
-4, 0, 2
Let o(u) be the first derivative of 3/4*u**2 - u + 2*u**3 + 7/8*u**4 + 68. Determine x, given that o(x) = 0.
-1, 2/7
Suppose -b = 5*o - 22, -37*b + 42*b = 4*o - 6. Factor 0 + 21/8*l**3 + 27/8*l + 3/8*l**o + 45/8*l**2.
3*l*(l + 1)*(l + 3)**2/8
Solve -182/3*k**2 + 2/3*k**3 - 754/3*k - 190 = 0 for k.
-3, -1,