200*q - 20*q**3 + 4091 + 120*q**2 + y*q**3 - 91.
-4*(q - 10)**3
Let f(x) = -56*x**2 + 8910*x - 3821. Let z(r) = 37*r**2 - 5940*r + 2548. Let i(u) = 5*f(u) + 7*z(u). Factor i(t).
-3*(t - 141)*(7*t - 3)
Let g be (-32)/5*45/(-18). Suppose g = 5*v - 31*f + 32*f, -2*v = -f - 5. Find t such that -2/21*t**v - 4/7*t**2 + 8/21*t + 16/21 + 2/21*t**4 = 0.
-2, -1, 2
Let f(z) be the second derivative of 20/3*z**2 + 35/36*z**4 + 35/9*z**3 + 0 - 100*z + 1/12*z**5. Factor f(l).
5*(l + 1)*(l + 2)*(l + 4)/3
Suppose 18*t - 2*q = 17*t, 12 = 4*t + 4*q. Suppose -l + 22 = 3*y + y, -16 = t*l - 4*y. Factor -21/5*d - 6/5*d**l + 3/5*d**3 - 12/5.
3*(d - 4)*(d + 1)**2/5
Let h(p) be the third derivative of -1/60*p**6 - 10/3*p**4 + 13/30*p**5 + 0 - 7*p**2 + 12*p**3 + 3*p. Solve h(j) = 0.
2, 9
Factor j**4 - 3497778*j - 806*j**3 - 9841500 + j**4 + 107730*j**2 - 1204272*j.
2*(j - 135)**3*(j + 2)
Suppose -2*h = -f, 155*f = -3*h + h + 157*f - 8. Determine s, given that -3/4 + 3/8*s - 3/2*s**h - 3/2*s**3 + 27/8*s**2 = 0.
-2, -1/2, 1/2, 1
Let p be ((-350)/42)/(-25)*6. Let s(l) be the second derivative of 0*l**p + 1/120*l**6 + 1/40*l**5 - 1/48*l**4 + 0 - 23*l - 1/12*l**3. Factor s(k).
k*(k - 1)*(k + 1)*(k + 2)/4
Let a be 0 + 4 - (396 + -397). Let o(d) be the third derivative of 12*d**2 + 1/30*d**a + 0*d + 0 + 1/20*d**6 - 2/3*d**4 + 4/3*d**3. Factor o(h).
2*(h - 1)*(h + 2)*(3*h - 2)
Let y(h) be the first derivative of 5*h**6/6 - 48*h**5 - 65*h**4 + 730*h**3/3 + 255*h**2/2 - 490*h + 6139. Determine s, given that y(s) = 0.
-2, -1, 1, 49
Factor -3588/5*m - 3/5*m**2 - 1072812/5.
-3*(m + 598)**2/5
Suppose 178 = 4*y - 3*t + 158, 2*y = 3*t - 2. Factor 1331/3*s + 1/3*s**4 + y*s**3 + 0 + 121*s**2.
s*(s + 11)**3/3
Suppose -3*x + 99 = -z, -5*x + 70 + 93 = -z. What is y in 6*y**2 + 14*y**3 - x - 5/2*y**4 - 80*y = 0?
-2, -2/5, 4
Suppose 0 - 1424/3*p**3 + 3740/3*p**2 + 140/3*p**4 - 200*p = 0. Calculate p.
0, 6/35, 5
Let t = -233 - -226. Let i be t/(-13)*30*(-11)/(-385). Suppose -i*y**2 + 40/13*y + 14/13 = 0. What is y?
-1/3, 7
Let h(d) = 4*d**4 + 10*d**3 - 66*d**2 - 200*d - 166. Let u(r) = -5*r**4 - 15*r**3 + 66*r**2 + 200*r + 165. Let p(w) = 3*h(w) + 2*u(w). Solve p(f) = 0.
-3, -2, 7
Let f(z) = 9*z**4 + 10*z**3 - 67*z**2 - 24*z + 248. Let s(q) = 2*q**4 - 2*q**2 - 1. Let a(b) = 3*f(b) - 12*s(b). Factor a(j).
3*(j - 3)**2*(j + 2)*(j + 14)
Determine x so that 314*x**3 + 4*x**4 - 126720*x + 33808*x**2 + 123904 - 621*x**3 - 413*x**3 = 0.
2, 88
Let g(s) = 18*s**2 - 6132*s - 2076. Let x(j) = -9*j**2 + 3061*j + 1038. Let o(c) = 5*g(c) + 9*x(c). Factor o(f).
3*(f - 346)*(3*f + 1)
Let h(b) be the first derivative of 9*b**2 + 0*b + 16/3*b**3 - 1/2*b**4 + 86. Determine k, given that h(k) = 0.
-1, 0, 9
Let h be 8/5 - (21 - 57/3) - 2/(-5). Factor -5/4*q**4 + 5/4*q**5 + h + 0*q**2 + 0*q - 5/2*q**3.
5*q**3*(q - 2)*(q + 1)/4
Let f = -19493/21 - -6500/7. Suppose f*o**3 + 8/3 + 17/3*o + 10/3*o**2 = 0. Calculate o.
-8, -1
Let q(l) be the second derivative of -l**5/5 - 12*l**4 - 216*l**3 + 2283*l. Find v such that q(v) = 0.
-18, 0
Let d(j) = -j**3 + 19*j**2 + 11*j + 185. Let b be d(20). Let p be 1 - (b + -11) - 19/3. Find s such that 0*s**4 - 4/3*s**3 + 0*s**2 + p*s**5 + 2/3*s + 0 = 0.
-1, 0, 1
Suppose -90*x + 18 = -88*x, n + x - 14 = 0. Let t be 17/21 + 6/(-9). Find z, given that 0*z**2 - 6/7*z**4 + t*z**3 + 0 + 9/7*z**n + 0*z = 0.
0, 1/3
Let v(j) be the second derivative of -j**4/18 + 241*j**3/9 - 80*j**2 - 3234*j. Suppose v(r) = 0. What is r?
1, 240
Factor 4*g**2 + 0*g**2 + 343 - 48 + 125 + 104*g.
4*(g + 5)*(g + 21)
Let p(y) be the third derivative of -y**5/75 - y**4/2 + 36*y**3/5 - 2150*y**2. Factor p(a).
-4*(a - 3)*(a + 18)/5
Let a(u) be the third derivative of -u**8/1512 + u**7/315 - u**6/540 - u**5/90 + u**4/54 - 5*u**2 - 353*u. Find t, given that a(t) = 0.
-1, 0, 1, 2
Let x = 52095 + -312569/6. What is u in x*u - 1/6*u**3 + 1/2 - 1/2*u**2 = 0?
-3, -1, 1
Let c(i) = 423*i + 77837. Let m be c(-184). Solve 1/5*z**m + 0*z**3 + 0 - 4/5*z**2 + 3/5*z**4 + 0*z = 0.
-2, 0, 1
Let i(f) be the first derivative of -125*f**6/6 + 470*f**5 + 3235*f**4/4 - 4640*f**3/3 - 610*f**2 + 400*f + 13252. Solve i(g) = 0 for g.
-2, -2/5, 1/5, 1, 20
Let l(v) be the second derivative of -64/21*v**3 - 50/147*v**7 - 7*v + 0 + 38/21*v**6 + 8/7*v**2 + 97/21*v**4 - 139/35*v**5. Factor l(t).
-4*(t - 1)**3*(5*t - 2)**2/7
What is o in 5/3*o**3 + 3680/3 + 640*o + 90*o**2 = 0?
-46, -4
Let n = 1327 - 1324. Let j(i) be the second derivative of 3/10*i**2 - 1/5*i**n + 16*i + 0 + 1/20*i**4. Factor j(d).
3*(d - 1)**2/5
Let h(z) be the first derivative of -28*z**6/15 + 572*z**5/25 - 366*z**4/5 - 272*z**3/15 + 152*z**2 - 60*z + 3256. Solve h(j) = 0.
-1, 3/14, 1, 5
Suppose -34/13*f**4 + 62/13*f**3 - 30/13*f**2 + 0*f + 0 + 2/13*f**5 = 0. What is f?
0, 1, 15
Let y(r) = -3*r**3 - 124*r**2 - 273*r + 3. Let m be y(-39). Determine j so that -j**4 + 5/4*j + 1/2*j**2 - 1/4*j**5 - j**m + 1/2 = 0.
-2, -1, 1
Let o(i) = 12*i**3 - 9*i**2 - 3*i - 5. Let y(m) = -14*m**3 + 10*m**2 + 4*m + 6. Let f(d) = -6*o(d) - 5*y(d). Factor f(g).
-2*g*(g - 1)**2
Let 8*f**4 + 276 + 540*f + f**4 - 3*f**4 - 93*f**2 - 9366*f**3 + 18677*f**3 - 9446*f**3 = 0. Calculate f.
-2, -1/2, 2, 23
Let j(w) = 3*w**2 + 24*w + 2. Let v be j(-8). Let d(b) = 1 + b**v + 11 - 12. Let z(q) = 7*q**2 - 72*q + 324. Let f(p) = -3*d(p) + z(p). Solve f(k) = 0.
9
Let u(p) be the second derivative of 3*p**5/40 - 16*p**4 + 3381*p**3/4 + 71415*p**2/2 + 14*p + 90. Let u(c) = 0. Calculate c.
-10, 69
Let f(b) = 97*b**2 + 137*b + 343. Let v(i) = 136*i**2 + 204*i + 515. Let c(u) = 7*f(u) - 5*v(u). What is j in c(j) = 0?
-58, -3
Let c(j) = 2*j**2 + 23*j - 14. Let d be c(-10). Let k(h) = 5*h + 220. Let o be k(d). Find l, given that o + 0*l**2 - 1/7*l**5 + 0*l + 0*l**4 + 1/7*l**3 = 0.
-1, 0, 1
Let y(k) = -k**2 - 80*k - 444. Let o be y(-6). Let g be (o - 4)*(-1)/3. Determine v, given that -2/9*v - 2/9*v**5 + 8/9*v**2 + 8/9*v**4 - g*v**3 + 0 = 0.
0, 1
Suppose 470 = -k + 5*k - 2*i, 3*k - 363 = -2*i. Factor -64*p - 36*p**2 + 15*p**2 - k - 12*p + 17*p**2 - 17.
-4*(p + 2)*(p + 17)
Let y = 130 + 1674. Factor 1020*t**2 - 9*t + 1321*t**4 + y*t**4 - 6750*t**3 - 31*t.
5*t*(t - 2)*(25*t - 2)**2
Let l be 1532/77 + (-286)/(-1001) + -20. Suppose -2/11*o**4 + 4/11 + l*o**3 - 10/11*o + 6/11*o**2 = 0. Calculate o.
-2, 1
Let -5/3*x**3 - 35/3*x - 40/3*x**2 + 0 = 0. Calculate x.
-7, -1, 0
Suppose 0 = 63*s - 85*s + 10494. Let t = 481 - s. Suppose 8/5*c**2 + 0 - 2/5*c**t - 8/5*c + 2/5*c**3 = 0. Calculate c.
-2, 0, 1, 2
Let z be (-5)/(1/7 - (-9)/(-14)). Suppose 0 = -8*c + z*c - 6. What is l in 5*l**4 + 1079*l - 1079*l + 5*l**2 + 10*l**c = 0?
-1, 0
Let c(n) be the second derivative of -n**4/4 - 7*n**3/6 - 7*n**2/2 + 28*n. Let h(k) = 10*k**2 + 22*k + 20. Let a(r) = 8*c(r) + 3*h(r). Factor a(i).
2*(i + 1)*(3*i + 2)
Let z be 69 + (-72 - -38 - 32). Factor 3*g**4 + 3/2*g**5 - 27*g**z + 9 - 69/2*g + 48*g**2.
3*(g - 1)**4*(g + 6)/2
Let l(b) be the third derivative of b**5/510 + 43*b**4/102 + 949*b**3/51 + 249*b**2 + 18*b. Factor l(m).
2*(m + 13)*(m + 73)/17
Let o(y) = -4*y**2 - 120*y - 222. Let c be o(-28). Let v be 14/(-8) - (-9 - -7). Solve -v*w - 1/2*w**c + 3/4*w**3 + 0 = 0 for w.
-1/3, 0, 1
Let n(t) = t**2 - 13*t + 8. Let q be n(13). Factor 9488*o + 0*o**4 - 4*o**4 - 9496*o + 4*o**2 + q*o**3.
-4*o*(o - 2)*(o - 1)*(o + 1)
Let b(j) = -99*j**3 + 84*j**2 + 2*j - 13. Let n(o) = o**2 + 1. Let a(r) = b(r) + 13*n(r). Factor a(k).
-k*(k - 1)*(99*k + 2)
Let t(h) be the first derivative of -h**4/15 + 89*h**3/30 - 11*h**2/5 + 113*h + 91. Let v(r) be the first derivative of t(r). Determine q so that v(q) = 0.
1/4, 22
Factor 0*m + 11233*m**4 + 0*m - 3084*m**2 - 5619*m**4 - 5618*m**4 + 1040*m**3.
-4*m**2*(m - 257)*(m - 3)
Let q(k) be the third derivative of -k**5/210 - 19*k**4/84 + 20*k**3/21 + 835*k**2 + 2*k. Solve q(g) = 0.
-20, 1
Determine a, given that 0*a**2 + 0*a**3 + 1/7*a**4 + 0*a - 1/7*a**5 + 0 = 0.
0, 1
Let z(x) be the third derivative of 5*x**8/336 + 409*x**7/21 + 223585*x**6/24 + 5142092*x**5/3 + 25293280*x**4/3 + 50309120*x**3/3 - 5348*x**2. Factor z(n).
5*(n + 1)**2*(n + 272)**3
Factor 7/2*i + 9/4*i**2 + 0 + 1/4*i**3.
i*(i + 2)*(i + 7)/4
Factor -87760*o**2 + 2083*o + 87676*o**2 + 1861*o - 1120.
-4*(3*o - 140)*(7*o - 2)
Determine f, given that 22*f**3 