et n(g) = -2*g**3 - 13*g**2 - 66*g - 255. Let y be n(-5). Factor 1/2*z**3 + y - 1/2*z**4 + 0*z - 1/2*z**5 + 1/2*z**2.
-z**2*(z - 1)*(z + 1)**2/2
Let v(t) = t**2 + 3*t - 10. Let i(f) = 36*f**2 + f - 80*f**2 - 1 + 43*f**2. Let a(l) = 12*i(l) - 3*v(l). Factor a(c).
-3*(c + 1)*(5*c - 6)
Let j(m) = 8*m - 158. Let s be j(22). Factor -2*p**4 + s*p**4 + 38*p**3 + 22*p - 62*p**3 + 4*p**5 - 16*p**2 - 2*p.
4*p*(p - 1)**2*(p + 1)*(p + 5)
Factor -2*i**5 - 64*i**4 - 258290*i**3 - 2*i**5 + 258034*i**3.
-4*i**3*(i + 8)**2
Let z(g) = -21*g**2 + 96*g + 63. Let i(d) = 5*d**3 - d**2 - 8*d + 7. Let v be i(2). Let q(c) = 3*c**2 - 14*c - 9. Let j(r) = v*q(r) + 4*z(r). Factor j(y).
-3*(y - 3)*(y + 1)
Let o(d) be the third derivative of -d**7/210 - 7*d**6/60 - 41*d**5/60 - d**4/6 + 10*d**3 + 508*d**2. Find v such that o(v) = 0.
-10, -3, -2, 1
Let s be (3 - 3) + -6 + 4/24*44. Let g(a) be the first derivative of -s*a**3 + 1/6*a**6 - 4/5*a**5 - 22 + 1/2*a**2 + 0*a + 3/2*a**4. Factor g(z).
z*(z - 1)**4
Suppose 1422 = 394*v + 634. Let -280/3*d**v + 5/3*d**3 - 290/3 - 575/3*d = 0. Calculate d.
-1, 58
Let g be (27 + 7)/(2*(-1 + 0)). Let r(j) = 2*j**3 - 124*j**2 - 118*j - 43. Let q(z) = z**3 - 42*z**2 - 39*z - 14. Let l(s) = g*q(s) + 6*r(s). Factor l(b).
-5*(b + 1)**2*(b + 4)
Let h(l) = -165*l**2 - 314*l - 5414. Let o(f) = -94*f**2 - 156*f - 2706. Let w(a) = -4*h(a) + 7*o(a). Factor w(j).
2*(j + 23)*(j + 59)
Let u(x) be the first derivative of x**3 - 5*x**2 - 24*x + 19. Let l(z) = -3*z**2 + 9*z + 24. Let h(r) = -4*l(r) - 3*u(r). What is m in h(m) = 0?
-2, 4
Let f(x) = -4*x**3 + 164*x**2 + 192*x + 6. Let o(z) = -8*z**3 + 326*z**2 + 386*z + 13. Let v(u) = 13*f(u) - 6*o(u). Factor v(p).
-4*p*(p - 45)*(p + 1)
Let l(r) be the second derivative of -r**7/18 - 41*r**6/90 + 9*r**5/20 + 389*r**4/36 + 140*r**3/9 - 8*r**2 + 92*r - 11. Suppose l(g) = 0. Calculate g.
-4, -1, 1/7, 3
Factor -893 - 160*u**2 + 503*u**2 - 165*u**2 - 529 - 705*u - 175*u**2.
3*(u - 237)*(u + 2)
Let h = -69 + 61. Let z be (-14)/112 + (-49)/h. Factor 4*k**4 - 6 + 2*k**2 + 7 - z*k**3 - 1.
2*k**2*(k - 1)*(2*k - 1)
Solve 4542*p - 181186 - 961599*p**2 + 2*p**3 + 961857*p**2 + 1152*p = 0 for p.
-73, 17
Let h(a) = 4*a**2 - 86*a - 137. Let v(i) = -17*i**2 + 351*i + 549. Let u(x) = -26*h(x) - 6*v(x). Factor u(r).
-2*(r - 67)*(r + 2)
Let j = -122 + 126. Factor 4*q**j + 149*q**2 - 157*q**2 - 4*q**3 + 8*q**3.
4*q**2*(q - 1)*(q + 2)
Let n be (-462220)/57300 - 52/(-5). Let g = 22/3 - 7. Suppose n*d - 8/3*d**2 + 0 + g*d**3 = 0. Calculate d.
0, 1, 7
Let x(u) = -15*u + 80. Let m be x(5). Factor 5*j**4 + 3*j - 112*j**2 - 3*j**3 - j**4 - m*j**4 + 113*j**2.
-j*(j - 1)*(j + 1)*(j + 3)
What is h in -1/6*h**3 + 647/6 + 431/2*h + 215/2*h**2 = 0?
-1, 647
Let n(g) be the third derivative of -g**5/15 + 27*g**4/2 + 164*g**3/3 - 4*g**2 + 46*g. Factor n(h).
-4*(h - 82)*(h + 1)
Let b(o) be the first derivative of -5*o**4/12 + 10*o**3 + 270*o**2 + 1800*o - 1059. Factor b(a).
-5*(a - 30)*(a + 6)**2/3
Let q(p) be the first derivative of -4/5*p**2 + 95 + 1/10*p**4 + 0*p**3 + 0*p. Factor q(o).
2*o*(o - 2)*(o + 2)/5
Let y(s) = s**3 - 25*s**2 + 68*s - 42. Let p be y(22). Factor 9*c - 9*c**2 - 14*c**p + 24*c**2 + 8.
(c + 1)*(c + 8)
Let a(t) be the second derivative of t**6/10 - 3*t**5/2 - 9*t**4/4 + 45*t**3 - 3*t + 1111. Solve a(l) = 0.
-3, 0, 3, 10
Suppose -25 = -3*d + 2*t, -3*d - 52 = -7*d - 2*t. Let v be ((-30)/(-9) + -3)*(d - 2). Factor -33/7*n**2 - 40/7*n**v - 16/7*n**4 - 10/7*n - 1/7.
-(n + 1)**2*(4*n + 1)**2/7
Let p(a) be the first derivative of -4/39*a**3 - 3/26*a**4 - 64 + 12/13*a**2 + 2/65*a**5 - 16/13*a. Solve p(c) = 0 for c.
-2, 1, 2
Solve 1/5*x**4 - 6432/5*x**3 + 6685658320896/5 + 15513984/5*x**2 - 16630990848/5*x = 0.
1608
Let -20014*f + 62583*f - 20833*f + 219*f**2 - 20206*f - 21 = 0. Calculate f.
-7, 1/73
Suppose -11*s - 4*l = -6*s - 171, -3*s + 4*l = -109. Factor 5*k**2 + 81*k - 24 + 9 - s*k - 28*k - 28*k.
5*(k - 3)*(k + 1)
Let q(n) be the first derivative of -32 + 3*n**5 - 5/2*n**4 - 5*n - 10/3*n**3 + 15/2*n**2 - 5/6*n**6. Factor q(j).
-5*(j - 1)**4*(j + 1)
Let h be (-2)/(-1)*(-4 - 41)/(-5). Suppose -x = -2*x + 5*l - h, -2 = -5*x + 2*l. Factor -x*q**2 - 9*q + 13*q**2 - 7*q - 7*q**2.
4*q*(q - 4)
Suppose 2*b - 4*x = -0*b + 14, -5*x - 4 = 2*b. Suppose 19*p**3 + 23*p**3 - 18*p**4 - b*p**5 - 5*p**2 + p**5 - 17*p**2 = 0. Calculate p.
-11, 0, 1
Let l(w) be the second derivative of -21*w**6/5 + 561*w**5/5 - 34213*w**4/42 - 2244*w**3/7 - 324*w**2/7 - 172*w - 1. Find n such that l(n) = 0.
-2/21, 9
Let 11/2*u**3 - 9/2*u**4 - 30*u + 14 + 29/2*u**2 + 1/2*u**5 = 0. Calculate u.
-2, 1, 2, 7
Let p = -160 + 162. Let 24 + 3*r + 27*r**3 - 11*r - 25*r**3 - 6*r**p = 0. What is r?
-2, 2, 3
Let j(s) = -331*s - 991. Let r be j(-3). Determine x, given that 8/3 + 5/3*x**4 - 2*x - 31/3*x**r - 4*x**3 = 0.
-1, 2/5, 4
Let g(x) be the second derivative of 2*x**7/21 + 8*x**6/3 - 44*x**5/5 - 18*x - 34. Let g(w) = 0. Calculate w.
-22, 0, 2
Let w be 3585/55 + 4/(-22). Suppose -63 + w = f. Find j such that -1/4*j**3 + 0 + 0*j + 1/2*j**f = 0.
0, 2
Let m(q) be the second derivative of -q**6/15 - 12*q**5/5 - 11*q**4 + 1936*q**3/3 + 11979*q**2 - 3500*q. Suppose m(y) = 0. Calculate y.
-11, 9
Let l be (-3)/(-5) - 536/335. Let p be (2 - -1)/l + (-735)/(-98). Factor -3*c + p - 3/2*c**2.
-3*(c - 1)*(c + 3)/2
Let y = -10 - -16. Suppose -57 + 21 = -y*f. Find a, given that 24*a**4 + 43*a**2 - 43*a**3 + a**3 - 11*a**2 - 4*a**5 - f*a**3 = 0.
0, 2
Let p(t) be the third derivative of t**6/180 + 23*t**5/180 - 13*t**4/72 - 2*t**3/3 + t**2 + 531. Determine q, given that p(q) = 0.
-12, -1/2, 1
Suppose 4 = 2*o + 2*u, -3*u = -3*o - 0*u - 6. Suppose r = -1, -13 = -3*d - r - 2. Factor 2*w**2 + 0*w**2 - 2*w**d - 5*w**3 + 5*w**5 + o*w**5.
w**2*(w - 1)*(w + 1)*(5*w - 2)
Factor 1/8*r**2 + 108*r + 23328.
(r + 432)**2/8
Let f(h) be the third derivative of 1/180*h**6 + 0*h + 13/120*h**5 - 4/9*h**3 - h**2 + 3/8*h**4 + 35. Let f(p) = 0. What is p?
-8, -2, 1/4
Suppose -19*u + 4 + 227 = -54. Suppose 3*v = 2*v + 2*g + 187, g = -5. Suppose -u*k**3 - 2916*k + 471 - 2658 - 1296*k**2 - v*k**3 = 0. What is k?
-9/4
Let g(h) be the second derivative of h**5/20 - 5*h**4/2 + 75*h**3/2 - 250*h**2 - 548*h. Factor g(o).
(o - 20)*(o - 5)**2
Factor -95*q + 45 - 283*q + 135 - 109*q + 221*q**2 - 9*q**3 + 103*q - 9*q**4 + q**5.
(q - 6)**2*(q - 1)**2*(q + 5)
Let m(o) be the second derivative of -o**6/1800 - o**5/100 + 7*o**4/120 - 17*o**3/6 + 3*o**2/2 - 55*o. Let x(g) be the second derivative of m(g). Factor x(z).
-(z - 1)*(z + 7)/5
Solve 2/3*s - 6*s**2 + 0 = 0 for s.
0, 1/9
Let i(r) be the third derivative of -r**7/70 - r**6/4 + 9*r**5/5 - 19*r**4/4 + 13*r**3/2 - 7*r**2 - 39*r - 1. Find g, given that i(g) = 0.
-13, 1
Let w(s) = -s**3 - 34*s**2 - 65*s - 72. Let x(l) = 2*l**3 + 68*l**2 + 130*l + 136. Let b(p) = -9*w(p) - 5*x(p). Factor b(a).
-(a + 1)**2*(a + 32)
Let u(t) be the third derivative of 5/6*t**3 - 1/12*t**5 - 3 + 2*t**2 + 1/24*t**6 - 5/24*t**4 + 0*t. Factor u(z).
5*(z - 1)**2*(z + 1)
Factor -16*q + 704*q**2 - 2145*q**2 - q**3 + 705*q**2 + 715*q**2 - 4*q.
-q*(q + 1)*(q + 20)
Let l = -15983 + 16020. Let d(z) be the first derivative of 0*z + 0*z**3 - 1/25*z**5 - l - 1/20*z**4 + 0*z**2. Suppose d(p) = 0. Calculate p.
-1, 0
Let n(b) be the first derivative of -b**5/20 + 2*b**4/3 - 10*b**3/3 + 8*b**2 - 6*b - 34. Let w(p) be the first derivative of n(p). Solve w(y) = 0.
2, 4
Factor 11 - 1/4*p**4 - 33/4*p**2 - p + 7/2*p**3.
-(p - 11)*(p - 2)**2*(p + 1)/4
Let m(f) be the second derivative of f**7/14 - 31*f**6/5 + 2691*f**5/20 + 496*f**4 + 512*f**3 - 743*f. Factor m(r).
3*r*(r - 32)**2*(r + 1)**2
Suppose -86 = -1634*f + 2192 + 7526. Let 1/9*s**2 + 81 - f*s = 0. Calculate s.
27
Let o = -576 + 510. Let h be o/363 + (-416)/(-110). Solve 2/15*d**3 - 6/5*d**2 - h + 18/5*d = 0 for d.
3
Let o = 408 + -406. Let z = -9 - -11. Factor 3*y**2 + 5*y**z + 72 - 24*y - 6*y**o.
2*(y - 6)**2
Let l(y) = 15*y**3 + 63*y**2 - 171*y - 80. Suppose -80 = 157*h - 162*h. Let z(j) = -44*j**3 - 188*j**2 + 512*j + 240. Let g(k) = h*l(k) + 5*z(k). Factor g(q).
4*(q - 2)*(q + 5)*(5*q + 2)
Let y(j) be the first derivative of -26*j**6/3 - 188*j**5/5 - 34*j**4 - 2080. Factor y(f).
-4*f**3*(f + 1)*(13*f + 34)
Let u = 29023 + -28999. Let j(z) be the seco