(z).
(z - 1)*(z + 1)**2/4
Suppose 8*s - 472 = -328. Solve 27/2*t**2 + 3*t + 0 + s*t**3 + 15/2*t**4 = 0.
-1, -2/5, 0
Let h(r) = r**4 + 6*r**3 - 3*r**2 + 4*r. Let k(y) = -2*y**4 - 11*y**3 + 4*y**2 - 7*y. Let n(z) = -5*h(z) - 3*k(z). Factor n(j).
j*(j + 1)**3
Let g(o) be the third derivative of -o**7/13860 + o**6/792 + 5*o**4/8 - 7*o**2. Let w(x) be the second derivative of g(x). Factor w(s).
-2*s*(s - 5)/11
Factor -146*f**3 - 4*f**5 + 141*f**3 + 4*f**4 + 3*f**5 + 2*f**2.
-f**2*(f - 2)*(f - 1)**2
Let j be (76/16 + 33/(-44))*6/36. Factor -1/3*n**2 - 1/3*n**4 + 0*n + 0 - j*n**3.
-n**2*(n + 1)**2/3
Let j be 2/(-12) - (21 - 86/4). Factor 1/2 + j*v - 1/6*v**2.
-(v - 3)*(v + 1)/6
Factor -4/5*o**3 - 16/15*o + 8/5*o**2 + 0 + 2/15*o**4.
2*o*(o - 2)**3/15
Let i(a) = 4*a**2 - a + 1. Let y(m) = -8*m**3 - 162*m**2 - 156*m - 38. Let d(j) = 6*i(j) + y(j). Solve d(z) = 0.
-16, -1, -1/4
Let r(x) be the third derivative of x**6/60 + 2*x**5 + 59*x**4/12 - 10*x**2 + 15. Factor r(b).
2*b*(b + 1)*(b + 59)
Let m(f) be the first derivative of -20/7*f**2 - 30 - 4/21*f**3 + 0*f. Suppose m(l) = 0. What is l?
-10, 0
Let b(i) = -2*i**2 + 12. Let f be b(5). Let s = f - -49. Suppose x + 13*x**2 - 25*x**2 + 1 + 1 + s*x**2 = 0. Calculate x.
-1, 2
Let h(z) = z + 14. Let b be h(-6). Factor 99 + b*s**2 + 109 + 5*s**3 + s**4 - 208 + 4*s.
s*(s + 1)*(s + 2)**2
Let p = -76 + 70. Let t be p/1 + (-200)/(-30). Factor -2/3*k**5 + 2/3*k**3 + 2/3*k**4 + 0*k + 0 - t*k**2.
-2*k**2*(k - 1)**2*(k + 1)/3
Factor -6*z**2 + 2*z + 8 - 2*z**2 - 109*z**3 + 2*z + 105*z**3.
-4*(z - 1)*(z + 1)*(z + 2)
Let o(g) = g**3 - g. Let x be o(-1). Factor x*h**4 - 5*h**3 + 5*h**5 - 20*h**2 - 3*h**5 + 20*h**4 + 3*h**5.
5*h**2*(h - 1)*(h + 1)*(h + 4)
Let v = -3578/3 + 1193. Let a(s) be the first derivative of 5 - 1/2*s**2 + 0*s + v*s**3. Factor a(q).
q*(q - 1)
Let j(n) be the third derivative of n**6/15 + 3*n**5/10 + 11*n**4/64 + n**3/24 - 3*n**2 + 31. Factor j(s).
(s + 2)*(8*s + 1)**2/8
Let k(r) be the first derivative of -2*r**3/9 - 23*r**2 + 113. Factor k(o).
-2*o*(o + 69)/3
Factor -40/7*k**3 - 2/7*k**5 - 32/7*k**2 - 16/7*k**4 + 0*k + 0.
-2*k**2*(k + 2)**2*(k + 4)/7
Suppose -9*w = -0*w - 27. Factor q**2 + 5*q + 144 - w*q - 147.
(q - 1)*(q + 3)
Determine k, given that 2/7*k**2 - 12/7*k + 18/7 = 0.
3
Let r(q) be the third derivative of -q**5/600 + 3*q**4/16 + 23*q**3/30 - 6*q**2 + 15. Suppose r(h) = 0. Calculate h.
-1, 46
Let d(i) be the first derivative of -5*i**4/8 - 3*i**3/2 + 3*i**2/2 + 4*i - 112. Factor d(g).
-(g - 1)*(g + 2)*(5*g + 4)/2
Let l(o) = -2*o**3 + 15*o**2 - 51*o + 43. Let u(m) = 2*m**3 - 14*m**2 + 50*m - 42. Let g(k) = -6*l(k) - 5*u(k). Factor g(t).
2*(t - 6)*(t - 2)**2
Suppose 330*a + 3/2*a**2 + 18150 = 0. What is a?
-110
Suppose -2*j - 1 = -5. Let x(v) be the second derivative of j*v + 0*v**3 + 0 + 1/2*v**2 - 1/12*v**4. Factor x(g).
-(g - 1)*(g + 1)
Let o(b) = -8*b**2 - 31*b - 3. Let v(t) = -17*t**2 - 64*t - 7. Let f(g) = -7*o(g) + 3*v(g). Factor f(w).
5*w*(w + 5)
Let p(r) be the first derivative of -6 + 10*r + 1/3*r**4 - 4/3*r**3 - 6*r**2. Let m(c) be the first derivative of p(c). Factor m(t).
4*(t - 3)*(t + 1)
Suppose i + 1 = 0, -2*t + 3 = t + 3*i. Factor 36*u - 12*u - 14*u + 50*u**t + 30*u + 8.
2*(5*u + 2)**2
Let -39*v**2 - 18 - 98*v + 14*v**3 + 20*v - 6 + v**3 = 0. Calculate v.
-1, -2/5, 4
Let a = 8 - 2. Let i(d) = a*d**2 + 2*d + 2*d - 3 + 6*d - 4*d. Let l(w) = w**3 + w**2 + 1. Let p(c) = i(c) + 3*l(c). Factor p(n).
3*n*(n + 1)*(n + 2)
Let v(u) be the second derivative of 5*u**4/48 - 15*u**3/4 + 405*u**2/8 + 53*u - 5. Factor v(w).
5*(w - 9)**2/4
Factor 12*r + 216 + 1/6*r**2.
(r + 36)**2/6
Let y = 96 - 89. What is q in -11*q - 20 + 8*q**2 - y*q + 2*q - 4*q**2 = 0?
-1, 5
What is j in 21/5*j**5 - 18/5*j**2 + 2/5 - j - 64/5*j**4 + 64/5*j**3 = 0?
-2/7, 1/3, 1
Factor 0 + 1/3*y**3 - 1/3*y**2 - 2/3*y.
y*(y - 2)*(y + 1)/3
Let b(l) = l**3 - 5*l**2 - 5*l + 6. Let v be b(6). Suppose -i = 1 - v. Factor -i*c**2 + c**2 - 2 + 10*c + 2*c**2.
-2*(c - 1)*(4*c - 1)
Let n(c) be the first derivative of 49*c**6/6 + 749*c**5/15 + 227*c**4/3 - 128*c**3/9 - 112*c**2/3 + 16*c + 8. What is l in n(l) = 0?
-3, -2, -2/3, 2/7
Let f = 86336/7 - 12332. Factor -3/7*p**4 + 9/7*p**2 + 12/7*p - f - 6/7*p**3.
-3*(p - 1)**2*(p + 2)**2/7
Let b(o) be the first derivative of 5*o**6/6 + 10*o**5 + 85*o**4/4 + 40*o**3/3 + 387. Factor b(i).
5*i**2*(i + 1)**2*(i + 8)
Let n(x) be the first derivative of x**3/15 + 3*x**2/5 + x - 661. Factor n(y).
(y + 1)*(y + 5)/5
Let v = 492 + -492. Let 1/5*h**2 + v*h - 1/5*h**3 + 0 = 0. What is h?
0, 1
Let a = -1555 + 1557. Factor 2/5*x**a + 4/5*x - 6/5.
2*(x - 1)*(x + 3)/5
Let d(m) be the third derivative of -m**5/210 - 2*m**4/7 - 23*m**3/21 - 17*m**2 - 1. Let d(c) = 0. Calculate c.
-23, -1
Factor -10*i**3 - 62*i**5 + 8*i**5 - 46*i**5 + 60*i**4 + 5*i**4.
-5*i**3*(4*i - 1)*(5*i - 2)
Let g(m) be the first derivative of 5*m**6/6 + 2*m**5 - 10*m**3/3 - 5*m**2/2 - 509. Factor g(s).
5*s*(s - 1)*(s + 1)**3
Factor 5*z**5 - 14*z**3 - 20*z**3 + 4*z**3 - 229*z**4 + 204*z**4.
5*z**3*(z - 6)*(z + 1)
Let f(l) = -2*l + 2. Let s be (-3)/(-4) - 24/32. Let x be f(s). Suppose 3*q**5 - 6*q**4 - 5*q**5 + 4*q**2 + x + 0 - 4*q**3 + 6*q = 0. What is q?
-1, 1
Let o(l) be the first derivative of l**4/2 + 4*l**3/3 - l**2/2 + l + 9. Let n be o(-2). Suppose 0 + 1/4*b**n + b**2 + b = 0. Calculate b.
-2, 0
Let d(t) be the third derivative of 11*t**2 + 7/120*t**6 + 0*t**3 + 0*t + 1/210*t**7 + 0*t**4 + 0 + 1/10*t**5. Let d(g) = 0. Calculate g.
-6, -1, 0
Let o(t) be the second derivative of -3*t**5/8 + 65*t**4/24 - 65*t**3/12 + 15*t**2/4 + 109*t. Factor o(j).
-5*(j - 3)*(j - 1)*(3*j - 1)/2
Let o be 114/(-513)*6/(-8). Let s be (-1 - -1 - -1)/6. Let -s - 1/3*x - o*x**2 = 0. What is x?
-1
Let w(k) be the first derivative of -11*k**3/2 - 465*k**2/2 - 84*k - 621. Suppose w(i) = 0. What is i?
-28, -2/11
Factor 2/7*q**5 + 286/7*q**3 + 0*q + 242/7*q**2 + 46/7*q**4 + 0.
2*q**2*(q + 1)*(q + 11)**2/7
Let s(b) be the first derivative of 4/21*b**3 + 0*b - 15 + 1/7*b**4 + 0*b**2. Factor s(t).
4*t**2*(t + 1)/7
Let g(n) = -10*n**2 - 167*n - 797. Let r(d) = -5*d**2 - 84*d - 399. Let m be (1 + 2)*3 + -2 + -1. Let q(w) = m*g(w) - 13*r(w). What is y in q(y) = 0?
-9
Let p(c) = -3*c**2 - 2*c - 11. Let q(h) = 4*h + 28. Let n be q(-6). Let i(o) = o**2 + o + 4. Let d(r) = n*p(r) + 11*i(r). Factor d(m).
-m*(m - 3)
Factor -346*k + 346*k + 3*k**3 + 9*k**2 - 12.
3*(k - 1)*(k + 2)**2
Let t be (-78)/(3 - 12/3). Let h be 50/t + (-21)/63. Factor 2/13*x**2 + 6/13*x + h.
2*(x + 1)*(x + 2)/13
Let m(f) be the second derivative of -f**6/300 + f**5/100 + 11*f**4/120 - f**3/5 - 9*f**2/5 - 80*f. Factor m(g).
-(g - 3)**2*(g + 2)**2/10
Suppose 4*q + q**4 - 4*q**3 + 4*q**5 - 4*q + 4*q**2 - 5*q**4 = 0. What is q?
-1, 0, 1
Let i(o) = -8*o**2 - 3*o + 14. Let k(s) = 7*s**2 + 2*s - 11. Let f(v) = -2*i(v) - 3*k(v). Factor f(z).
-5*(z - 1)*(z + 1)
Let b be -3 - 12/20*-5. Let z(a) be the third derivative of 0*a**4 + b*a**3 + 0 + 1/70*a**7 + 0*a + 1/112*a**8 - 1/40*a**6 - 4*a**2 - 1/20*a**5. Factor z(t).
3*t**2*(t - 1)*(t + 1)**2
Let k(q) be the second derivative of -q**7/840 - q**6/80 + 19*q**4/12 - 39*q. Let w(l) be the third derivative of k(l). Factor w(y).
-3*y*(y + 3)
Determine i so that 1/8*i + 1/8*i**5 - 1/2*i**2 + 0 + 3/4*i**3 - 1/2*i**4 = 0.
0, 1
Let c(b) = -b**4 + 4*b**3 + 6*b**2 + 6*b - 6. Let t(j) = -1 + j**3 + 0*j**3 + j - 3*j**2 + 3*j**2 + j**2. Let f(l) = c(l) - 6*t(l). Factor f(q).
-q**3*(q + 2)
Suppose 4*g - 33 = -u - 25, -2*g + 26 = -5*u. Let n(w) be the third derivative of 0 - w**2 + 1/3*w**g - 1/24*w**4 - 1/60*w**5 + 0*w. Let n(y) = 0. What is y?
-2, 1
Let w(m) = -m**4 - m**2 + 2*m. Let f(d) = -d**4 + 13*d**3 + 58*d**2 + 116*d + 64. Let q(g) = -3*f(g) + 6*w(g). Factor q(j).
-3*(j + 1)*(j + 4)**3
Let l = -41/40 + 2/5. Let j = l + 17/8. Factor 3/2 - 3*g + j*g**2.
3*(g - 1)**2/2
Let x(y) be the third derivative of -y**5/75 + 19*y**4/15 - 74*y**3/15 + 62*y**2. Solve x(c) = 0.
1, 37
Suppose -2*s + 11 = -11. Factor 9*m**2 - s*m + 4*m**2 + 5 - 11*m**2.
(m - 5)*(2*m - 1)
Let x(l) = 5*l**3 + l**2 + l + 1. Let a be x(-1). Let m be (16/40)/(a/(-40)). Factor 14/9*v - 2/9*v**m + 10/9*v**3 - 2*v**2 - 4/9.
-2*(v - 2)*(v - 1)**3/9
Let p(b) be the first derivative of 3*b**5/5 - 21*b**4