be (-30)/(-9) - 1/3. Suppose r + m*l = -r + 6, -5*r + 2*l + 53 = 0. Factor -3*f - r*f + 10*f - 3*f**2 - 7*f.
-3*f*(f + 3)
Let h(f) be the third derivative of f**6/540 + f**5/270 - f**4/54 + f**2 + 28. Factor h(w).
2*w*(w - 1)*(w + 2)/9
Let b(u) be the first derivative of u**5/20 + 5*u**4/2 + 50*u**3 + 33*u**2/2 - 41. Let g(x) be the second derivative of b(x). Factor g(r).
3*(r + 10)**2
Let z = 122 - 120. Factor 0 + 1/2*y**3 + 9/4*y**z - 9/4*y**4 - 1/2*y.
-y*(y - 1)*(y + 1)*(9*y - 2)/4
Factor 3*f**2 - f**2 - 36*f - 33 - 3*f**2 - 2*f**2.
-3*(f + 1)*(f + 11)
Let k = -27124/7 - -27610/7. Determine z so that -74/7*z - 282/7*z**2 - 18*z**3 - 4/7 + k*z**4 = 0.
-1/3, -2/27, 1
Let l(o) = o**3 - 6*o**2 + 6. Let m be l(7). Suppose i + m = 67. Find c such that -6*c**5 + 3*c**5 + 4*c**2 + 12*c**4 - c**5 - i*c**3 = 0.
0, 1
Let z(q) = 12*q. Let p be z(1). Let a = p + -9. Solve -6*i + 3*i**2 - 4*i**4 + i**4 - 2*i**3 + 8*i**a = 0.
-1, 0, 1, 2
Suppose 4*l + 6 = 38. Factor 7*u**3 - 2*u**3 - 4*u**2 - u**3 + l*u + 16*u**2.
4*u*(u + 1)*(u + 2)
Let b(n) be the third derivative of n**7/1575 + 4*n**6/45 + 13*n**5/25 + 58*n**4/45 + 77*n**3/45 + 828*n**2. Factor b(g).
2*(g + 1)**3*(g + 77)/15
Let f(x) = 284*x**2 - 10068*x. Let h(d) = d**3 + 1136*d**2 - 40265*d. Let r(j) = -9*f(j) + 2*h(j). Suppose r(g) = 0. What is g?
0, 71
Let r(h) be the second derivative of h**6/2160 + h**5/120 - 31*h**3/6 - 2*h - 4. Let c(t) be the second derivative of r(t). Let c(k) = 0. Calculate k.
-6, 0
Let g(r) = 3*r**3 - 7*r**2 + 10*r + 10. Let i(k) = -8*k**3 + 15*k**2 - 21*k - 19. Let t(v) = 5*g(v) + 2*i(v). Solve t(p) = 0.
-6, -1, 2
Suppose 0 = -2*d - 5*x - 51, 5*x - 21 = -5*d + 7*d. Let f be d/(-8)*8/24. What is z in -1/4*z**2 + f*z - 1/2 = 0?
1, 2
Let w(d) be the second derivative of -d**5/10 - 2*d**4/3 - 5*d**3/3 - 2*d**2 - 37*d + 3. Let w(g) = 0. Calculate g.
-2, -1
Let c(a) = -33*a**2 + 38*a**2 - 10*a**3 + 20*a**2 - 10*a**4. Let t(z) = 5*z**4 + 5*z**3 - 12*z**2. Let s(i) = -2*c(i) - 5*t(i). Factor s(u).
-5*u**2*(u - 1)*(u + 2)
Determine u, given that 22*u - 5/2*u**3 + 17/2*u**2 - 10 = 0.
-2, 2/5, 5
Let u(y) be the second derivative of y**5/130 - 7*y**4/78 + 4*y**3/13 - y + 1. What is a in u(a) = 0?
0, 3, 4
Suppose -3*i - l = -8*i + 17, -39 = 5*i + 7*l. Factor -12/5*h - 8/5 + 4/5*h**3 + 0*h**i.
4*(h - 2)*(h + 1)**2/5
Solve 43*x + 2*x**4 - 3*x**4 + 160*x**2 + 11*x**4 + 30 + 90*x**3 - 5*x**5 + 72*x = 0.
-1, 6
Let i(l) be the second derivative of -l**5/70 + 5*l**4/21 - 3*l**3/7 - 68*l. Factor i(h).
-2*h*(h - 9)*(h - 1)/7
Let o(b) be the third derivative of -b**8/294 + 4*b**7/147 - 37*b**6/420 + b**5/7 - 3*b**4/28 + 86*b**2. Determine j, given that o(j) = 0.
0, 1, 3/2
Suppose 0*j - g + 30 = 2*j, -3*j + 45 = -4*g. Let l = -193/13 + j. Let 6/13*m**4 + 2/13*m**5 - l*m**3 + 8/13 + 0*m - 14/13*m**2 = 0. Calculate m.
-2, -1, 1
Let t be (-16)/(-6)*6/4. Let w(k) = -k**3 - 3*k**2 - 5*k - 2. Let y be w(-2). Factor -11 + t + 9 + 2*r**2 + y*r.
2*(r + 1)**2
Let w(r) = 185*r**3 - 270*r**2 + 85*r + 50. Let v(u) = 11*u**3 - 16*u**2 + 5*u + 3. Let c(x) = 50*v(x) - 3*w(x). Let c(p) = 0. Calculate p.
0, 1
Suppose -k - 15 = -6*o, -6*k = -3*o - k + 21. Factor 4/3*j + 4/3 + 1/3*j**o.
(j + 2)**2/3
Factor -154*n**3 - 4*n**4 - 9*n - 6*n**2 + 138*n**3 + n - 14*n**2.
-4*n*(n + 1)**2*(n + 2)
Let t be 3/(-18) - (-2)/12. Determine g, given that -9*g**2 - g + 8*g**2 + t*g = 0.
-1, 0
Suppose -6*k**2 + 9/2*k - 3/2*k**3 + 27 = 0. What is k?
-3, 2
Let y(u) = 2*u**4 - 14*u**3 + 28*u**2 - 4*u - 6. Let w(i) = -2*i**4 + 14*i**3 - 27*i**2 + 5*i + 5. Let z(f) = -6*w(f) - 5*y(f). Factor z(g).
2*g*(g - 5)*(g - 1)**2
Let v(h) = -7*h**3 - 3*h**2 - 5*h - 25. Let x(n) = -4*n**3 - 2*n**2 - 3*n - 15. Let r(c) = 3*v(c) - 5*x(c). Determine u, given that r(u) = 0.
0, 1
Factor 133*b**2 + 3*b**4 - 17*b**4 + 11*b**4 + 36 + 564*b**2 - 248*b**3 + 19*b**4 - 303*b.
(b - 12)*(b - 3)*(4*b - 1)**2
Suppose 132*l + 10 = -22 + 32. Let b be (-4)/(-10) - (-4)/90. Factor 8/9*q**2 + l + 4/9*q**3 + b*q.
4*q*(q + 1)**2/9
Solve -31*f - 15/2*f**2 - 4 = 0.
-4, -2/15
Let r(m) be the first derivative of -3*m**4/20 + 3*m**3 - 57*m**2/5 + 72*m/5 + 19. Let r(f) = 0. Calculate f.
1, 2, 12
Let t be ((-18)/40)/((-297)/396). Let f = 22 - 19. Factor t*i**f + 3/5*i + 6/5*i**2 + 0.
3*i*(i + 1)**2/5
Suppose v = 2*t + 12, 0*t - 4*t - 48 = -5*v. Let r = 10 - v. Factor -3 + 4*n**r + 1 - 6*n**2 - 4*n.
-2*(n + 1)**2
Let a(d) be the second derivative of -5*d - 1/15*d**3 + 0*d**2 - 1/60*d**4 + 0. Factor a(y).
-y*(y + 2)/5
Suppose 5 = 3*p + 3*x - 10, 3*p + 4*x - 18 = 0. Factor 9*i**3 + 70*i + i**4 + 3*i**p - 6 - 79*i + 2*i**4.
3*(i - 1)*(i + 1)**2*(i + 2)
Let q(u) be the first derivative of -4*u**3/3 + 178*u**2 - 352*u - 301. Factor q(l).
-4*(l - 88)*(l - 1)
Let c be ((-2)/3)/(6/(-405)). Factor n**4 - n**4 - 44*n**5 + c*n**5.
n**5
Let k be 80/(-28) - -2 - (-18)/210*20. Factor 0 - 2/7*s**3 + k*s**2 + 0*s.
-2*s**2*(s - 3)/7
Factor -19*s + 9*s**2 - 218*s**3 + 15 + 221*s**3 - 8*s.
3*(s - 1)**2*(s + 5)
Solve 26/9*d**2 - 70/9*d - 98/9 - 2/9*d**3 = 0 for d.
-1, 7
Suppose 4*u - 3*u = -3*u. Let b = -5 + 5. Factor b*p - 3/5*p**4 + 6/5*p**3 - 3/5*p**2 + u.
-3*p**2*(p - 1)**2/5
Let v(a) = -4*a**2 - 24*a + 10. Let d(c) be the second derivative of c**4/12 + c**3/6 + c**2/2 - 5*c. Let m(k) = -6*d(k) - v(k). Factor m(w).
-2*(w - 8)*(w - 1)
Suppose -12*n = 312 - 360. Suppose 0 + 0*k + 0*k**2 + 2/5*k**n - 4/5*k**3 = 0. Calculate k.
0, 2
Factor 0*c + 1/3*c**4 + 0*c**2 + 0 + 0*c**3.
c**4/3
Let p(k) = 27*k**2 - 114*k + 111. Let z(r) = -95*r**2 + 343*r - 332. Let q(u) = 7*p(u) + 2*z(u). Solve q(x) = 0.
-113, 1
Let l(p) be the second derivative of -p**4/3 - 14*p**3 - 40*p**2 - 8*p + 3. Find b, given that l(b) = 0.
-20, -1
Let n = -30259 + 4629655/153. Let z = 2/51 + n. Determine k so that -z*k**5 + 2/3*k**4 - 2/9*k**3 + 4/9*k + 0 - 2/3*k**2 = 0.
-1, 0, 1, 2
Let q(l) be the first derivative of -l**6/8 + 21*l**5/20 - 45*l**4/16 + 9*l**3/4 + 553. Solve q(o) = 0.
0, 1, 3
Suppose 11 = 5*z - 39. Factor 4 + 4*n**3 - 2*n**3 + z*n + 0*n**2 + 2*n**2 + 6*n**2.
2*(n + 1)**2*(n + 2)
Suppose -2*x - 10 = -4*l, x - 6*x - l = -8. Let u(m) = 7*m**4 + 3*m**3 - 7*m**2 + 2*m. Let k(j) = -j**3. Let b(a) = x*u(a) + 5*k(a). Factor b(y).
y*(y - 1)*(y + 1)*(7*y - 2)
Let z(s) = 5*s**3 - 15*s**2 + 19*s - 5. Suppose 0 = 95*g - 93*g - 8. Let w(a) = a. Let p(k) = g*w(k) - z(k). Factor p(y).
-5*(y - 1)**3
Let u(m) be the first derivative of -m**7/1050 + m**5/300 + 25*m**2 + 11. Let j(v) be the second derivative of u(v). Factor j(h).
-h**2*(h - 1)*(h + 1)/5
Let s(l) = 3*l**5 - l**4 - 4*l**3 + 9*l**2 + 6*l + 2. Let w(i) = 2*i**5 - 2*i**3 + 5*i**2 + 3*i + 1. Let y(z) = 3*s(z) - 5*w(z). Suppose y(x) = 0. What is x?
-1, 1
Suppose 0 = -5*g - 5 - 20. Let k be 319/(-715) + (-3)/g. Factor k*s + 0 + 2/13*s**2.
2*s*(s + 1)/13
Let m(r) be the first derivative of -21/2*r**2 + 9/4*r**4 + 3/5*r**5 + 4 + 18*r - 3*r**3. Factor m(w).
3*(w - 1)**2*(w + 2)*(w + 3)
Suppose -7 = -9*c + 11. Let d be (c - (-12)/(-3))*3/(-24). Let -1/4*k**4 + 0*k + 1/4*k**3 + 1/4*k**2 - d*k**5 + 0 = 0. Calculate k.
-1, 0, 1
Let m(v) = -4*v**4 + 39*v**3 - 14*v**2 - 39*v + 62. Let y(r) = r**4 - 10*r**3 + 3*r**2 + 10*r - 16. Let t(d) = 6*m(d) + 22*y(d). Suppose t(a) = 0. Calculate a.
-1, 1, 2, 5
Suppose -30 = -i - 4*i. Let d be 2/i*(-11 - -13). Factor 0*g - 2/3 + 0*g**3 + 4/3*g**2 - d*g**4.
-2*(g - 1)**2*(g + 1)**2/3
Let k(h) = -h**3 + 8*h**2 + h - 3. Let x(q) = -q**3 - q. Let u(v) = -k(v) - x(v). Let g be u(4). Factor 5/7*l**g + 0*l + 0 + 1/7*l**5 + 2/7*l**2 + 4/7*l**4.
l**2*(l + 1)**2*(l + 2)/7
Let v(y) be the first derivative of -y**4/24 + y**3/6 + y**2/12 - y/2 + 103. Find c such that v(c) = 0.
-1, 1, 3
Let h be 12/(-8)*1*-18. Let p be 10*-5*3/(-75). Factor -3*t**2 + h + 4*t**2 + 0*t**p + 18*t + 2*t**2.
3*(t + 3)**2
Let r be (-48)/(-40)*(-5)/(-2). Let w(i) be the first derivative of -3 - 18/5*i - 2/15*i**r - 6/5*i**2. Solve w(p) = 0.
-3
Let c = 471 - 469. Find l such that 26/11*l - 4/11 - 26/11*l**c - 56/11*l**3 = 0.
-1, 1/4, 2/7
Let v = 23 + -20. Suppose -3*r + 3*f + 21 = 0, 8*f - v*f = 2*r - 23. Let -4*c + r - 5 + 0*c**4 + 4*c**3 - 2*c**2 + 2*c**4 + c**4 = 0. Calculate c.
-1, -1/3, 1
Let o = -1416 - -1416. Determine d, given that -16/5*d**4 + 0 + o*d + 2/3*d**3 - 42/5*d**