 + 11*g + 5. Let v(f) = 14*f**4 - f**3 - 12*f**2 + 5*f + 2. Let r(p) = 5*v(p) - 2*z(p). Factor r(q).
3*q*(q - 1)*(q + 1)*(4*q - 1)
Let b(w) be the first derivative of 0*w**2 - 3/140*w**5 + 1/105*w**6 + 0*w**3 + w + 1/84*w**4 + 12. Let v(x) be the first derivative of b(x). Factor v(j).
j**2*(j - 1)*(2*j - 1)/7
Let x = -4181/2 + 2091. Determine s, given that x*s**5 + 0 - 1/2*s**2 - 1/2*s**3 + 0*s + 1/2*s**4 = 0.
-1, 0, 1
Let q(i) = 3*i - 3. Let u be q(1). Let l(r) be the first derivative of r**2 + 4 + u*r + 1/3*r**3. Solve l(y) = 0.
-2, 0
Let k(u) be the first derivative of u**2/2 + u - 15. Let h(q) = 3*q**5 - 15*q**4 + 30*q**3 - 30*q**2 + 24*q + 6. Let f(x) = h(x) - 9*k(x). Factor f(r).
3*(r - 1)**5
Let v(j) = 12*j**2 + 21*j - 33. Let i(s) = 2*s**2 + 10 + 5*s - 18 + s**2. Let o(a) = 9*i(a) - 2*v(a). Suppose o(w) = 0. What is w?
-2, 1
Let y(j) be the first derivative of 105*j**4 - 356*j**3/3 - 40*j**2 + 16*j - 813. Solve y(x) = 0 for x.
-2/7, 2/15, 1
Factor -38/7*n + 24/7 - 2/7*n**3 + 16/7*n**2.
-2*(n - 4)*(n - 3)*(n - 1)/7
Let c(u) = u**2 + u + 1. Let y(v) = 8*v**2 + 100*v - 204. Let z(o) = 4*c(o) - y(o). Factor z(n).
-4*(n - 2)*(n + 26)
Let v(z) = -8*z**4 - 10*z**3 + 4*z**2 + 48*z + 36. Let c(k) = 9*k**4 + 10*k**3 - 5*k**2 - 49*k - 36. Let p(n) = -6*c(n) - 7*v(n). Let p(h) = 0. What is h?
-3, -1, 2
Let v(m) = m**3 - 4*m**2 + 4*m - 1. Let d be v(5). Find a, given that 52*a + 4*a**4 + 19*a**2 - d*a + 16*a**3 + a**2 = 0.
-2, -1, 0
Suppose -4*r = 4*v + v - 37, -2*r + 6 = 0. Suppose 0 = -j - 4*j + v. Suppose -3*c**2 + 4*c + j + 2*c**2 + 1 + 3*c**2 = 0. Calculate c.
-1
Suppose 17 = 9*n - 1. Factor 0*y**n - 1 - 27*y - y**3 - 3*y**2 + 24*y.
-(y + 1)**3
Let p(a) be the first derivative of 2*a**5/15 - 4*a**4/3 + 28*a**3/9 + 8*a**2/3 - 10*a + 64. Find u such that p(u) = 0.
-1, 1, 3, 5
Let a(v) be the third derivative of 5*v**8/336 - 9*v**7/14 + 73*v**6/8 - 505*v**5/12 + 95*v**4 - 120*v**3 - 2*v**2 + 58. Factor a(f).
5*(f - 12)**2*(f - 1)**3
Let k(m) be the third derivative of -14*m**2 + 0*m - 1/60*m**5 + 0*m**6 + 1/840*m**7 + 0*m**3 + 0*m**4 + 0. Factor k(x).
x**2*(x - 2)*(x + 2)/4
Solve 7*l**3 + 12*l**2 - 5*l**3 + 64*l**2 = 0.
-38, 0
Let t(l) = -2*l**2 + 2*l. Let g(a) = a**2 + 14*a + 60. Let m(b) = g(b) + 3*t(b). Solve m(w) = 0.
-2, 6
Let n(f) = -10*f**3 + 20*f**2 + 10*f + 5. Let h(w) = -9*w**3 + 19*w**2 + 8*w + 4. Let j(p) = 5*h(p) - 4*n(p). Factor j(d).
-5*d**2*(d - 3)
Let z = -47 - -33. Let x = -7 - z. What is f in -5*f**2 - 44*f - 125 - x*f + f = 0?
-5
Let 277*x**4 - 804*x**2 + 232*x**3 - 88 - 516*x**4 + 640*x + 219*x**4 + 488 = 0. What is x?
-2/5, 2, 5
Let s(v) = v**3 + 16*v**2 - 15*v + 37. Let q be s(-17). Find u such that 0*u**3 + u**q + u**3 = 0.
0
Let f(z) be the first derivative of -11*z**6/720 + z**5/48 + z**4/8 - 4*z**3 - 21. Let s(p) be the third derivative of f(p). What is n in s(n) = 0?
-6/11, 1
Let a(r) = -38*r**2 - 36*r + 29. Let i(n) = 13*n**2 + 12*n - 10. Let v(j) = 6*a(j) + 17*i(j). Solve v(b) = 0 for b.
-2, 2/7
Let k(q) be the first derivative of -2*q**5/35 + q**4/14 + 10*q**3/21 + 3*q**2/7 - 331. Solve k(n) = 0.
-1, 0, 3
Factor -79/2*q**2 - 46*q - 10 - 7/2*q**3.
-(q + 1)*(q + 10)*(7*q + 2)/2
Determine s, given that 0 - 1/4*s**2 + s = 0.
0, 4
Let h be 0/(-1) + (23 - 4). Factor 2*f**4 + 19*f**2 - 4*f + 4*f**3 - 2 - h*f**2.
2*(f - 1)*(f + 1)**3
Let f be 22/(-5) - (-4)/10. Let r(a) = 28*a**3 - 51*a**2 - 8*a. Let j(t) = 4 - 203*t - t**2 - 3 + 204*t. Let c(p) = f*j(p) - r(p). Let c(q) = 0. Calculate q.
-2/7, 1/4, 2
Let r be 3 + -19*2/16. Let x = r - 9/40. Solve 1/5 - x*c**2 - 1/5*c = 0 for c.
-1, 1/2
Let p(w) be the third derivative of -7*w**6/96 - w**5/80 + 35*w**4/96 + w**3/8 + 519*w**2. Factor p(l).
-(l - 1)*(l + 1)*(35*l + 3)/4
Let q be (-2 - (6 + -4)) + -19. Let l = 27 + q. Suppose 0 - 23/2*c**l - 13/2*c**2 + 27/2*c**3 + 7/2*c**5 + c = 0. Calculate c.
0, 2/7, 1
Let p(k) = k**5 + k**4 + 3*k**3 - 7*k**2 - 2*k + 6. Let q(j) = 4*j**5 + 3*j**4 + 8*j**3 - 22*j**2 - 5*j + 19. Let t(a) = 7*p(a) - 2*q(a). Solve t(i) = 0.
-2, -1, 1, 2
Let j(k) be the third derivative of k**8/168 + k**7/105 - k**6/20 - k**5/30 + k**4/6 - 24*k**2 + k. Solve j(m) = 0 for m.
-2, -1, 0, 1
Let j be (0*3/(-18))/(0 + -2). Let d(z) be the first derivative of 1/5*z**5 + 5 - 1/3*z**3 + j*z + 0*z**4 + 0*z**2. Factor d(r).
r**2*(r - 1)*(r + 1)
Determine v, given that -9/5*v + 1/5*v**3 + 1/5*v**2 - 9/5 = 0.
-3, -1, 3
Factor 31*g**2 - 365 + 341 + 9*g**2 - 3*g + 64*g + 7*g.
4*(g + 2)*(10*g - 3)
Let j(q) be the second derivative of 27*q**7/14 + 306*q**6/5 + 8019*q**5/10 + 5687*q**4 + 142417*q**3/6 + 58564*q**2 - 254*q. Suppose j(m) = 0. What is m?
-8, -11/3
Let h(q) be the second derivative of -1/150*q**6 + 1/20*q**5 + 0 + 2/5*q**2 - 1/20*q**4 - 1/6*q**3 - 25*q. Suppose h(b) = 0. What is b?
-1, 1, 4
Let x(u) be the second derivative of -3*u + 0*u**2 - 1/60*u**5 + 1/9*u**4 - 2/9*u**3 + 0. Factor x(k).
-k*(k - 2)**2/3
Let t(b) = -3*b**3 - 48*b**2 - 2*b - 29. Let g be t(-16). Let x = -5857/2 - -2991. Let -15/2*l**2 - x + 75/2*l + 1/2*l**g = 0. Calculate l.
5
Suppose -119*m + 122*m = -4*f, 5*f + 27 = 3*m. Let h(w) be the second derivative of 0 + 1/78*w**m + 1/39*w**3 + 0*w**2 + w. Solve h(i) = 0 for i.
-1, 0
Solve 870*n - 854*n - n**5 - n**4 + 2*n**4 - 28*n**2 + 12*n**3 = 0.
-4, 0, 1, 2
Let f = -2091 + 6275/3. Let t(g) be the first derivative of -f*g**3 + g**2 + 0*g + 9. Factor t(h).
-2*h*(h - 1)
Let y(w) be the third derivative of -w**9/3024 - w**8/560 + w**6/90 + w**3/3 - w**2. Let f(a) be the first derivative of y(a). Factor f(k).
-k**2*(k - 1)*(k + 2)**2
Let s(k) be the second derivative of k**5/30 + 25*k**4/6 + 370*k + 1. Suppose s(c) = 0. What is c?
-75, 0
Let p be 3/(-9)*304/(-114). Let 8/9*a**2 + 0 - 2/9*a**3 - p*a = 0. Calculate a.
0, 2
Let g(f) be the first derivative of 2/3*f**3 + 7 + 0*f + 0*f**4 + 2/3*f**2 - 2/15*f**5. Determine j so that g(j) = 0.
-1, 0, 2
Determine r so that 3*r**4 + 1344*r + 1/4*r**5 - 2304 - 24*r**3 - 160*r**2 = 0.
-12, 4
Factor 8/3*x**2 + 4 + 19/3*x + 1/3*x**3.
(x + 1)*(x + 3)*(x + 4)/3
Suppose 2 - 12 = -5*i. Suppose 12 = 4*l - 5*n, 0 = 4*l + 4*n - i - 10. Factor -6/11*p + 2/11*p**l + 4/11 + 0*p**2.
2*(p - 1)**2*(p + 2)/11
Let b(y) be the first derivative of -y**7/210 - y**6/24 - 2*y**5/15 - y**4/6 - 39*y**2/2 + 26. Let m(g) be the second derivative of b(g). Solve m(p) = 0.
-2, -1, 0
Let y(j) be the second derivative of 3*j**5/100 + 3*j**4/20 + j + 53. Factor y(x).
3*x**2*(x + 3)/5
Let m(k) be the second derivative of 3*k**5/20 - k**3/2 + 2*k - 2. Suppose m(c) = 0. Calculate c.
-1, 0, 1
Suppose 3*x + 4 = 10. Determine a so that a + 2*a + 5*a**x + 2*a = 0.
-1, 0
Let w(t) = -t**2 - 59*t - 1 + 59*t. Let u(l) = 3*l**3 - 8*l**2 - 21*l - 14. Let c(d) = -u(d) + 2*w(d). Factor c(j).
-3*(j - 4)*(j + 1)**2
Suppose 2*w = w + 5. Suppose -3*k - o = -3, -3 = -w*k - o + 4. Find t such that -t**2 - t**2 + k*t**4 + 0*t**3 + 2*t**3 - 2*t = 0.
-1, 0, 1
Let v be (8/20)/((6 + (-1224)/225)/60). Factor -60/7*s + 3/7*s**2 + v.
3*(s - 10)**2/7
Suppose 132 - 134 = -w. Let y(l) be the first derivative of w*l - 2/3*l**3 + 0*l**2 - 3. Factor y(h).
-2*(h - 1)*(h + 1)
Let l = 38 + -31. Let a(w) = -6*w**2 + 16*w - 1. Let y(m) = -5*m**2 + 14*m - 2. Let z(i) = l*y(i) - 6*a(i). Factor z(j).
(j - 2)*(j + 4)
Suppose -7 + 23 = 2*s. Suppose h + h = s*h. Solve h*w**2 + 18/5*w - 3/5 - 96/5*w**3 = 0.
-1/2, 1/4
Let o be (-130)/(-20)*20/195. Factor -o*u - 4/3*u**2 + 0 + 4/3*u**4 + 0*u**3 + 2/3*u**5.
2*u*(u - 1)*(u + 1)**3/3
Suppose 5*b = 5*q - 35, -75*q + 71*q + 19 = -b. Let 0*i + 0*i**q + 0 + 2/13*i**5 - 4/13*i**2 - 6/13*i**3 = 0. What is i?
-1, 0, 2
Let a(s) = 2*s**5 + s**4 - 28*s**3 - 5*s**2 + 17*s - 5. Let r(y) = -y**5 - y**4 + 14*y**3 + 2*y**2 - 9*y + 3. Let c(h) = -4*a(h) - 9*r(h). Factor c(t).
(t - 1)**3*(t + 1)*(t + 7)
Let d(a) = 4342*a**3 + 14564*a**2 + 16184*a + 6000. Let w(i) = -1448*i**3 - 4855*i**2 - 5395*i - 2000. Let z(j) = -5*d(j) - 16*w(j). Factor z(t).
2*(9*t + 10)**3
Suppose 0 = -4*c - s + 94, -3*c + 4*s = -6*c + 77. Let u = 25 - c. Factor 0 - 2 + u*h**2 + 2 - 2*h.
2*h*(h - 1)
Find j, given that -2*j**2 + 312*j + 295*j + 370*j - 873*j = 0.
0, 52
Let v(g) be the first derivative of g**6/24 - g**5/5 + 3*g**4/16 + g**3/3 - g**2/2 + 107. Factor v(a).
a*(a - 2)**2*(a - 