6*u**4 + 3*u**3 + 8*u**2 - 4*u + 5. Let b(t) = -5*t**4 - 3*t**3 - 7*t**2 + 3*t - 4. Let c(s) = v*z(s) - 5*b(s). Factor c(l).
l*(l + 1)**3
Let a(r) be the third derivative of r**7/70 - r**5/10 + r**3/2 - 4*r**2. Suppose a(z) = 0. Calculate z.
-1, 1
Let a(w) be the second derivative of w**5/270 - w**4/54 - w**2/2 - w. Let b(f) be the first derivative of a(f). Suppose b(m) = 0. What is m?
0, 2
Let v(m) = -4*m**2 - 14*m + 14. Let k(h) = -7*h**2 - 27*h + 27. Let c(j) = 6*k(j) - 11*v(j). Find w such that c(w) = 0.
2
Let k(q) = -8*q**5 - 9*q**4 - 11*q**3 + 5*q**2 - 5*q + 5. Let o(p) = -9*p**5 - 9*p**4 - 12*p**3 + 6*p**2 - 6*p + 6. Let b(y) = 6*k(y) - 5*o(y). Factor b(u).
-3*u**3*(u + 1)*(u + 2)
Suppose -3*o + 387 = -567. Let r be 2/11 + o/66. Factor -r*l**4 + 5*l**2 - 1 - 3*l**2 + 4*l**4.
-(l - 1)**2*(l + 1)**2
Solve 25 + 35/2*g + 5/2*g**2 = 0 for g.
-5, -2
Let t be (2/(-8))/(12/(-8) - 0). Let b(h) be the second derivative of -t*h**3 + 0 - 1/9*h**4 + 2*h + 1/6*h**2. Let b(g) = 0. What is g?
-1, 1/4
Let y(x) = x**3 - x - 2. Let m be y(2). Suppose -h + b + 3 = -m*b, 0 = 2*h - 2*b - 6. Factor 0*r**h + 11*r**5 - 10*r**5 - r**3.
r**3*(r - 1)*(r + 1)
Factor 26*y + 10 - 2*y - 46 - 4*y**2.
-4*(y - 3)**2
Let o = 12 + -8. Solve l**2 + 3*l**2 - 4*l - o*l**4 + 2*l + 3*l**5 - l**5 = 0.
-1, 0, 1
Let v = 86 - 84. Solve -2/5*j - 2/5*j**3 + 4/5*j**v + 0 = 0 for j.
0, 1
Let y = -7/6 + 4/3. Factor -y*n**2 - 1/6*n**3 + 0*n + 0.
-n**2*(n + 1)/6
Let s = 286 + -497/2. Let o = s - 36. Factor 1 - 1/2*c**3 + o*c + 0*c**2.
-(c - 2)*(c + 1)**2/2
Let n(r) = r**3 + r. Let c(x) = -4*x**3 - 5*x**2 - 10*x - 3. Let o(g) = -c(g) - 3*n(g). What is a in o(a) = 0?
-3, -1
Let l(y) be the first derivative of -2*y**5/85 + 5*y**4/34 - 2*y**3/17 - 9*y**2/17 + 4. Factor l(x).
-2*x*(x - 3)**2*(x + 1)/17
Solve 1/11*r**2 + 6/11 - 5/11*r = 0.
2, 3
Let y(a) be the second derivative of -3*a**5/160 + 3*a**3/16 + 3*a**2/8 + 15*a. Suppose y(h) = 0. Calculate h.
-1, 2
Factor 4*f**2 + 8*f**2 - 3*f**5 - 9*f**4 - 6*f**2 + 6*f**2.
-3*f**2*(f - 1)*(f + 2)**2
Suppose 5*r + 20 = 0, -4*i - 3*r = -i - 33. Let h be 58/56 + i/(-20). Factor 4/7*k - h*k**3 + 0 + 2/7*k**2.
-2*k*(k - 2)*(k + 1)/7
Let f(b) be the second derivative of b**7/420 - b**5/20 - b**4/6 + b**3/2 - 4*b. Let o(z) be the second derivative of f(z). Solve o(w) = 0.
-1, 2
Let t(f) be the first derivative of -2/3*f**3 + 0*f - 3 - 2*f**2. Solve t(i) = 0.
-2, 0
Let w(h) be the first derivative of h**3/12 + 5*h**2/8 + h + 10. Determine i, given that w(i) = 0.
-4, -1
Let g(d) = -22*d**3 - 8*d**2 + 82*d - 36. Let x(y) = 7*y**3 + 3*y**2 - 27*y + 12. Let t(k) = 5*g(k) + 16*x(k). Suppose t(j) = 0. What is j?
-6, 1
Let j(f) = f**3 + 5*f**2 - 7*f - 1. Suppose -5*z = 2*l + 20, -3*l = z + 3*z + 9. Let m be j(z). Solve -x**2 + x**3 - 2*x**3 + m + x - 4 = 0 for x.
-1, 1
Let y = -43 - -45. Let r(n) be the second derivative of 0*n**2 + 1/105*n**6 - 1/42*n**4 + 1/21*n**3 + 0 - 1/70*n**5 - y*n. Factor r(q).
2*q*(q - 1)**2*(q + 1)/7
Let y(j) be the third derivative of -j**7/315 - j**6/90 - j**5/90 - 2*j**2. Factor y(v).
-2*v**2*(v + 1)**2/3
Factor 8*o + 2/5*o**3 + 32/5 + 16/5*o**2.
2*(o + 2)**2*(o + 4)/5
Let k(q) be the first derivative of -5*q**4 + 8*q - 7 + 28/5*q**5 - 12*q**3 + 10*q**2. Factor k(i).
4*(i - 1)**2*(i + 1)*(7*i + 2)
Let d = -230550928/126071 + 132/11461. Let s = 1830 + d. What is j in 0 - 4/11*j + s*j**2 = 0?
0, 2/7
Let y(t) be the first derivative of 1/2*t**6 - 5 + 3/4*t**4 + 0*t**2 - 6/5*t**5 + 0*t + 0*t**3. Factor y(u).
3*u**3*(u - 1)**2
Factor 7/3*y - 4 - 1/3*y**2.
-(y - 4)*(y - 3)/3
Let d(z) be the first derivative of -8*z**6/3 + 116*z**5/5 - 39*z**4 - 224*z**3/3 + 32*z**2 + 19. Solve d(v) = 0.
-1, 0, 1/4, 4
Let u(c) = -8*c**3 - 4*c**2 + 2*c - 2. Let a(b) = -b**3 - b**2. Let h(d) = 6*a(d) - u(d). Solve h(x) = 0 for x.
-1, 1
Let z(o) = -3*o**3 - 18*o**2 + 17*o - 8. Let c(q) = 10*q**3 + 53*q**2 - 50*q + 23. Let x(p) = 6*c(p) + 17*z(p). Let x(i) = 0. What is i?
-2, 1/3
Let m = -6 - 0. Let b be m/(-2)*(-3)/(-3). Let g(c) = -3*c**3. Let o(i) = 22*i**3 + i**2 - i - 1. Let x(d) = b*o(d) + 21*g(d). Suppose x(a) = 0. What is a?
-1, 1
Solve 0 + 2/9*f**2 + 0*f = 0.
0
Suppose 4*l - 24 = 4*a, 8 = 5*l + 4*a - 13. Suppose -2*r + 4*r - z = 3, 3*z - 3 = 0. Factor -6*v**3 + r*v**3 + l*v**3.
v**3
Let x(l) be the third derivative of l**6/24 - l**5/4 + 10*l**3/3 - 4*l**2. Factor x(c).
5*(c - 2)**2*(c + 1)
Let z(d) be the third derivative of 1/1785*d**7 + 1/204*d**4 - 4*d**2 - 1/510*d**5 + 0*d**3 - 1/1020*d**6 + 0*d + 0. Factor z(x).
2*x*(x - 1)**2*(x + 1)/17
Let r(o) be the first derivative of 2/3*o**2 + 2/9*o - 2 + 2/3*o**3. Factor r(u).
2*(3*u + 1)**2/9
Suppose -11*j = -21 - 12. Let 2/9*f**4 - 2/9*f**2 - 2/9*f + 2/9*f**j + 0 = 0. Calculate f.
-1, 0, 1
Let h(f) be the third derivative of -f**5/240 + f**4/12 - 2*f**3/3 + f**2. Suppose h(g) = 0. Calculate g.
4
Let p be (2/2)/(-1 - 0). Let w(v) = -2*v**3 - 4*v**2 + 6*v. Let c(n) = -n + n + n - n**3. Let r(k) = p*w(k) + 4*c(k). Determine z so that r(z) = 0.
0, 1
Factor -6*d + 2*d**3 + 5 - 10*d**2 - d**5 + 2*d**4 + 3*d**4 + 2*d + 3*d.
-(d - 5)*(d - 1)**2*(d + 1)**2
Let r be (-45)/(-12) + (-1)/(-4). Suppose 2*f + r - 8 = 0. What is y in f*y**3 + 9/2*y**2 + 3*y + 1/2 = 0?
-1, -1/4
Let t(z) = -2*z. Let g be t(-5). Let u be (g/4 - 2)*0. Solve 0*f**2 + 0*f**3 + 0 - 3/4*f**5 - 1/2*f**4 + u*f = 0.
-2/3, 0
Let d = -137/2 - -70. Factor -d*l**2 + 0 + 0*l.
-3*l**2/2
Suppose -4*x - 4*b = -7*x + 2, 3*b = x + 1. Factor -g**2 + g**2 - g**x - g**4 + 2*g**2.
-g**2*(g - 1)*(g + 1)
Suppose -180*l + 180*l - 4*l**2 = 0. Calculate l.
0
Factor -2*o**2 - 464*o**3 + 460*o**3 - 6*o**2.
-4*o**2*(o + 2)
Suppose 5*q = -23 - 7. Let o = q + 8. Let -2*x**o - 2*x**4 - 4*x**3 + 4*x**3 + 4*x**3 = 0. Calculate x.
0, 1
Let o(z) = z**3 + z**2 - 1. Let j = -1 + 3. Let a(q) = -q**4 + 12*q**3 + 12*q**2 - q - 11. Let f(w) = j*a(w) - 22*o(w). Factor f(u).
-2*u*(u - 1)**2*(u + 1)
Let m(g) = -g**3 - g + 1. Let i be m(1). Let l be (16/20)/(-2)*i. Suppose 2/5*c + 2/5 - l*c**3 - 2/5*c**2 = 0. What is c?
-1, 1
Let t(i) be the third derivative of -i**8/40320 + i**5/60 - 2*i**2. Let m(u) be the third derivative of t(u). Factor m(f).
-f**2/2
Let l(t) be the second derivative of 3*t**5/80 + t**4/4 + t**3/2 + 22*t. Factor l(s).
3*s*(s + 2)**2/4
Let i(d) be the third derivative of 0*d - 1/27*d**3 + 0 - 1/108*d**4 + 1/270*d**5 + 1/540*d**6 + 3*d**2. Find r such that i(r) = 0.
-1, 1
Let g(b) be the first derivative of -b**5/5 + 2*b**3/3 - b + 10. What is l in g(l) = 0?
-1, 1
Let h(o) be the second derivative of 0*o**3 + 0 + 1/6*o**4 - o**2 - o. Factor h(j).
2*(j - 1)*(j + 1)
Let v(j) be the third derivative of 0*j**3 + 0 - 1/40*j**5 - 1/16*j**4 + 1/80*j**6 + 0*j + 1/140*j**7 - j**2. Suppose v(f) = 0. Calculate f.
-1, 0, 1
Let i(d) = d + 1. Let x(k) = 2*k**2 + 6*k + 6. Let u(z) = -2*i(z) - x(z). Factor u(t).
-2*(t + 2)**2
Determine o, given that 4/5*o**4 - 12/5 + 8/5*o**2 + 16/5*o - 16/5*o**3 = 0.
-1, 1, 3
Suppose -h + 3*w - 24 = -0*h, -3*h - 51 = -2*w. Let l = h + 46/3. Factor 1/3*f**2 + 0 + 0*f + l*f**3.
f**2*(f + 1)/3
Let x(m) = -m**3 + m**2 - 2*m - 2. Let c(o) be the first derivative of 3*o**4/4 - 4*o**3/3 + 7*o**2/2 + 7*o + 2. Let b(z) = -2*c(z) - 7*x(z). Factor b(y).
y**2*(y + 1)
Suppose -v + 5*v - 20 = 0. Suppose 6 = -v*f + 2*b, 2*f = -0*f - 4*b + 12. Let 1/2*c**4 + f*c**3 - c**2 + 1/2 + 0*c = 0. What is c?
-1, 1
Let p(x) be the second derivative of -x**7/70 + x**6/20 + x**5/20 - x**4/4 + 3*x**2 - 4*x. Let a(i) be the first derivative of p(i). Let a(t) = 0. Calculate t.
-1, 0, 1, 2
Let f(z) be the third derivative of -z**5/60 - 11*z**4/96 + 5*z**3/8 + 4*z**2 - z. Factor f(a).
-(a - 1)*(4*a + 15)/4
Let n(b) be the third derivative of -b**10/37800 + b**8/1680 + b**7/630 + b**5/12 + 3*b**2. Let d(j) be the third derivative of n(j). Factor d(h).
-4*h*(h - 2)*(h + 1)**2
Let r(v) = 8*v**2 - 8. Let g(z) = z**2 - 1. Let o(y) = 21*g(y) - 3*r(y). Find c, given that o(c) = 0.
-1, 1
Let w(m) = -m**3 - m + 1. Let d be 3/(-3) + 0/2. Let f(i) = -i**4 - 7*i**3 + i**2 - 5*i + 6. Let u(a) = d*f(a) + 6*w(a). Factor u(p).
p*(p - 1)*(p + 1)**2
Let m(g) be the third derivative of 0*g + 0*g**4 + 0*g**6 - 1/672*g**8 + 0*g**3 + 0 - 2*g**2 + 0*g**5 - 1/420*g**7. Factor m(y).
-y**4*(y + 1)/2
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