15120 + p**8/1680 - p**6/360 - p**4/8 + 3*p**2. Let y(j) be the second derivative of r(j). Factor y(l).
-2*l*(l - 1)**2*(l + 1)**2
Let o be (-28)/(-9)*9/(-6). Let p = o - -5. Determine d so that 2/3*d - 2/3*d**3 - p + 0*d**2 + 1/3*d**4 = 0.
-1, 1
Suppose 5*m - 2 = 18. Let n(b) be the first derivative of 4/21*b**3 - 2 + 1/7*b**2 - 3/14*b**m + 0*b. Factor n(o).
-2*o*(o - 1)*(3*o + 1)/7
Let r(g) = -4*g**4 - 8*g**3 - 4*g**2 - 3*g + 3. Let w(n) = -3*n**4 + 2*n - 4 + 2 + 7*n**4 + 3*n**2 + 0 + 7*n**3. Let v(k) = 2*r(k) + 3*w(k). Factor v(c).
c**2*(c + 1)*(4*c + 1)
Let -1/5*k**3 - k**2 - 4/5 - 8/5*k = 0. What is k?
-2, -1
Let v be (2 - 2)/(-1 + 4). Let 0*z**3 - 1/2*z**4 + v*z + 0*z**2 + 0 = 0. Calculate z.
0
Let n = -5 + 5. Let 0 + 0*k**4 - 2/7*k**5 - 2/7*k + n*k**2 + 4/7*k**3 = 0. Calculate k.
-1, 0, 1
Suppose -2*d + 3*q + 20 = 0, 3*q - 8 = -3*d + 2*q. What is f in f**2 - d*f**3 - 4*f**2 + 3*f**3 - f + 5*f**2 = 0?
0, 1
Let a(l) be the first derivative of -l**3/3 + l**2/2 + 5. Let a(c) = 0. What is c?
0, 1
Let o(h) be the third derivative of -h**7/4200 + h**6/900 - h**5/600 - 7*h**3/6 - 2*h**2. Let i(n) be the first derivative of o(n). Factor i(g).
-g*(g - 1)**2/5
Let o(l) be the third derivative of l**7/70 + l**6/8 + 3*l**5/20 - 9*l**4/8 + 3*l**2. Factor o(m).
3*m*(m - 1)*(m + 3)**2
Let k = 128/165 + 4/165. What is z in -2/5*z**2 + 2/5*z + k = 0?
-1, 2
Let z(k) be the first derivative of k**4/48 - k**3/12 - 4*k + 5. Let a(t) be the first derivative of z(t). Solve a(c) = 0 for c.
0, 2
Let y(t) = 4*t**4 + 2*t**3 + 4*t**2 + 3*t. Let w(g) = -9*g**4 - 4*g**3 - 9*g**2 - 7*g. Let b(o) = 3*w(o) + 7*y(o). Find j, given that b(j) = 0.
-1, 0
Let t(x) = -x**2 + 24*x + 52. Let m be t(26). Factor 1/6*z**2 - 1/3*z + m.
z*(z - 2)/6
Let f = 152720/603 + -874/67. Let w = f - 240. Let 4/9*q + 0 + w*q**3 + 2/3*q**2 = 0. Calculate q.
-2, -1, 0
Let q(i) = i**2 + 9*i - 13. Let s be q(-9). Let p(y) = -3*y**2 + 9. Let o(d) = 6*d**2 - 19. Let a(m) = s*p(m) - 6*o(m). Factor a(h).
3*(h - 1)*(h + 1)
Let z(d) be the third derivative of 2/21*d**7 - 2/3*d**3 - 1/42*d**8 + 0 + 0*d - 1/15*d**6 + 2/3*d**4 - 4/15*d**5 + 2*d**2. Suppose z(j) = 0. Calculate j.
-1, 1/2, 1
Let u be (-4)/(-8)*11 - 0. Determine j, given that u*j**4 + 7*j**3 - 1/2*j - 1/2 + 3*j**2 + 3/2*j**5 = 0.
-1, 1/3
Suppose -96 = 2*i + i. Let r = i - -48. Factor 0 - 30*z**3 + 50/3*z**4 + r*z**2 - 8/3*z.
2*z*(z - 1)*(5*z - 2)**2/3
Let b(v) be the first derivative of 0*v**2 + 4 + 0*v + 0*v**3 + 1/5*v**4 - 4/25*v**5. Find l such that b(l) = 0.
0, 1
Factor 4/5*r**4 + 0 + 1/5*r**3 + 3/5*r**5 + 0*r + 0*r**2.
r**3*(r + 1)*(3*r + 1)/5
Let r be (-2)/(-8) + 12/16. Let m = 3 - r. Factor 0*v**2 + 0*v**m - 2*v - 2*v**2.
-2*v*(v + 1)
Let b(q) = -q**2 + 4*q + 3. Let r = 10 - 6. Let w be b(r). Determine a, given that -3*a + 0*a**2 + 5*a + a**2 - 1 - 3*a + a**w = 0.
-1, 1
Suppose -2*o**2 + 1 + 4 - 4*o + 1 + 0*o = 0. Calculate o.
-3, 1
Let c(m) be the second derivative of -m**6/300 - m**5/100 + m**3/30 + 2*m**2 + 6*m. Let v(k) be the first derivative of c(k). Factor v(a).
-(a + 1)**2*(2*a - 1)/5
Suppose -2*u - 52 = -18. Let c(y) = 14*y**3 + 2*y**2 - 7*y + 5. Let p(i) = 5*i**3 + i**2 - 2*i + 2. Let w(s) = u*p(s) + 6*c(s). Let w(r) = 0. What is r?
-2, -1
Suppose -5*p + p + 20 = 0. Solve -1 + 3*n**4 - 2*n**2 + n + 0 - 2*n + 2*n**3 + n**p - 2*n = 0.
-1, 1
Let l = -14 + 17. Suppose 0 = -l*s + 9*s. Factor -1/3*f + s + 5/3*f**2 - 4/3*f**3.
-f*(f - 1)*(4*f - 1)/3
Let s = -6 + 9. Find f such that -f**3 - 2*f + 6*f - s*f = 0.
-1, 0, 1
Let s(v) be the first derivative of -2*v**5/25 - v**4/2 - 6*v**3/5 - 7*v**2/5 - 4*v/5 - 5. Factor s(i).
-2*(i + 1)**3*(i + 2)/5
Let m be (0 + -1)/(2 + -1). Let u be (-1)/((1/4)/m). Factor 0 + 0*y**u + 1/4*y**5 + 0*y**2 + 1/4*y - 1/2*y**3.
y*(y - 1)**2*(y + 1)**2/4
Let f be (1 - 4) + (-12)/(-2). Factor 0*l - 5*l**3 + 1 + f*l**3 - 4*l + 0*l**3 + 5*l**2.
-(l - 1)**2*(2*l - 1)
Let v be (-2 + 4)/(-3*(-3)/9). Let p(f) be the second derivative of 0*f**2 + 0*f**4 - 1/70*f**5 + 0 + 1/21*f**3 - v*f. Determine n so that p(n) = 0.
-1, 0, 1
Let i(a) be the first derivative of -a**3/9 + 5*a**2/6 - 4*a/3 + 8. Determine c so that i(c) = 0.
1, 4
Find r, given that -242*r**3 - 4*r + 3*r**4 + 16*r + 233*r**3 = 0.
-1, 0, 2
Let f be (1 + 0 + -1)/(-2) + 0. Factor -2/5*y - 2/5*y**2 + f.
-2*y*(y + 1)/5
Let b be (-2)/(-7) + 1/7. Factor -b*p**3 + 0 + 12/7*p**2 - 12/7*p.
-3*p*(p - 2)**2/7
Let l be (1 - 1)*2/6. Let h(z) be the first derivative of l*z - 2/15*z**3 - 2 + 0*z**2 + 0*z**4 + 2/25*z**5. Suppose h(d) = 0. Calculate d.
-1, 0, 1
Let h(j) be the third derivative of j**8/26880 + j**7/10080 - j**6/2880 - j**5/15 - 4*j**2. Let c(v) be the third derivative of h(v). Factor c(i).
(i + 1)*(3*i - 1)/4
Suppose -3*c**3 + 405*c**2 - 4*c - 411*c**2 + c**3 = 0. Calculate c.
-2, -1, 0
Let v(z) = 5*z**3 + 8*z. Let p(m) = -m**3 - m**2 - m. Let a(c) = 4*p(c) + v(c). Factor a(l).
l*(l - 2)**2
Factor -a**2 - a**2 - 6 - 8*a - 2 + 0*a**2.
-2*(a + 2)**2
Suppose 10 - 25 = -5*o + 3*a, 5 = -3*o - a. Factor -1/4*h**2 + 1/4*h + o.
-h*(h - 1)/4
Let q(k) = -3*k**2 + k. Suppose -d - f - 18 = 3*f, 2*d + 21 = -5*f. Let y(t) = -t**2 + t - 1. Let j(l) = d*q(l) - 4*y(l). Factor j(o).
-2*(o - 1)*(o + 2)
Let v be 119/252 + 4/(-18). Let o(p) be the first derivative of -v*p**2 - 2 + 1/12*p**3 + 1/4*p. Let o(l) = 0. What is l?
1
Let r = -9 + 12. Factor -3*p**4 - 4*p**3 + p**5 + 3*p**3 + 3*p**r.
p**3*(p - 2)*(p - 1)
Factor 18/5 + 2/5*n**2 - 12/5*n.
2*(n - 3)**2/5
Let d be -1 + (0 - (1 - 2)). Suppose d = -4*u + 3*u. Solve u*x + 1/5*x**4 + 0 - 2/5*x**3 + 1/5*x**2 = 0 for x.
0, 1
Suppose 5*l - 9 = 11. Let d(p) = p**2 - p + 1. Let w(i) = -3*i**2 + 4*i - 4. Let h(x) = l*d(x) + w(x). Solve h(a) = 0 for a.
0
Let d(i) = -126*i**3 - 286*i**2 - 92*i - 13. Let u(w) = -127*w**3 - 286*w**2 - 92*w - 14. Let n(t) = 6*d(t) - 5*u(t). Factor n(q).
-(q + 2)*(11*q + 2)**2
Let q = 1 - 0. Let i(v) be the first derivative of 1/24*v**6 + 1/5*v**5 + 1/8*v**2 + 3/8*v**4 + 1/3*v**3 - q + 0*v. Factor i(x).
x*(x + 1)**4/4
Let 72*s**3 - 304/7*s + 28*s**4 - 48/7 - 348/7*s**2 = 0. Calculate s.
-3, -2/7, 1
Let k = 4 - 1. Let y = k - 0. Solve 2/9*v**y - 2/9*v + 0*v**2 + 0 = 0 for v.
-1, 0, 1
Determine u so that 0 - 1/2*u**4 + 1/2*u**2 - u**3 + u = 0.
-2, -1, 0, 1
Let i(s) be the second derivative of -s**7/2100 + s**6/180 - 2*s**5/75 + s**4/15 + 2*s**3/3 + 3*s. Let n(j) be the second derivative of i(j). Factor n(t).
-2*(t - 2)**2*(t - 1)/5
Let r = -27 + 29. Factor 3*m + 36*m**4 - 4*m**3 + 25*m**5 - 11*m**2 + 2*m**5 - m**r - 2*m**3.
3*m*(m + 1)**2*(3*m - 1)**2
Let h(v) be the third derivative of v**5/210 - v**4/21 + v**3/7 - 3*v**2. Solve h(q) = 0 for q.
1, 3
Let n(p) = -17*p**2 - 21*p - 7. Let a(s) = -33*s**2 - 41*s - 13. Let k(h) = -h + 12. Let r be k(9). Let g(l) = r*a(l) - 5*n(l). Suppose g(v) = 0. What is v?
-1, -2/7
Suppose -4 = -2*h, 2*h = -2*s + h + 8. Factor 3*d**3 - d**2 + 3*d - s*d**2 - 2*d**2.
3*d*(d - 1)**2
Let h(j) = 8*j**2 + 14*j + 11. Let f(z) = z**2 + z + 1. Let w(c) = 5*f(c) - h(c). Solve w(d) = 0.
-2, -1
Let d be 1/((-14)/(-6) - 2). Determine v so that 2 - 3*v - 9*v**2 + 5*v**d - 2*v**3 + 2*v**2 + 5*v**4 = 0.
-1, 2/5, 1
Let b(v) be the second derivative of -v**6/15 + v**5/20 + v**4/4 - v**3/6 - v**2/2 + 3*v. Factor b(y).
-(y - 1)**2*(y + 1)*(2*y + 1)
Let r(d) be the second derivative of d**4/36 - 4*d**3/9 + 8*d**2/3 + 21*d. Factor r(z).
(z - 4)**2/3
Let t be (((-9)/6)/(6/(-32)))/2. Factor 26/9*x**2 + 8/9 + 8/3*x + 4/3*x**3 + 2/9*x**t.
2*(x + 1)**2*(x + 2)**2/9
Let r = -44 - -44. Determine a so that r*a**2 + 0 + 0*a + 1/3*a**4 - 1/3*a**3 = 0.
0, 1
Solve -4/15*m**2 + 0*m - 6/5*m**4 + 0 - 22/15*m**3 = 0 for m.
-1, -2/9, 0
Determine x, given that -9*x**5 - 5*x**4 + x**4 + 10*x**4 = 0.
0, 2/3
Suppose -2*w - a = -6, 8 + 2 = 3*w + 2*a. Factor -2*p - 3 - p**w + 3 + 3*p.
-p*(p - 1)
Let w(y) be the second derivative of y**5/90 - y**4/36 - y**2 - 2*y. Let g(f) be the first derivative of w(f). Factor g(t).
2*t*(t - 1)/3
Let u(h) be the second derivative of -1/20*h**4 + 0 + 0*h**3 + 3/10*h**2 - 6*h. Determine v so that u(v) = 0.
-1, 1
Let n(m) be the first derivative of -4*m**3/3 + 4*m + 1. Find l such that n(l) = 0.
-1, 1
Let f(p) be the first derivative of -3/10*p**5 - 1/4*p**6 + 6 - 3/4*p**2 + 3/4*p**