
Factor 2*j**2 - 2*j**2 - 8*j - 2*j**2 + 0*j**2 - 8.
-2*(j + 2)**2
Let d(x) be the first derivative of -2*x**3/51 - 18*x**2/17 - 162*x/17 + 2. Factor d(k).
-2*(k + 9)**2/17
Suppose -4*c - 40 - 4 = 0. Let g = -8 - c. Factor -2/9*k**5 + 0 + 8/9*k**2 - 2/9*k - 4/3*k**g + 8/9*k**4.
-2*k*(k - 1)**4/9
Let x(h) be the second derivative of h**4/36 + h**3/18 - 11*h. Factor x(f).
f*(f + 1)/3
Suppose 0 = 4*g - g - 6. Suppose -g*n = -3*c + 2, 4*n + n = -c + 12. Factor n*z**4 + 2*z - 3*z**4 - 3*z**2 + 5*z**5 - 7*z**3 + 4*z**4.
z*(z - 1)*(z + 1)**2*(5*z - 2)
Let c(g) be the third derivative of g**8/504 - 2*g**7/315 + g**6/180 - 6*g**2. Suppose c(l) = 0. What is l?
0, 1
Let 2*u**2 + 8*u + 2*u - 25*u**4 - 5*u**2 - 2*u**2 - 40*u**3 = 0. What is u?
-1, 0, 2/5
Let k(r) = r**3 - r. Let q(a) = 5*a**4 + 9*a**3 + 4*a**2 + 3*a. Let l(f) = 3*k(f) + q(f). Factor l(n).
n**2*(n + 2)*(5*n + 2)
Factor 26*s**2 + 6*s**2 + 36*s + s**2 - 6*s**2 + 12.
3*(3*s + 2)**2
Let h = 5 + 0. Let d(p) be the first derivative of -7/3*p**2 - 25/6*p**4 + 38/9*p**3 + 1 - 4/9*p**6 + 32/15*p**h + 2/3*p. Factor d(l).
-2*(l - 1)**3*(2*l - 1)**2/3
Let x(t) be the third derivative of -t**8/84 - 2*t**7/21 - t**6/3 - 2*t**5/3 - 5*t**4/6 - 2*t**3/3 - t**2. Find f such that x(f) = 0.
-1
Let c be (-2)/(-4)*(8 - 0). Determine k so that -5*k**4 + 2*k**3 - k**4 + 4*k**c = 0.
0, 1
Let v(c) = c**2 - 41*c - 132. Let h be v(44). Factor -1/4*q**4 + 0 + 1/2*q**3 + h*q - 1/4*q**2.
-q**2*(q - 1)**2/4
Let y = 104 + -104. Factor -6/7*g**3 + 0 + y*g + 6/7*g**4 + 2/7*g**2 - 2/7*g**5.
-2*g**2*(g - 1)**3/7
Let w(o) be the second derivative of -o**6/10 + o**5/20 + 5*o**4/12 - o**3/6 - o**2 - 7*o. Find c, given that w(c) = 0.
-1, -2/3, 1
Let s be (1/22)/((-15)/(-60)). Suppose 0 + 2/11*o**3 + 4/11*o**2 + s*o = 0. Calculate o.
-1, 0
Let c(j) = -105*j**2 - 495*j - 5. Let g(s) = -s**3 - 104*s**2 - 496*s - 4. Let d(t) = -4*c(t) + 5*g(t). Factor d(a).
-5*a*(a + 10)**2
Let a be (3 + (-30)/8)*-4. Suppose 3*w + w = 8. Factor a*p**2 - p**2 + 2*p + w*p.
2*p*(p + 2)
Factor -4/3*v - 2/3*v**3 - 2*v**2 + 0.
-2*v*(v + 1)*(v + 2)/3
Let -1/5*g - 1/5*g**3 + 0 + 2/5*g**2 = 0. Calculate g.
0, 1
Let b(u) be the first derivative of u**5/15 - u**4/2 + 4*u**3/3 - 5*u**2/3 + u + 5. Factor b(d).
(d - 3)*(d - 1)**3/3
Let k(b) be the third derivative of -b**7/1155 - b**6/660 + b**5/330 + b**4/132 + 2*b**2. Factor k(i).
-2*i*(i - 1)*(i + 1)**2/11
Let i(t) be the second derivative of 5*t**6/9 - 2*t**5/3 - 7*t**4/6 + 20*t**3/9 - 4*t**2/3 + 7*t. Determine k, given that i(k) = 0.
-1, 2/5, 1
Determine d, given that -2/3*d**5 - 4/3*d**3 + 0*d + 0*d**2 + 2*d**4 + 0 = 0.
0, 1, 2
Let t(h) be the first derivative of 1/6*h**3 - 1/4*h**2 + 0*h - 3. Factor t(v).
v*(v - 1)/2
Factor 0*g - 8*g**5 - 12*g**4 + 0 - 9/2*g**3 - 1/2*g**2.
-g**2*(g + 1)*(4*g + 1)**2/2
Let v be (-4827)/45 - (-6)/(-15). Let r = 109 + v. Factor 1/3*k**2 + 4/3 + r*k.
(k + 2)**2/3
Let i = 7 - 10. Let q(v) = -2*v - 3. Let n be q(i). Find r, given that -7*r - 3*r**3 + 4*r**2 + 8*r - n*r + r**3 = 0.
0, 1
Let j(r) be the second derivative of -r**4/30 - 4*r**3/15 - 4*r**2/5 - 7*r. Factor j(b).
-2*(b + 2)**2/5
Let i(d) be the first derivative of -d**8/2520 - d**7/1260 + 8*d**3/3 + 4. Let l(k) be the third derivative of i(k). Factor l(o).
-2*o**3*(o + 1)/3
Determine x so that 48/11*x**3 - 16/11*x**4 - 68/11*x**2 - 12/11 + 2/11*x**5 + 46/11*x = 0.
1, 2, 3
Solve 0 - 3/7*v**2 + 3/7*v = 0.
0, 1
Let i(r) be the third derivative of -r**5/135 - 5*r**4/54 - 18*r**2. Factor i(t).
-4*t*(t + 5)/9
Let x(r) be the second derivative of -r**4/4 - 3*r**3/2 + 6*r**2 - 14*r. Factor x(t).
-3*(t - 1)*(t + 4)
Let g(f) be the second derivative of -f**5/10 + 2*f**4/3 - f**3/3 - 6*f**2 + 7*f. Suppose g(z) = 0. Calculate z.
-1, 2, 3
Let j(q) be the third derivative of 1/96*q**6 + 0*q**4 + 2*q**2 + 0 + 0*q + 0*q**3 - 1/120*q**5. Factor j(o).
o**2*(5*o - 2)/4
Let v(w) be the first derivative of -w**6/9 + w**4/2 + 4*w**3/9 + 11. Find t, given that v(t) = 0.
-1, 0, 2
Let c(h) = h - 1. Let j(q) = -5*q**2 - 19*q - 21. Let t(z) = c(z) - j(z). Suppose t(s) = 0. Calculate s.
-2
Let u(o) be the third derivative of o**6/30 - 4*o**5/15 + o**4/2 + 18*o**2. Find c, given that u(c) = 0.
0, 1, 3
Suppose -3*c + 0*c - 3*g = -15, 21 = c + 5*g. Let p be (-1)/2*-8*c. Factor 4*b**5 + 4 - 4 - 2*b**p.
2*b**4*(2*b - 1)
Let l(v) = 5*v + 3 + 3*v**2 + 6*v**3 + 4 + 6*v**4 - 2. Let s(d) = -7*d**4 - 7*d**3 - 4*d**2 - 6*d - 6. Let n(p) = -6*l(p) - 5*s(p). Find t such that n(t) = 0.
-2, 0, 1
Suppose 8*h = 25*h - 16*h. Factor h*x + 9/2*x**3 - 9/2*x**4 + 3/2*x**5 + 0 - 3/2*x**2.
3*x**2*(x - 1)**3/2
Let i be (-56)/(-21)*6/4. Suppose 12 = i*v + 2*t - 6, -4*v - t = -21. Factor -4*l**2 + 2*l**3 - 4*l**2 + v*l**2.
2*l**2*(l - 1)
Let h(o) = o**2 + 5*o - 1. Let f be h(-6). Let q(z) be the first derivative of -2*z**3 + 0*z - 2/5*z**f + 1 + z**2 + 3/2*z**4. Suppose q(d) = 0. What is d?
0, 1
Suppose -4*x + 6*x = -x. Factor 0*n**4 + 0 + 3/2*n**5 + 0*n + x*n**2 - 3/2*n**3.
3*n**3*(n - 1)*(n + 1)/2
Let w = -96809/105 - -922. Let h(c) be the second derivative of 1/21*c**3 - 2*c - w*c**6 - 1/70*c**5 + 0*c**2 + 1/42*c**4 + 0. Factor h(g).
-2*g*(g - 1)*(g + 1)**2/7
Suppose 0 = -0*z + 2*z - 4. Suppose z*k = -0*k - 10, -s = -4*k - 22. Factor 0 - r**3 + 1/3*r**s + r**4 + 0*r - 1/3*r**5.
-r**2*(r - 1)**3/3
Let j(a) be the first derivative of a**4/2 - 3*a**2 + 4*a - 17. Factor j(g).
2*(g - 1)**2*(g + 2)
Let -2/13*a**4 + 0 + 2/13*a**2 + 0*a + 0*a**3 = 0. Calculate a.
-1, 0, 1
Factor 4*z**3 + 34*z**2 - 5*z**2 + 47*z - 11*z - 5*z**2 + 16.
4*(z + 1)**2*(z + 4)
Let n(p) be the first derivative of -2/3*p - 4 + 2/9*p**3 + 0*p**2. Determine a so that n(a) = 0.
-1, 1
Let m be (-43)/3 - 0/(-3). Let k = m - -15. Factor -k*u**2 - 4/3*u - 2/3.
-2*(u + 1)**2/3
Let b(r) = -7*r. Let q be b(-3). Let -12*g**2 + 21 - q - 12*g**3 + 0*g**3 - 3*g**4 = 0. What is g?
-2, 0
Factor 12/11 - 6/11*g**2 + 6/11*g.
-6*(g - 2)*(g + 1)/11
Suppose 12*n - 14 - 34 = 0. Let b(m) be the first derivative of -n*m - 1 - m**2 + 2/3*m**3. Let b(r) = 0. What is r?
-1, 2
Factor -6/7*i**3 + 9/7*i - 6/7*i**2 - 3/7 + 9/7*i**4 - 3/7*i**5.
-3*(i - 1)**4*(i + 1)/7
Let f(u) = -u**2 + u - 1. Let i(s) = 5*s**3 + 25*s**2 - 35*s + 35. Let b(a) = -30*f(a) - i(a). Factor b(z).
-5*(z - 1)**2*(z + 1)
Let n(d) = 7*d**2 + d. Let y(b) = b**2 + b. Let l(p) = -n(p) + 4*y(p). Factor l(k).
-3*k*(k - 1)
Let d = -1 - -4. Factor 3*u**2 + 6*u - d*u**3 - 3 + 0 - 3*u.
-3*(u - 1)**2*(u + 1)
Let x(q) be the third derivative of -q**5/180 + q**4/36 - 6*q**2. What is d in x(d) = 0?
0, 2
Let t(l) = -3*l**3 + l + 1. Let y be t(-1). Let j be y/(-3)*(-2)/7. Factor 2/7*m**2 + j*m - 4/7.
2*(m - 1)*(m + 2)/7
Let s(w) = -w**3 - w - 1. Let c(b) = -10*b**3 - 4*b**2 + 14*b - 18. Let i(z) = -c(z) + 6*s(z). Factor i(h).
4*(h - 1)**2*(h + 3)
Let d be 0/(-7) - (-4 - 0). Factor -2*w + w**d - 2*w**4 + 1 + 2*w**3 + 0*w.
-(w - 1)**3*(w + 1)
Let v be (1/2)/(11/8). Find g such that 2/11 + v*g + 2/11*g**2 = 0.
-1
Let t = 22 + -19. Factor 4*j**t + 19*j + 2 + 12*j**2 + 2 - 7*j.
4*(j + 1)**3
Suppose j + 2*j = 0. Let s be (2 - 5)/(-3) - j. Find r such that -1 - 6*r**3 + s + r**2 + 8*r**4 = 0.
0, 1/4, 1/2
Let b(l) be the first derivative of -2*l**3/27 - 2*l**2/9 + 16. Let b(t) = 0. Calculate t.
-2, 0
Let z = -3214/9 + 358. Suppose -4/3*u**2 + 8/9*u**3 + z*u - 2/9*u**4 - 2/9 = 0. Calculate u.
1
Let s be 12/(-14)*(-14)/20. Suppose s*i**3 - 3/5*i + 0*i**2 + 0 = 0. What is i?
-1, 0, 1
Let f(b) = 12*b - 22. Let l be f(2). Factor -2/5*x**3 + 0 + 0*x + 0*x**l - 2/5*x**4.
-2*x**3*(x + 1)/5
Let 20*w**2 + 16*w**2 + 2*w**4 - 38*w**2 = 0. What is w?
-1, 0, 1
Let t = 12 - 10. Find b such that -2/9*b**3 - 2/9*b**4 + 0 + 0*b + 4/9*b**t = 0.
-2, 0, 1
Let y(r) = 3*r**4 + r**3 + 2*r**2. Let g(n) = -n**4 + n**3. Let i(q) = 6*g(q) + 3*y(q). Let i(k) = 0. Calculate k.
-2, -1, 0
Suppose -2*w - 2*w = 8. Let i be (0/w)/(-7 - -5). Suppose 1/3*v**2 - 1/3*v**4 + i + 1/3*v - 1/3*v**3 = 0. Calculate v.
-1, 0, 1
Suppose -t = -6*t + 90. Let m be (4/t)/(16/24). Let m*w**3 - 1/3*w + 0*w**2 + 0 = 0. What is w?
-1, 0, 1
Suppose -3*k - 30 = -39. Suppose -14/5*i + 8/5*i**k - 16/5*i**4 + 6/5*i**5 + 4/5 + 12/5*i**2 = 0. What is i?
-1, 2/3, 1
Suppose -u + 5*p = u - 25, -3*u + 44 = -p. Factor -u*n**2 - 2*n**4 + 10*n**2 - 2