
Let c(j) = j - 2. Let q be c(6). Factor 2 + 2*l**4 - 2*l**3 - 6 + q*l**3 - 10*l - 6*l**2 + 0*l**3.
2*(l - 2)*(l + 1)**3
Let b = -13 + 17. Suppose 0*k + k - b = 0. Solve 0*q + 0*q**3 - 2/5*q**k + 4/5*q**2 - 2/5 = 0.
-1, 1
Let h(p) be the first derivative of -p**5/40 + p**4/16 - p**2/8 + p/8 + 10. Determine r so that h(r) = 0.
-1, 1
Let g(l) be the second derivative of l**7/252 - l**5/30 + 19*l. Factor g(c).
c**3*(c - 2)*(c + 2)/6
Factor -1/4*f**2 + 0*f + 1/4.
-(f - 1)*(f + 1)/4
Let c(w) = w**3 - 7*w**2 - 9*w + 12. Let y be c(8). Suppose g = 2 + y. Factor -8*b**3 - 3 + b**3 + 3*b**4 + g*b + b**3.
3*(b - 1)**3*(b + 1)
Let q(z) be the third derivative of -z**6/380 - z**5/570 + z**4/76 + z**3/57 - 14*z**2. Find w such that q(w) = 0.
-1, -1/3, 1
Let c(g) be the first derivative of 2*g**6/15 + 2*g**5/5 + 3*g**4/8 + g**3/6 - g**2/2 + 4. Let j(p) be the second derivative of c(p). Factor j(x).
(x + 1)*(4*x + 1)**2
Let q(y) be the first derivative of 2 + y + 0*y**2 + 1/48*y**4 + 1/80*y**5 + 0*y**3. Let v(w) be the first derivative of q(w). Factor v(j).
j**2*(j + 1)/4
Let q = -6 + 9. Let r be (-3)/(q/(-2 + -1)). Find a, given that -6*a**2 - 3*a**r - 2*a - 2*a + a**3 = 0.
-2, -1, 0
Let l = -685 + 56857/83. Let p = l + 148/747. Factor -2/9*o**2 - p + 4/9*o.
-2*(o - 1)**2/9
Let w(a) be the third derivative of -1/12*a**4 + 0*a**3 + 0 + 0*a - 1/120*a**6 - 6*a**2 - 1/20*a**5. Factor w(s).
-s*(s + 1)*(s + 2)
Let r(v) be the second derivative of v**8/2240 - v**7/840 - v**4/6 + 3*v. Let w(o) be the third derivative of r(o). Factor w(j).
3*j**2*(j - 1)
Let c be (-2 + (-8)/(-4))/1. Factor -2/3*y**2 + c + 2/3*y.
-2*y*(y - 1)/3
Factor 1/2*j - 1/2*j**2 + 1/2 - 1/2*j**3.
-(j - 1)*(j + 1)**2/2
Factor 0 - 8/3*t - 28/3*t**2 + 12*t**3.
4*t*(t - 1)*(9*t + 2)/3
Determine r, given that -54/11*r**4 + 16/11 + 130/11*r**3 + 24/11*r + 8/11*r**5 - 124/11*r**2 = 0.
-1/4, 1, 2
Let b(p) = -p - 1. Let t be b(-4). Let h be t/(-12) + 9/4. Factor 1 - 15*g**2 - 4*g**4 + g**3 + 16*g**3 + 7*g - h - 4*g**3.
-(g - 1)**3*(4*g - 1)
Suppose -10*u = -15*u + 20. Let r(z) be the second derivative of 0*z**u + 1/12*z**3 + 0 + 1/8*z**2 - 1/120*z**6 - z - 1/40*z**5. Determine x so that r(x) = 0.
-1, 1
Let b be (-18)/4*(-6)/15. Let 0 + 9/5*t**2 + 3/5*t**4 + b*t**3 + 3/5*t = 0. What is t?
-1, 0
Factor -1/2*s - 3/2*s**3 - 3/2*s**2 + 0 - 1/2*s**4.
-s*(s + 1)**3/2
Let y(t) = t**3 + 1. Let v be (-14)/(-21) + 1/3. Let l(n) = -n**5 + 3*n**3 - n + 1. Suppose 4*k + 1 = 3*k. Let p(b) = k*y(b) + v*l(b). Factor p(s).
-s*(s - 1)**2*(s + 1)**2
Let x(m) = m + 1. Let q be (-2 + 0 - -3)*5. Let j be x(q). What is y in 6 - j + 28*y + 49*y**2 + 4 = 0?
-2/7
Determine z so that 10*z**3 + 3*z**2 - 12*z**2 + 0*z**2 + 13*z**2 + 8*z**4 + 2*z**5 = 0.
-2, -1, 0
Factor 0*s + 0 + 0*s**2 + 2/5*s**3 - 4/5*s**4 + 2/5*s**5.
2*s**3*(s - 1)**2/5
Let j(n) be the third derivative of n**10/302400 + n**9/120960 - n**5/10 - 6*n**2. Let h(v) be the third derivative of j(v). Solve h(x) = 0.
-1, 0
Let m(g) be the second derivative of 1/3*g**2 - g + 0 + 1/45*g**6 + 4/9*g**3 + 2/15*g**5 + 1/3*g**4. Factor m(f).
2*(f + 1)**4/3
Let r(y) be the first derivative of 2/7*y**3 + 0*y + 1/7*y**4 - 2/7*y**2 + 1 - 6/35*y**5. Find s such that r(s) = 0.
-1, 0, 2/3, 1
Let k(r) be the third derivative of 0 + 1/30*r**4 + 0*r + 1/150*r**5 + 0*r**3 - 7*r**2. Suppose k(x) = 0. Calculate x.
-2, 0
Factor -3*u**3 - 4*u**3 - 2*u**3 + 2*u**2 + 7*u**3.
-2*u**2*(u - 1)
Let w(f) be the third derivative of f**5/20 - 9*f**4/4 + 81*f**3/2 - 18*f**2. Determine v so that w(v) = 0.
9
Determine k, given that 0*k - 2/5 + 2/5*k**2 = 0.
-1, 1
Let c(o) be the first derivative of -o**6/300 + o**5/50 - o**4/20 + o**3/15 + 3*o**2 + 6. Let l(y) be the second derivative of c(y). Solve l(u) = 0.
1
Let w(v) be the second derivative of -v**6/10 + 9*v**5/10 - 3*v**4 + 4*v**3 + 14*v. Factor w(j).
-3*j*(j - 2)**3
Factor 0 - 18/11*j - 2/11*j**2.
-2*j*(j + 9)/11
Let s = -12 + 13. Let u be -3*(s - 2) + -3. Suppose 2/5*j + 2*j**2 + u = 0. What is j?
-1/5, 0
Suppose a**2 - a**4 + 2/3*a**3 - 2/3*a + 0 = 0. Calculate a.
-1, 0, 2/3, 1
Let l be (-133)/95 - 29/(-10). Let y be (-4)/14 + (-25)/(-14). Determine n, given that -l*n - y*n**2 - 1/2*n**3 - 1/2 = 0.
-1
Let j(w) = -w**2 + 4. Let o = 8 - 10. Let t be j(o). Factor 2/5*s + t + 2/5*s**2.
2*s*(s + 1)/5
Let h(t) be the third derivative of 1/60*t**5 + 0 + 0*t + 1/24*t**4 + 2*t**2 + 1/18*t**3 + 1/360*t**6. Factor h(s).
(s + 1)**3/3
Let h(w) be the third derivative of w**7/4620 - w**6/990 - w**5/660 + w**4/66 + w**3/2 - w**2. Let g(r) be the first derivative of h(r). What is c in g(c) = 0?
-1, 1, 2
Suppose -2*m - 4*j - 12 = 0, 2*m + 1 = 4*j + 13. Determine f, given that 2/3*f**4 + 0 - 2/3*f**2 + 2/3*f**3 + m*f - 2/3*f**5 = 0.
-1, 0, 1
Let t(z) = z**3 + z + 1. Let q(j) = 2*j**3 - 2*j**2 + 2*j + 1. Let y(d) = -5*q(d) + 5*t(d). Determine k so that y(k) = 0.
0, 1
Let u(g) be the first derivative of -g**5/15 - g**4/12 + g**3/3 + 5*g**2/6 + 2*g/3 + 18. Find z such that u(z) = 0.
-1, 2
Suppose -5*f = p + 3 - 18, -2*f - 5*p = -29. Solve 1/2*g**4 - 1 + 1/2*g**f - 3/2*g + 3/2*g**3 = 0 for g.
-2, -1, 1
Let d(u) be the second derivative of u**6/33 + 4*u**5/55 + u**4/66 - 2*u**3/33 + 6*u. Factor d(x).
2*x*(x + 1)**2*(5*x - 2)/11
Let x be 86/6 + -4 - (4 + -1). Find p such that -x*p**4 + 0 + 10/3*p**3 + 4/3*p**2 + 8/3*p**5 + 0*p = 0.
-1/4, 0, 1, 2
Factor -1/2*t**2 + 1/2 + 7/4*t - 7/4*t**3.
-(t - 1)*(t + 1)*(7*t + 2)/4
Suppose 0 = 5*b + 4 - 19. What is w in -5*w**3 + 4*w**2 + b*w**3 + w**4 - 3*w**2 = 0?
0, 1
Let k = 23 + -20. Let o(i) be the first derivative of 1/8*i**4 + 1/12*i**k - 2 + 1/20*i**5 + 0*i**2 + 0*i. Factor o(l).
l**2*(l + 1)**2/4
Let 2/3*q - 1/6*q**3 + 1/6*q**2 - 2/3 = 0. Calculate q.
-2, 1, 2
Let 6*f - 2*f**2 + 0 + 2 - 3 - 3 = 0. Calculate f.
1, 2
Let q(n) be the first derivative of 0*n**2 + 1/2*n**6 - 5 - 9/5*n**5 + 9/4*n**4 + 0*n - n**3. Suppose q(u) = 0. Calculate u.
0, 1
Let f(n) be the first derivative of -1 + 1/60*n**6 + 0*n**4 + 0*n + 0*n**3 - n**2 - 1/30*n**5. Let b(l) be the second derivative of f(l). Solve b(d) = 0.
0, 1
Let s(a) be the first derivative of 3/7*a**2 + 1 - 1/14*a**4 + 0*a**3 - 4/7*a. Let s(x) = 0. Calculate x.
-2, 1
Let n(s) = 2*s - 4. Let r be n(3). What is h in -2*h**2 + h**3 + 0*h**3 + 3*h**r - 2*h**3 = 0?
0, 1
Let w = -1025 - -1028. Factor 2/5 - 3/5*n**w + 3/5*n - 2/5*n**2.
-(n - 1)*(n + 1)*(3*n + 2)/5
Factor -3*f**4 + 10*f**4 - 4*f**4 + f**5.
f**4*(f + 3)
Let h be 4*2/(1 + 3). Factor -15*z**2 + 2 - 3 - 2 + 3*z**h + 15*z.
-3*(z - 1)*(4*z - 1)
Let r be 1/2 + (-21)/(-6). Find x, given that 4*x**3 + 0*x**4 + 2*x**r - 2*x**3 = 0.
-1, 0
Let k(m) = -m**4 - m**3 + m**2 + m. Let w(t) = 4*t**4 - 4*t**3 - 8*t**2 + 8*t. Let i(v) = 8*k(v) + w(v). Factor i(q).
-4*q*(q - 1)*(q + 2)**2
Let f(p) = -p**3 - 8*p**2. Let u be f(-8). Factor 4 + u*h**2 - 4*h**3 - 6 + 6*h**2.
-2*(h - 1)**2*(2*h + 1)
Factor -1/2 - 9/4*n**2 - 11/4*n.
-(n + 1)*(9*n + 2)/4
Suppose 4*p - 3*p = 3. Solve 0*w**3 + w**p + 5*w**2 - 3*w**3 - w**2 = 0.
0, 2
Let b(a) be the first derivative of 2*a**5/75 + a**4/30 - 2*a**3/45 - a**2/15 + 3. Factor b(t).
2*t*(t - 1)*(t + 1)**2/15
Suppose 2*r = -2*o + 2, -2*o + 3*r - 2*r + 11 = 0. Suppose -5*p = -m - 6, -m + 14 = p + o*p. Factor -9*z**3 - 2*z**2 + 3*z**p - 3*z**2 - 3*z**5 - 9*z**4 - z**2.
-3*z**2*(z + 1)**3
Let c(z) be the second derivative of 0 - 28/33*z**3 - 49/66*z**4 - 4/11*z**2 - 4*z. Factor c(h).
-2*(7*h + 2)**2/11
Let s(f) = -f**3 - 5*f**2 + 4*f - 8. Let x be s(-6). Let w = -1 + x. Factor -1/3*b**5 + 0*b**2 + 0 + 1/3*b**w + 0*b**4 + 0*b.
-b**3*(b - 1)*(b + 1)/3
Let h(b) = -5*b**2 - 29*b + 8. Let n be h(-6). Factor 6*v**n + 2/3*v**4 - 14/3*v - 10/3*v**3 + 4/3.
2*(v - 2)*(v - 1)**3/3
Suppose 6*h - 15 = h. Let d(b) = b**2 - 3*b - 8. Let s be d(5). Factor 0*k - k**2 + 3*k**2 - k - s + k**h.
(k - 1)*(k + 1)*(k + 2)
Let p(r) be the third derivative of r**9/272160 + r**8/90720 - r**5/30 - 5*r**2. Let t(b) be the third derivative of p(b). Factor t(f).
2*f**2*(f + 1)/9
Factor -1/3*p**5 + 14/3*p**3 - 26/3*p**2 - 1/3*p**4 - 5/3 + 19/3*p.
-(p - 1)**4*(p + 5)/3
Let q(r) be the second derivative of r**7/210 + r**6/120 - r**5/60 - r**4/24 - 3*r**2/2 - 4*r. Let c(h) be the first derivative of q(h). Factor c(g).
g*(g - 1)*(g + 1)**2
Let i(l