Let k(d) be the second derivative of -5/24*d**3 + 0 + 1/16*d**b - 1/4*d**2 - d + 1/24*d**4. Factor k(t).
(t - 1)*(t + 1)*(5*t + 2)/4
Let f(a) = -a**2 + a. Let q(h) = -4*h**2 + 5*h - 1. Let d(x) = 5*f(x) - q(x). Determine w so that d(w) = 0.
-1, 1
Let g(m) be the second derivative of -m**4/24 - 17*m**3/6 - 289*m**2/4 - 2*m - 11. Solve g(x) = 0.
-17
Let c(t) = -t**3 - 2*t**2 + 3*t - 13. Let u be c(-6). Let r = 567/5 - u. Factor 4/5*l - r - 2/5*l**2.
-2*(l - 1)**2/5
Let l(w) be the second derivative of w**4/12 + w**2/2 + 4*w. Let h(a) = -a**2 + 2*a - 5. Let y(q) = -h(q) - 2*l(q). Factor y(n).
-(n - 1)*(n + 3)
Let m(q) be the second derivative of -1/40*q**5 - 1/360*q**6 + 0 + 1/6*q**3 + 0*q**2 - q - 1/12*q**4. Let r(z) be the second derivative of m(z). Factor r(i).
-(i + 1)*(i + 2)
Let t(z) = -7*z**2 + 4*z + 4. Let w(c) = -4 + 20 + 15*c - 27*c**2 - 1. Let q(r) = 15*t(r) - 4*w(r). What is l in q(l) = 0?
0
Let c be (-4)/(3/((-6)/4)). Factor -4*p**3 + 8*p**2 - 2 - 4*p**2 - 2*p**c + 2*p**3 + 2*p.
-2*(p - 1)**2*(p + 1)
Let i = 965/4 + -240. Let m(t) be the first derivative of t - 1/8*t**4 + i*t**2 - 1/10*t**5 - 2 + 1/2*t**3. Solve m(o) = 0.
-1, 2
Let o be (-8)/5*(1 - -4). Let c be 23/20 - o/(-20). Suppose 0*a - 3/4*a**2 + c = 0. What is a?
-1, 1
Suppose -30*h = -8*h - 15*h. Suppose -2/5*k + 6/5*k**2 - 6/5*k**3 + h + 2/5*k**4 = 0. Calculate k.
0, 1
Let o(n) be the second derivative of n**6/72 - 13*n**5/120 - n**4/4 + n**3/6 + n. Let d(q) be the second derivative of o(q). Factor d(p).
(p - 3)*(5*p + 2)
Let -1/6*r**2 + 1/6*r + 1/3 = 0. What is r?
-1, 2
Let f(o) = 2*o**5 + 2*o**4 + 3*o**3 + 7*o**2 + 4*o. Let y(s) = -s**5 - s**4 - s**3 - 3*s**2 - 2*s. Let z(k) = -4*f(k) - 9*y(k). Factor z(p).
p*(p - 1)**2*(p + 1)*(p + 2)
Let w(f) be the first derivative of f**4/14 + 2*f**3/7 - 8*f/7 + 13. Factor w(t).
2*(t - 1)*(t + 2)**2/7
Let s(x) be the third derivative of -x**8/6720 + x**7/840 - x**6/240 + x**5/30 + 5*x**2. Let u(r) be the third derivative of s(r). Factor u(b).
-3*(b - 1)**2
Let c be (-6)/(-6) + 2 + -1. Suppose 5*k = 2*n - 8, -c*k + n = 1 + 3. Determine a, given that 2/5*a**5 + k*a**2 + 0*a**3 + 0*a + 0 - 2/5*a**4 = 0.
0, 1
Suppose -o + 2 + 5 = 0. Let n(l) = -l**3 - 7*l**2 - 6*l + 2. Let w be n(-6). Find q such that 5*q**2 + 4 + o*q - q - 3*q**w = 0.
-2, -1
Let t = 35/3 - 34/3. Factor t*l**3 + 0*l + 0*l**2 + 0*l**4 + 0 - 1/3*l**5.
-l**3*(l - 1)*(l + 1)/3
Solve -4/3*z**2 + 0 + 7/6*z**3 + 1/2*z - 1/3*z**4 = 0 for z.
0, 1, 3/2
Suppose -4 = -2*z + 6. Factor -2*v**3 + 4*v**4 - 2*v**z + 0*v**4 + 2*v**5 - 2*v**5.
-2*v**3*(v - 1)**2
Let a(x) = -3*x**4 - 4*x**3 + 2*x**2 + 1. Let m(z) = -4*z**4 - 5*z**3 + 3*z**2 + 1. Let f(l) = 5*a(l) - 4*m(l). Solve f(t) = 0.
-1, 1
Let c = -6 - -2. Let h be (2/(-5))/(4/c). Factor 0 - h*w + 2/5*w**3 + 2/5*w**4 - 2/5*w**2.
2*w*(w - 1)*(w + 1)**2/5
Factor -762*a**3 - 16*a - 20*a**4 + 0*a**4 + 4*a**5 + 20*a**2 + 774*a**3.
4*a*(a - 4)*(a - 1)**2*(a + 1)
Let v(q) be the third derivative of -q**6/420 + 7*q**2. Factor v(r).
-2*r**3/7
Let g(x) be the first derivative of 2*x - 3 + 1/3*x**3 - 3/2*x**2. Determine h, given that g(h) = 0.
1, 2
Let p(n) = -2. Let u(c) = -5*c**3 + 15*c**2 + 30. Let h(v) = -15*p(v) - u(v). What is x in h(x) = 0?
0, 3
Let d(k) be the first derivative of 2*k - 1/105*k**6 - 1/70*k**5 + 0*k**2 + 0*k**4 + 3 + 0*k**3. Let s(q) be the first derivative of d(q). Factor s(v).
-2*v**3*(v + 1)/7
Let l(w) = -2*w**2 + 0*w**4 + 0 - 3*w**4 - 2 + 4*w**3. Let m(q) = q**3 - q**2 - 1. Let x(z) = -l(z) + 2*m(z). What is p in x(p) = 0?
0, 2/3
Let y(u) be the second derivative of u**5/30 - u**4/6 - u**3 - 3*u**2/2 - 2*u. Let g(j) be the first derivative of y(j). Suppose g(w) = 0. What is w?
-1, 3
Let y(a) be the first derivative of 3*a**5/5 + 3*a**4/4 - 3*a**3 - 15*a**2/2 - 6*a + 7. Find v such that y(v) = 0.
-1, 2
Let k(r) = 0 - 7*r**2 + 6*r**2 + 2. Let u be k(0). Factor 7*o + o**u - 2*o**2 - 8*o + 2*o**3.
o*(o - 1)*(2*o + 1)
Let l = 3/17 - -25/51. Let y(c) be the first derivative of 1 + 5/3*c**2 + 4/3*c - l*c**3. Let y(i) = 0. Calculate i.
-1/3, 2
Let g = 15 - 10. Let w(j) = j - 3. Let y be w(g). Factor 4/9*u**y - 2/9*u**5 - 2/9*u - 2/9*u**4 - 2/9 + 4/9*u**3.
-2*(u - 1)**2*(u + 1)**3/9
Let d(c) be the first derivative of 14*c**3/3 + 2*c**2 - 2. Factor d(s).
2*s*(7*s + 2)
Let d(f) be the first derivative of f**5/5 + f**4/2 - f**3/3 - f**2 + 12. Find t such that d(t) = 0.
-2, -1, 0, 1
Let p(n) be the first derivative of 5*n**3/3 + 11*n**2 + 8*n + 14. Suppose p(j) = 0. Calculate j.
-4, -2/5
Let m(w) be the third derivative of -w**5/180 + w**4/18 - w**2. Find b such that m(b) = 0.
0, 4
Let r(b) be the first derivative of -6 + 27/5*b + 1/5*b**3 + 9/5*b**2. Factor r(w).
3*(w + 3)**2/5
Let o(l) be the second derivative of -2*l**4/3 + l**3 + l**2 + 22*l. Factor o(v).
-2*(v - 1)*(4*v + 1)
Let a(s) be the second derivative of -1/18*s**4 + 0 + 0*s**2 - 1/60*s**5 + 0*s**3 - 2*s. Let a(h) = 0. Calculate h.
-2, 0
Let g(k) be the first derivative of k**3/5 + 3*k**2/5 - 9*k/5 - 11. Factor g(y).
3*(y - 1)*(y + 3)/5
Let t(x) be the third derivative of x**5/15 + x**4/2 + 3*x**3/2 + 10*x**2. Factor t(j).
(2*j + 3)**2
Let n(s) = 5*s**2 - 6*s + 3. Let l be n(2). Suppose -4 = 9*y - l*y. Find t, given that 20/3*t - 3*t**3 + 2*t**y + 8/3 = 0.
-2/3, 2
Let o(x) = -17*x**3 + 20*x**2 - 3*x. Let u = 8 + -23. Let w(i) = -120*i**3 + 141*i**2 - 21*i. Let r(z) = u*o(z) + 2*w(z). Factor r(m).
3*m*(m - 1)*(5*m - 1)
Let w be 18/(-216) - (-1)/4. Let v(i) be the second derivative of -w*i**2 + 2*i + 1/36*i**4 + 0 + 0*i**3. Factor v(u).
(u - 1)*(u + 1)/3
Let l(k) = 5*k - 1. Let t be l(-1). Let z = t + 9. Solve 112*u**z - 9 + 0 - 66*u**2 - 56*u - 32*u**4 + 1 = 0 for u.
-1/4, 2
Let l = -7 + 27. Let o be 5/12 + 5/l. Factor o*x**3 + 0 - 2/3*x + 0*x**2.
2*x*(x - 1)*(x + 1)/3
Let i(o) be the second derivative of -o**5/60 - o**4/8 - o**3/3 + o**2/2 - 2*o. Let u(c) be the first derivative of i(c). Factor u(f).
-(f + 1)*(f + 2)
Let -4*c**3 + 10/3*c**4 - 2/3*c**5 + 0*c**2 + 0 + 0*c = 0. What is c?
0, 2, 3
Let s(y) = -y**4 - y**2. Let r(a) be the second derivative of 3*a**7/7 + 8*a**6/15 + a**5/5 - a**4/2 - 2*a. Let h(q) = -r(q) + 6*s(q). Solve h(d) = 0.
-1, -2/9, 0
Let y be 1/((-3)/(-15)) - -2. Determine u so that 15*u**2 + 17*u + u**3 + 8 + 2*u**3 + y*u + 4 = 0.
-2, -1
Factor -7*v + 4*v**2 - 3*v + 2*v + 12*v**3 + 0*v**2.
4*v*(v + 1)*(3*v - 2)
Let v(o) be the third derivative of 0 - 1/540*o**6 + 0*o**5 + 0*o**3 + 0*o + 2*o**2 + 0*o**4. Suppose v(s) = 0. Calculate s.
0
Suppose -28*p = -32*p + 8. Factor 3/2*i**p + 3/2*i - 3/2 - 3/2*i**3.
-3*(i - 1)**2*(i + 1)/2
Let l(z) be the third derivative of z**5/20 + 3*z**4/8 + z**3 - 10*z**2. Factor l(r).
3*(r + 1)*(r + 2)
Let x(l) be the third derivative of l**8/1120 + l**7/1260 - l**6/180 - l**4/3 - 6*l**2. Let z(p) be the second derivative of x(p). Factor z(s).
2*s*(s + 1)*(3*s - 2)
Let t(f) be the first derivative of f**4/4 + 11*f**3/3 - 13*f**2/2 - 12*f - 4. Let o be t(-12). Factor -1/3*m**2 + 1/3*m**3 + 0*m + o.
m**2*(m - 1)/3
Suppose p = -2*i + 4, -3*i + 6*i - 4*p + 16 = 0. Solve -1/3*v**3 + i*v + 0 + 0*v**2 = 0 for v.
0
Factor -8/9 - 8/9*r - 2/9*r**2.
-2*(r + 2)**2/9
Suppose -b - 5 = -5*w + 4*b, -17 = w + 5*b. Let h be 2/(w/3) - -6. Factor -1/4*a**h + 1/4*a - 1/4*a**4 + 1/4*a**2 + 0.
-a*(a - 1)*(a + 1)**2/4
Let c(a) be the third derivative of -1/6*a**4 + a**2 + 0*a**3 - 1/168*a**8 + 0*a + 1/105*a**7 + 1/20*a**6 + 0 - 1/30*a**5. Determine h so that c(h) = 0.
-1, 0, 1, 2
Let i(v) be the second derivative of v**6/10 + 3*v**5/20 - 3*v**4/4 - v**3/2 + 3*v**2 + 18*v. Factor i(s).
3*(s - 1)**2*(s + 1)*(s + 2)
Let 0 - 3*x + 45/2*x**2 = 0. What is x?
0, 2/15
Let z = 1/228 + 1063/228. Solve 0 - 6*p**3 + 10/3*p**4 - 4/3*p - 2/3*p**5 + z*p**2 = 0.
0, 1, 2
Suppose -8*w + 30 = 2*w. Suppose -q**2 - 1/3*q**w - 1/3 - q = 0. Calculate q.
-1
Suppose -5*n = -6 - 4. Factor 2*x**n + x**3 - 2*x**4 - x**3.
-2*x**2*(x - 1)*(x + 1)
Let v be 10 + -3 - (-1 - -4). Solve 3*h**2 + h**5 + 3*h**4 - 2*h**2 - h**3 - 4*h**v = 0 for h.
-1, 0, 1
Let d(l) be the second derivative of 4*l - 1/3*l**3 + 1/2*l**2 + 0 + 1/12*l**4. Find f, given that d(f) = 0.
1
Let q = -2598/7 + 372. Suppose -4*u = -1 - 7. Factor -8/7*m + 2/7 + q*m**u.
2*(m - 1)*(3*m - 1)/7
Let p(d) be the th