+ 0*k**2 - 2*k**3 - 2*k**2 = 0.
-2, -1, 1
Let q(m) be the second derivative of m**8/2240 + m**7/420 - m**6/80 + m**4/6 + 2*m. Let y(j) be the third derivative of q(j). Factor y(c).
3*c*(c - 1)*(c + 3)
Let m(r) be the third derivative of r**7/1680 + r**6/240 + r**5/80 + r**4/12 - 2*r**2. Let z(w) be the second derivative of m(w). Determine x so that z(x) = 0.
-1
Suppose 4 = 2*r - 4. Suppose -r*m - 4*a - 8 = -m, 5*a + 10 = 4*m. Determine k, given that 2/3*k**5 + m*k**2 + 0 - 4/3*k**3 + 2/3*k + 0*k**4 = 0.
-1, 0, 1
Suppose -4 + 1 = -z. Find q, given that 36*q + 6*q**2 + 14*q**2 + 4*q**2 + 4*q**z = 0.
-3, 0
Let s(l) be the first derivative of -10*l**3/39 + 4*l**2/13 + 2*l/13 + 5. Suppose s(m) = 0. Calculate m.
-1/5, 1
Let o(y) be the first derivative of y**6/120 - y**5/80 - y**4/48 + y**3/24 + 5*y - 4. Let w(a) be the first derivative of o(a). Factor w(k).
k*(k - 1)**2*(k + 1)/4
Let a(h) be the third derivative of h**9/448 - h**8/1120 - 2*h**3/3 - 4*h**2. Let v(l) be the first derivative of a(l). Let v(u) = 0. What is u?
0, 2/9
Let q(p) be the second derivative of -2/75*p**6 + 0*p**2 + 1/105*p**7 + 1/15*p**4 + 5*p + 0*p**5 + 0 - 1/15*p**3. Factor q(z).
2*z*(z - 1)**3*(z + 1)/5
Suppose 5*c + 5*x = 15, -5*x - 3 = c - 6. Let -b**2 - 2*b**2 + 3*b**4 + 4*b**2 + b**5 - c*b**3 + 6*b**3 = 0. Calculate b.
-1, 0
Let r(k) be the third derivative of -2*k**7/21 + k**6/15 + k**5/3 - k**4/3 + k**2. Factor r(o).
-4*o*(o - 1)*(o + 1)*(5*o - 2)
Let k(d) = -5*d**3 - 60*d + 40. Let t(l) = l**3 + 15*l - 10. Let x(b) = -6*k(b) - 25*t(b). Determine r, given that x(r) = 0.
-2, 1
Suppose -3 + 125*v + 3*v**2 - 33 - 122*v = 0. Calculate v.
-4, 3
Let c(x) = x**2 - 4*x + 3. Let s be c(3). Suppose s = -h + 3*h - 4. Factor 2*u**4 - 2*u**2 + 0*u**4 - u**h + u**2 + 3*u**5 - 3*u**3.
u**2*(u - 1)*(u + 1)*(3*u + 2)
Let w(u) be the second derivative of 0 - 1/30*u**5 + u - 1/3*u**3 - u**2 - 1/6*u**4. Let t(o) be the first derivative of w(o). Solve t(j) = 0 for j.
-1
Suppose 5*i - 133 = -4*z + 30, 0 = 5*i + 5*z - 160. Suppose -7*x + i = -2*x. Factor 0*a + 2*a + x*a**2 - 2*a**3 - 2 - 5*a**2.
-2*(a - 1)**2*(a + 1)
Suppose -5*t - 2 = 18, 0 = 2*w - 2*t - 20. Factor -f**3 + 3*f**3 + 2*f**5 - w*f**3 + 2*f**4.
2*f**3*(f - 1)*(f + 2)
Let o(b) be the second derivative of -b**4/3 - 2*b**3/3 - b. What is f in o(f) = 0?
-1, 0
Let y(k) = -k - 5. Let w be y(-4). Let j be (-4)/(-6) + -1 - w. Factor -2/3*n**5 - 4/3*n**4 + 0*n**2 - j*n**3 + 0*n + 0.
-2*n**3*(n + 1)**2/3
Suppose -b + 4*b + 5*q = -14, 0 = 2*b + q. Determine r, given that -2*r**2 - 6*r**2 - 4*r - b + 4 + 10*r = 0.
-1/4, 1
Let a = -170 + 170. Find j such that 1/2*j**4 + a*j**2 - j - 1/2 + j**3 = 0.
-1, 1
Let l(p) be the second derivative of -p**3/6 - 4*p**2 + 6*p. Let z be l(-8). Factor 0*c**2 + z*c**3 + 0*c - 1/4*c**4 - 1/2*c**5 + 0.
-c**4*(2*c + 1)/4
Let t(s) be the first derivative of -s**4/5 - 2*s**3/3 - 4*s**2/5 - 2*s/5 + 2. Solve t(y) = 0.
-1, -1/2
Suppose 0 = -7*y + 12*y - 10. Let i(j) be the second derivative of 0*j**y - 1/6*j**3 + 0 + 1/4*j**4 + j - 3/20*j**5 + 1/30*j**6. Let i(n) = 0. What is n?
0, 1
Factor 0*b**2 - 1/8*b**3 + 0*b + 0.
-b**3/8
Factor 4/13*n - 2/13*n**2 + 0.
-2*n*(n - 2)/13
Let c(l) be the second derivative of l**7/1050 - l**5/150 + l**3/30 + l**2 + 8*l. Let t(n) be the first derivative of c(n). Suppose t(q) = 0. Calculate q.
-1, 1
Let a(m) be the second derivative of -m**5/4 - 5*m**4/4 - 5*m**3/2 - 5*m**2/2 + 9*m. Determine l, given that a(l) = 0.
-1
Let z(d) be the third derivative of d**5/14 + 11*d**4/84 + 2*d**3/21 + 11*d**2. Factor z(l).
2*(3*l + 1)*(5*l + 2)/7
Let w = 22 - 12. Let b = w + -6. Find a, given that 0*a**3 + 0*a**2 - 2/3*a**b + 2/3*a**5 + 0 + 0*a = 0.
0, 1
Let d be 222/56 + (-6)/(-21). Let g = 55/12 - d. Factor -g*k**2 - 2/3*k + 0 + k**3.
k*(k - 1)*(3*k + 2)/3
Let w(m) = m**4 + 7*m**3 + 9*m**2 - 2*m + 5. Let d(i) = i**4 + 4*i**3 + 5*i**2 - i + 3. Suppose -5*v + 8*v - 9 = 0. Let u(g) = v*w(g) - 5*d(g). Factor u(l).
-l*(l - 1)*(l + 1)*(2*l - 1)
Solve -3*j - 12*j**2 + 16*j**3 + 6*j**4 - 10*j**4 + 3*j = 0.
0, 1, 3
Let o be 9/2 + 21/14. Factor 19 - 2*a**4 - a**4 - o*a**3 - 16 + 6*a.
-3*(a - 1)*(a + 1)**3
Let f be (-9)/(-1 - (-2 - 0)). Let b be (-11)/f + (-2)/9. Solve 4*g - 2 - 1 - b - g**2 = 0.
2
Let i(v) = 2*v**2 - 4*v - 72. Let p(c) = -5*c**2 + 10*c + 145. Let r(b) = -5*i(b) - 3*p(b). Factor r(w).
5*(w - 5)*(w + 3)
Suppose -12/11 + 10/11*j + 2/11*j**2 = 0. Calculate j.
-6, 1
Suppose 36 = 6*g + 18. Find x such that -45/2*x**g - 12*x**2 - 25/2*x**4 + 0 - 2*x = 0.
-1, -2/5, 0
Let s(y) be the second derivative of -y**4/36 + 18*y. Factor s(w).
-w**2/3
Let a(n) be the second derivative of n**7/14 + 7*n**6/20 + 27*n**5/40 + 5*n**4/8 + n**3/4 - 8*n. Suppose a(f) = 0. Calculate f.
-1, -1/2, 0
Let k be 0*(0 + 1)/2. Factor k*m**5 + 0*m**5 + m**5.
m**5
Let a(m) = -5*m - 10. Let i be a(-4). Suppose n = -3*q + i + 7, -n = -q + 3. What is l in 0 + 1/2*l**n + 1/4*l**3 + 1/4*l = 0?
-1, 0
Let m(u) = -u**2 - u - 1. Let n(j) = 384*j**2 - 256*j + 20. Let r(d) = -16*m(d) + n(d). Determine z, given that r(z) = 0.
3/10
Factor 8*u + 36*u**2 + 25*u**3 - 6 + u - 4*u**3.
3*(u + 1)**2*(7*u - 2)
Let c(q) be the second derivative of -q**6/180 - q**5/30 - q**3/6 + 4*q. Let u(w) be the second derivative of c(w). Factor u(z).
-2*z*(z + 2)
Let p(m) be the first derivative of 2*m**3/39 - 2*m/13 - 6. Determine a, given that p(a) = 0.
-1, 1
Let t(b) be the first derivative of -b**8/504 + b**6/90 - b**4/36 + 3*b**2/2 - 5. Let r(o) be the second derivative of t(o). Factor r(s).
-2*s*(s - 1)**2*(s + 1)**2/3
Let p(c) = -2*c + 26. Let r be p(12). Factor 1/4*x**3 - 1/4*x + 0 + 0*x**r.
x*(x - 1)*(x + 1)/4
Suppose -78 = -21*i - 18*i. Factor 0*c**i - 1/3*c**5 + 0*c + 0 + 2/3*c**4 + 0*c**3.
-c**4*(c - 2)/3
Let y(w) = w**2 - w - 5. Let n be y(-4). Let t = n - 11. Solve j + j**5 - 4*j**t + 4*j**4 - 2*j**3 = 0 for j.
-1, 0, 1
Let l = 225 + -2695/12. Let f(n) be the first derivative of 1/5*n**5 - 3/16*n**4 - 1 + 3/8*n**2 + 1/4*n - l*n**3. Factor f(o).
(o - 1)**2*(o + 1)*(4*o + 1)/4
Let c(g) = g**4 - g**2 - g + 1. Let z(k) = -7*k**4 - 8*k**3 - 5*k**2 + k - 5. Let h(j) = -5*c(j) - z(j). Let h(i) = 0. What is i?
-2, -1, 0
Factor -2*n**3 + 0 + 17*n**3 + 9*n - 23*n**2 + 2 - 3.
(n - 1)*(3*n - 1)*(5*n - 1)
Let y(g) = -8*g**4 + 40*g**3 - 29*g**2 - 67*g. Let f(o) = -44*o**4 + 220*o**3 - 160*o**2 - 368*o. Let d(h) = 5*f(h) - 28*y(h). Factor d(l).
4*l*(l - 3)**2*(l + 1)
Find t, given that -100*t**3 + 12*t**4 - 35*t**5 + 20*t**2 + 45*t**4 + 91*t**4 - 33*t**4 = 0.
0, 2/7, 1, 2
Suppose -39*t**2 - 8 + 43*t**2 - 8 = 0. Calculate t.
-2, 2
Let -6*u**2 - 2 + 6*u**2 - u - u + 2*u**2 + 2*u**3 = 0. Calculate u.
-1, 1
Let h(z) be the third derivative of -1/40*z**6 + 1/8*z**4 + 0*z + 0 + 0*z**5 + 3*z**2 + 0*z**3. Let h(l) = 0. Calculate l.
-1, 0, 1
Let s(g) be the third derivative of -g**5/20 + 2*g**4 - 32*g**3 - 45*g**2. Solve s(u) = 0 for u.
8
Let q(d) = -16*d**3 + 5*d**2 + 20*d - 9. Let a(n) = 3*n**3 - n**2 - 4*n + 2. Let i(k) = 33*a(k) + 6*q(k). Factor i(g).
3*(g - 2)*(g - 1)*(g + 2)
Let b(v) be the first derivative of 4/3*v - 2*v**2 - 4 + 8/9*v**3. Solve b(w) = 0.
1/2, 1
Let h(j) be the second derivative of j**4/12 - 3*j**3/2 - 5*j**2 + 17*j. Let z be h(10). Suppose 1/3*o**2 + z - 2/3*o = 0. Calculate o.
0, 2
Let j = -53/6 - -9. Let o(p) be the third derivative of 0*p**4 + 3*p**2 + 0*p + j*p**3 - 1/60*p**5 + 0. Factor o(r).
-(r - 1)*(r + 1)
Let l(d) be the second derivative of -d**8/1680 - d**7/420 + d**6/120 + d**5/30 + d**4/3 + 4*d. Let r(f) be the third derivative of l(f). Factor r(a).
-2*(a - 1)*(a + 2)*(2*a + 1)
Let h = -85/7 - -100/7. Suppose 0*b**2 - h*b**4 + 0*b + 0 + 3/7*b**3 = 0. Calculate b.
0, 1/5
Factor -4/3*m - 2/3*m**3 + 2*m**2 + 0.
-2*m*(m - 2)*(m - 1)/3
Let t(w) = -19*w**2 + 15*w + 4. Let n(h) = 10*h**2 - 8*h - 2. Let y(m) = -11*n(m) - 6*t(m). Find c, given that y(c) = 0.
-1/2, 1
Let m = 5348/5 - 1078. Let w = -8 - m. Solve w*p**4 - 4/5*p**3 + 0 + 2/5*p**2 + 0*p = 0 for p.
0, 1
Factor 0*h**2 + 1/4*h - 1/4*h**3 + 0.
-h*(h - 1)*(h + 1)/4
Factor 0 + 3/5*z - 3/5*z**3 + 8/5*z**2.
-z*(z - 3)*(3*z + 1)/5
Find w such that 0*w**2 - 12 - 3*w**2 + 6*w**2 = 0.
-2, 2
Suppose 2*m - 6 = 0, -5*m = q - 24 + 5. Suppose 8 - q*n - 12*n - 2*n**2 - 8*n**2 = 0. What is 