**2 + 1. Let n be 6/4*4/6. Let h(g) = 6*g + 2. Let p(q) = n*h(q) + 2*t(q). Factor p(w).
2*(w + 1)*(w + 2)
Let c(n) be the third derivative of -n**10/151200 + n**8/16800 - n**6/3600 - n**4/24 - n**2. Let q(s) be the second derivative of c(s). Factor q(k).
-k*(k - 1)**2*(k + 1)**2/5
Suppose 26*g = 29*g - 6. Factor -2/5*a**g + 0 - 1/5*a**3 + 0*a.
-a**2*(a + 2)/5
Let h be (-17)/(-10) - (-6 - (-75)/10). Factor -1/5*p**3 + 1/5*p - 1/5 + h*p**2.
-(p - 1)**2*(p + 1)/5
Suppose -2/7*k**2 + 1/7*k + 1/7*k**3 + 0 = 0. Calculate k.
0, 1
Let l(s) be the first derivative of s**5/5 - s**4/4 - s**3 + s**2/2 + 2*s - 1. Factor l(o).
(o - 2)*(o - 1)*(o + 1)**2
Let q(n) be the third derivative of -n**8/1680 + n**7/525 + n**6/600 - n**5/150 + 2*n**2. Solve q(x) = 0.
-1, 0, 1, 2
Let v(l) = -5 - 2*l**2 - 2*l**2 + l**3 + l + 5*l**2 + 4. Let z(y) = -21*y**3 - 9*y**2 - 24*y + 18. Let c(w) = 18*v(w) + z(w). Factor c(q).
-3*q*(q - 2)*(q - 1)
Suppose -3*x + p + 4 + 6 = 0, -x - 14 = 4*p. Suppose d - 2*d + x = 0. Factor -2*y**2 - y**2 + 2*y**2 + d*y.
-y*(y - 2)
Let q be (-10)/(-4) - 6/(-4). Suppose -q*m = m + 5. Let f(b) = -b**3 - b**2 + 1. Let g(x) = -x**3 - 6*x**2 + 4*x + 2. Let s(v) = m*g(v) + 2*f(v). Factor s(z).
-z*(z - 2)**2
Let z(n) = n**3 + n. Let f be z(0). Let w(t) = -t**3 + t**2 - t + 5. Let x be w(f). Solve -q - q - 2*q**5 + 0*q**x + 4*q**3 = 0.
-1, 0, 1
Let a = 20 - 14. Let r(f) be the first derivative of -f**4/4 - f**3/3 + f + 1. Let j(n) = 4*n**3 + 4*n**2 - 6. Let y(k) = a*r(k) + j(k). Factor y(l).
-2*l**2*(l + 1)
Determine x, given that 0 + 4/7*x + 10/7*x**3 - 2*x**2 = 0.
0, 2/5, 1
Let o(w) be the second derivative of 3/4*w**2 + 1/72*w**4 + 6*w + 0 + 1/6*w**3. Factor o(q).
(q + 3)**2/6
Let r be 11/(-55) + (-36)/(-20). Factor -6/5*f - 2/3*f**3 + 4/15 + r*f**2.
-2*(f - 1)**2*(5*f - 2)/15
Let v(d) be the third derivative of 5*d**8/1344 - d**7/168 - d**6/96 + d**5/48 - 2*d**2. Factor v(q).
5*q**2*(q - 1)**2*(q + 1)/4
Let m(q) be the third derivative of -q**5/100 - q**4/40 + q**3/5 + 6*q**2. Determine w, given that m(w) = 0.
-2, 1
Suppose o = -2*a + 4, 3*a + 46 = 2*o + 3*o. Suppose o - 20 = -3*y. Factor -2*l**4 + y*l**3 - 4*l**4 + l**2 - 2*l + 3*l**4.
-l*(l - 1)**2*(3*l + 2)
Let r = 14 - 14. Factor 0 + 1/3*u**3 + r*u**2 + 0*u - 1/3*u**4.
-u**3*(u - 1)/3
Let r = 120 + -118. Factor 0 + 4/3*p + 2/3*p**3 - r*p**2.
2*p*(p - 2)*(p - 1)/3
Suppose 6 = -a + 9. Let g be (2/3)/((-1)/(-3)). Factor -3*r + 1 + 4*r**4 - 4*r**2 - 5*r**g + 4*r**2 + 3*r**a.
(r - 1)*(r + 1)**2*(4*r - 1)
Let b(w) be the first derivative of 9*w**5/40 - w**4/4 - 5*w**3/3 - 2*w**2 + 5*w - 1. Let g(m) be the first derivative of b(m). Find r such that g(r) = 0.
-2/3, 2
Let n = 5 - 2. Factor -2/7 - 2/7*a + 10/7*a**2 - 6/7*a**n.
-2*(a - 1)**2*(3*a + 1)/7
Suppose 0*x - 7 = -x - 5*o, x = -3*o + 5. Factor 4/3 - 2/3*g - 2/3*g**x.
-2*(g - 1)*(g + 2)/3
Let w = 29 - 27. Let f(q) be the second derivative of 0*q**2 + 1/3*q**6 - 8/3*q**3 + 1/21*q**7 - 2/3*q**4 + 3/5*q**5 + 0 + w*q. Factor f(n).
2*n*(n - 1)*(n + 2)**3
Suppose 0 = -4*m + 5*v + 3 - 1, 0 = -4*m - 4*v + 20. Let x(t) be the first derivative of 2*t + 2 + m*t**2 + 5/2*t**4 - 6*t**3. Factor x(r).
2*(r - 1)**2*(5*r + 1)
Let i be 1/(-3) - ((-28)/(-12))/(-7). Factor 1/3*z**3 + 0*z**2 + i - 1/3*z.
z*(z - 1)*(z + 1)/3
Let h(i) be the third derivative of -i**5/60 - i**4/120 - 3*i**2. Factor h(w).
-w*(5*w + 1)/5
Suppose 5 = 3*r + a, -3*a - 61 = 3*r - 58. Factor -2/5 - 6/5*f**2 + 6/5*f + 2/5*f**r.
2*(f - 1)**3/5
Let n(z) = -z**3 + 4*z**2 + 7*z - 3. Let j be n(5). Let u - 2*u**5 - 5*u - 3*u**4 - j*u**4 - 14*u**2 - 18*u**3 = 0. Calculate u.
-2, -1, 0
Let y(l) be the second derivative of -l**5/270 - l**4/54 - l**3/27 - 3*l**2/2 - 2*l. Let v(u) be the first derivative of y(u). Determine d so that v(d) = 0.
-1
Let s(r) = -9*r**2 - 1. Let m(k) = -6*k + 5*k**2 + 6*k + 1. Suppose -y + 3*y + 7 = 3*z, 2*z + 2 = 0. Let p(n) = y*m(n) - 3*s(n). Factor p(v).
2*(v - 1)*(v + 1)
Let t = -23057/2 + 1775153/154. Let p = 20/11 + t. Determine j so that p*j**2 - 8/7*j + 8/7 = 0.
2
Let k(g) = -3*g + 7. Let d be k(3). Let w = d - -4. Factor -2/3*b**3 + 2/3*b + 0 + 2/3*b**4 - 2/3*b**w.
2*b*(b - 1)**2*(b + 1)/3
Suppose -2*w + 4*i = -12, w - 4*i = 4*w + 2. Factor -2/7*c**3 - 2/7*c**4 + 2/7*c + 2/7*c**w + 0.
-2*c*(c - 1)*(c + 1)**2/7
Let h(b) = -b**2 - 6*b - 1. Let i be h(-5). What is a in a - 6*a**3 - a**2 + 0*a**2 + 5*a**3 + a**i = 0?
-1, 0, 1
Suppose 11 + 9 = 5*s. Let k(r) be the first derivative of 1/16*r**s - 1/4*r + 1/12*r**3 - 1 - 1/8*r**2. Factor k(f).
(f - 1)*(f + 1)**2/4
Let m(s) be the first derivative of -s**3/15 - 9*s**2/5 - 81*s/5 - 28. Factor m(r).
-(r + 9)**2/5
Let r be (3/1)/((-2)/(-12)). Suppose c - 14 = -4*x, x - r = -3*c - 3*x. Factor 8 + 5*v**3 + 34*v**c + 28*v - 12*v**2 + 0*v**3.
(v + 2)**2*(5*v + 2)
Suppose -2*p = -2*x - 16, 5 = 3*p + 2*p + 2*x. Let z = -154 - -156. Suppose 2*i + 1/2 + i**z - 3/2*i**4 - 2*i**p = 0. Calculate i.
-1, -1/3, 1
Factor -3/7*q**2 + 0*q - 3/7*q**5 - 9/7*q**3 + 0 - 9/7*q**4.
-3*q**2*(q + 1)**3/7
Factor 6*l**3 - l**4 - 10*l**3 + 4*l**5 - 2*l**4 + 4*l**2 - l**4.
4*l**2*(l - 1)**2*(l + 1)
Solve 2*y**2 + 14*y + 15*y**2 + 3*y**3 + 8 - 2*y + 10*y = 0 for y.
-4, -1, -2/3
Let r(p) = p - 11. Let t be r(15). Let v(i) = -2*i**2 + 4*i - 6. Let h(o) = -o**2 + 3*o - 5. Let l(j) = t*h(j) - 3*v(j). Factor l(a).
2*(a - 1)*(a + 1)
Suppose 5*b = 2*b + 24. Suppose 0 = -3*k + 2*m + 17, b - 1 = k - m. Find c such that -60*c**2 - 24*c + k*c**4 + 3 - 12*c**4 - 42*c**3 - 3 = 0.
-2, -2/3, 0
Let z(l) be the second derivative of l**6/90 + l**5/60 - 5*l. Factor z(u).
u**3*(u + 1)/3
Let g(r) be the third derivative of -r**5/60 - r**4/24 + 3*r**2. Factor g(n).
-n*(n + 1)
Let o(m) be the second derivative of -m**7/63 - m**6/15 - m**5/15 + 4*m. Factor o(r).
-2*r**3*(r + 1)*(r + 2)/3
Let f be -3 + (-7)/7*2 + 5. Factor -3/2*m - 3/4*m**3 + 9/4*m**2 + f.
-3*m*(m - 2)*(m - 1)/4
Let u = -124079/110 - -1128. Let p = u + 217/330. Let -1/3*v**2 - p*v**3 + 0*v + 0 - 1/3*v**4 = 0. What is v?
-1, 0
Let d(q) = 7*q**3 - 12*q**2 + 19*q - 11. Let v(f) = -3*f**3 + 6*f**2 - 10*f + 6. Let c(z) = 4*d(z) + 10*v(z). Factor c(h).
-2*(h - 2)**3
Suppose -u + 11 = 9. Let k(w) be the second derivative of 0*w**2 + 1/30*w**4 + 0*w**5 + 0 - 1/75*w**6 + 0*w**3 + u*w. Solve k(b) = 0 for b.
-1, 0, 1
Let m be (0 + 1)/(-6 - 100/(-15)). Solve -m*f - 3/2*f**3 + 0 - 3*f**2 = 0.
-1, 0
Let h(k) = 11*k**2 - 3. Let n be h(-2). Factor 7*u**5 - 33 + n - 3*u**5 - 16*u**3 + 12*u - 8*u**2.
4*(u - 2)*(u - 1)*(u + 1)**3
What is w in -25*w**3 - 3*w**4 - 2537*w**5 + 10*w**2 + 23*w**4 + 2532*w**5 = 0?
0, 1, 2
Let a be (0 - -20)*(-1 - -2). Suppose -4*y = -a, i - 3*y - 3 + 15 = 0. Determine u, given that 2*u + 3*u**4 + 2*u**i - 1 - 4*u**3 - 2*u**4 = 0.
-1, 1
Let w = 136/213 - -2/71. Suppose -142 = 4*g - 150. Factor 0 - 2*r**g - w*r.
-2*r*(3*r + 1)/3
Suppose 6*y = 3*y. Let w(v) be the third derivative of 0*v + 0*v**6 + 0 + v**2 - 1/15*v**5 + y*v**4 + 1/3*v**3 + 1/105*v**7. Factor w(a).
2*(a - 1)**2*(a + 1)**2
Let d be ((-36)/16 + 3)/((-15)/(-2)). Let n(j) be the first derivative of 1/2*j**4 - d*j**5 - 1/2*j - j**3 + j**2 - 1. Find f, given that n(f) = 0.
1
Let y = 2793/4 + -698. Suppose -y + 5/4*j**2 + j = 0. Calculate j.
-1, 1/5
Let v be (-3)/720*58 - (-2)/8. Let a(x) be the third derivative of 0 + 1/240*x**6 - 2*x**2 + 0*x**3 + 0*x**4 - v*x**5 + 0*x. Solve a(b) = 0.
0, 1
Let y(f) = 16*f**3 - 80*f**2 - 100*f + 32. Let n(k) = -k**3 + k**2 - k. Let i(q) = 12*n(q) - y(q). Factor i(r).
-4*(r - 4)*(r + 1)*(7*r - 2)
Let n = 22/57 - 244/665. Let p(k) be the third derivative of 0 + 1/6*k**3 - 13/120*k**6 - 7/24*k**4 + 0*k + k**2 + n*k**7 + 1/4*k**5. Factor p(x).
(x - 1)**3*(4*x - 1)
Let p(r) be the first derivative of 0*r**2 + 5/3*r**6 - 4 + 0*r**3 + 0*r - 14/5*r**5 + r**4. Factor p(n).
2*n**3*(n - 1)*(5*n - 2)
Let o(t) be the first derivative of -t**5/390 + t**4/52 - 2*t**3/39 + t**2/2 - 7. Let m(j) be the second derivative of o(j). Let m(n) = 0. What is n?
1, 2
Suppose -19*b = -11*b. Determine m so that b*m - 1/3*m**2 - 5/3*m**3 - 4/3*m**4 + 0 = 0.
-1, -1/4, 0
Let r(w) be the third derivative of -w**8/56 - w**7/15 - w**6/20 + w**5/10 + w**4/6 + 4*w**2. Solve r(l) = 0 for l.
-1, 0, 2/3
Factor 12*f**2 + 0*f**3 + 4*f**4 + 4*f - f**3 + 13