(c - 1)*(c + 1)**3
Let b be -3*4/((-3)/(-2)*-6). Factor 4/3*z**2 + 10/3*z - b - 10/3*z**3.
-2*(z - 1)*(z + 1)*(5*z - 2)/3
Let p(a) = -a**5 + a**4 - a**3. Let k(j) = 6*j**5 + 238*j**4 + 5762*j**3 + 69120*j**2 + 414720*j + 995328. Let c(u) = k(u) + 2*p(u). Factor c(v).
4*(v + 12)**5
Let j(i) be the third derivative of -1/24*i**4 - 3*i**2 - 1/20*i**6 - 1/15*i**5 + 0 - 2/105*i**7 - 1/336*i**8 + 0*i + 0*i**3. Factor j(s).
-s*(s + 1)**4
Suppose -n = n - 5*z + 11, -5*n = -5*z + 5. Solve 4*s**3 - n*s**2 + 3*s**2 + s**2 - 2 - 2*s - 2*s = 0.
-1, -1/2, 1
Suppose -5*b = 3*i - i, 0 = 3*b + 3*i + 9. Determine y so that 8*y**3 + 68*y**b + 23*y**3 + 4 + 11*y**3 + 30*y = 0.
-1, -1/3, -2/7
Let k be 20/36*123/2. Let b = k + -67/2. Factor -2/3 - 2/3*w**3 + b*w**2 + 2/3*w.
-2*(w - 1)**2*(w + 1)/3
Let y be (-2)/(-14) + (-276)/21. Let u = -8 - y. Factor u*x**5 - 97/5*x**2 - 19*x**4 + 32/5*x - 4/5 + 139/5*x**3.
(x - 1)**3*(5*x - 2)**2/5
Factor -2/3*d**3 - 22/3*d - 4 - 4*d**2.
-2*(d + 1)*(d + 2)*(d + 3)/3
Let k(j) = -5*j**2 - 5*j + 6. Let p(n) = n**2 + n - 1. Let c(d) = -2*k(d) - 11*p(d). Let q(s) = 4*s**2 - 2*s + 4. Let x(g) = -2*c(g) - q(g). Factor x(z).
-2*(z - 1)**2
Factor -1 + 2*u**4 + 4*u**2 - 4*u**4 - 1.
-2*(u - 1)**2*(u + 1)**2
Let y(n) be the first derivative of 3*n**4/4 + n**3/3 - n**2 + 12. Find d such that y(d) = 0.
-1, 0, 2/3
Let b(n) = 7*n**4 + 4*n**3 - 19*n**2 - 80*n - 59. Let j(i) = 3*i**4 + 2*i**3 - 10*i**2 - 40*i - 30. Let f(x) = 2*b(x) - 5*j(x). Factor f(s).
-(s - 4)*(s + 2)**3
Let h(s) = -1 - 6*s**5 - 2 - 9*s**4 - 18*s**2 - 12*s**3 + 2 - 2*s. Let y(l) = -8*l - l**3 + l**5 + l**2 - 3*l + 10*l. Let m(u) = h(u) + 4*y(u). Factor m(p).
-(p + 1)**4*(2*p + 1)
Let i be (-15)/(-20)*12/27. Let j(a) be the first derivative of -i*a**2 + a - 1/9*a**3 - 3. Factor j(v).
-(v - 1)*(v + 3)/3
Suppose 3*g = -2*g + 25. Let j(o) be the third derivative of 2*o**2 + 1/90*o**g + 0 + 1/9*o**3 - 5/72*o**4 + 0*o. Suppose j(b) = 0. Calculate b.
1/2, 2
Factor -2*b**3 - 2*b**5 - 2*b**4 - 3*b**4 + b**4 + 0*b**4.
-2*b**3*(b + 1)**2
Let k(d) be the first derivative of -2/33*d**3 + 3 - 18/11*d - 6/11*d**2. Factor k(n).
-2*(n + 3)**2/11
Factor 129*y**2 - 24 + 5*y**3 - 7*y**3 + 10*y**3 + 78*y + 19*y**3.
3*(y + 1)*(y + 4)*(9*y - 2)
Let p = -88418 - -617846/7. Let w = -154 - p. Suppose -2/7 - 10/7*i - w*i**5 - 10/7*i**4 - 20/7*i**3 - 20/7*i**2 = 0. Calculate i.
-1
Factor 43 + 20*k**2 - 33 - 8*k + 53*k.
5*(k + 2)*(4*k + 1)
Let -80 - 85/4*w**2 - 100*w - 5/4*w**3 = 0. What is w?
-8, -1
Let s(n) be the first derivative of -9*n**4/4 - 11*n**3/3 - n**2 + 25. Factor s(z).
-z*(z + 1)*(9*z + 2)
Factor 18/5 + 8/5*v**2 - 26/5*v.
2*(v - 1)*(4*v - 9)/5
Let r(m) be the third derivative of -m**9/7056 + m**8/3920 - m**3/3 + 5*m**2. Let o(c) be the first derivative of r(c). Factor o(s).
-3*s**4*(s - 1)/7
Suppose 4*a + 5*t = 29, 4*a - 9 = -4*t + 15. Let x = a + 1. Determine w so that 5*w + w**2 - x*w**2 - 5*w = 0.
0
Let j = 541007/1491 + 1858/213. Let r = j + -371. Solve -2/7*q**4 - 2/7 + 0*q + 0*q**3 + r*q**2 = 0.
-1, 1
Find u, given that 3/2*u**2 - u + 0 = 0.
0, 2/3
Let c(q) be the first derivative of q**6/36 - q**5/30 - q**4/8 + q**3/18 + q**2/6 - 65. Factor c(r).
r*(r - 2)*(r - 1)*(r + 1)**2/6
Let b be 78/(-12) + 7 + (-4)/(-24). Let y = 18 + -13. Factor 2/3*f**4 - 2/3*f**2 + b*f**y + 0 + 0*f - 2/3*f**3.
2*f**2*(f - 1)*(f + 1)**2/3
Determine m, given that -1/2*m**3 + 4*m**2 + 0 - 7/2*m = 0.
0, 1, 7
Let z(p) = -7*p**4 - 2*p**3 + 5*p**2 + 6*p. Let j(y) = y**4 - y**2 - y. Let n(v) = 6*j(v) + z(v). Factor n(c).
-c**2*(c + 1)**2
Let l(y) = -11*y**3 - 5*y**2 + 8*y - 13. Let p(q) = 4*q + 3*q**3 - 2*q**2 - 8*q**3 - 1 + 0 - 5. Let m(a) = -6*l(a) + 13*p(a). Factor m(w).
w*(w + 2)**2
Let l(h) be the first derivative of -h**3/24 - h**2/2 - 2*h - 11. Factor l(u).
-(u + 4)**2/8
Let c(i) be the first derivative of -5*i**6/6 + i**5 + 5*i**4/4 - 5*i**3/3 - 7. Find m, given that c(m) = 0.
-1, 0, 1
Let i(y) = 4*y**3 - 10*y**2 - 6*y + 6. Let u(g) = -20*g**3 + 51*g**2 + 31*g - 29. Let w(x) = -11*i(x) - 2*u(x). Factor w(p).
-4*(p - 2)*(p - 1)*(p + 1)
Suppose 5*k - 37 = -3*g, 3*k = -2*g + 20 + 3. Factor m**2 + k*m**2 + m - m - 3*m**3.
-3*m**2*(m - 2)
Factor -2/3*s**5 + 0*s**4 + 0*s**2 + 2/3*s**3 + 0 + 0*s.
-2*s**3*(s - 1)*(s + 1)/3
Factor -30 - 5*n**2 - n - 14*n - 43 + 63.
-5*(n + 1)*(n + 2)
Let q = -731/5 - -147. Let u(p) be the first derivative of -3 + 14/15*p**3 - 2/5*p**5 + 3/5*p**2 - 3/10*p**4 - q*p. Find s such that u(s) = 0.
-1, 2/5, 1
Let f(q) = 5*q - 7. Let n be f(2). Let m(k) be the first derivative of 1 - 2/7*k**4 + 2/7*k - 4/7*k**2 + 4/7*k**n + 2/35*k**5. Factor m(l).
2*(l - 1)**4/7
Let j = 19 - 11. Let h(z) = -2*z**3 - z - 1. Let t be h(-1). Determine a so that 13*a**2 - a**2 + t*a**4 + j*a**3 + 0*a**4 + 2 + 8*a = 0.
-1
Suppose o + 7 = -k, k - 3*o = -2*o - 5. Let l be (3/k)/((-2)/8). What is d in -d**4 + 8*d**l + d**5 - 8*d**2 = 0?
0, 1
Let o(x) = 2*x**2 - 12*x + 13. Let y(d) = d**2 - 6*d + 7. Let u(n) = -4*o(n) + 10*y(n). Let u(v) = 0. What is v?
3
Let h = 21 - 21. Suppose -4*q + 18 = -h*o - 5*o, 5*q + 3*o = 4. Determine x, given that -1/2 - 7/4*x - x**q + x**3 = 0.
-1/2, 2
Let f be 17 + (1 - -3) + -6. Suppose z + 5*g + f = 0, -2*z + g = 4*g + 9. Factor z*o**3 + 1/2*o**4 + 0*o**2 + 0 + 0*o.
o**4/2
Suppose 5*z = 49 - 9. Let t be ((-2)/z)/((-21)/24). What is b in -t*b**3 + 0*b**2 + 0 + 0*b**4 + 0*b + 2/7*b**5 = 0?
-1, 0, 1
Let i(v) be the first derivative of 0*v**2 - 4/9*v**3 - 3 + 0*v - 1/2*v**4 - 2/15*v**5. Factor i(l).
-2*l**2*(l + 1)*(l + 2)/3
Let i be 3/3 + (6 - 4). Suppose 0*t - 2/3*t**i - 1/3*t**4 + 0 - 1/3*t**2 = 0. Calculate t.
-1, 0
Let t(p) be the second derivative of -p + 0*p**2 - 1/18*p**4 - 1/60*p**5 + 0 - 1/18*p**3. Suppose t(d) = 0. What is d?
-1, 0
Let a be (-1)/(4 - 0) - (-39)/12. What is v in -1/4 - 1/4*v**5 - 5/4*v**4 - 5/2*v**a - 5/4*v - 5/2*v**2 = 0?
-1
Let w = -5 + 8. Let l(o) be the first derivative of 1/14*o**4 + 0*o**2 + 0*o + 2 + 0*o**w. Factor l(f).
2*f**3/7
Let d be 1/1 + 9/4. Let i = -5/2 + d. Factor 0 - 1/2*m + i*m**2 - 1/4*m**3.
-m*(m - 2)*(m - 1)/4
Let o be (-32)/(-7) - 128/32. Factor -2/7*k**5 + 6/7*k**3 + o*k + 10/7*k**2 - 2/7*k**4 + 0.
-2*k*(k - 2)*(k + 1)**3/7
Let f = 32 - 98/3. Let l = 1 + f. Factor l*g**2 + 0 + 2/3*g.
g*(g + 2)/3
Let m(h) be the first derivative of h**8/1680 + h**7/840 - h**6/180 + h**3 - 3. Let p(x) be the third derivative of m(x). Let p(u) = 0. What is u?
-2, 0, 1
Let q(a) = -2*a**2 - 8*a - 6. Let u(t) be the first derivative of 2*t**3/3 + 9*t**2/2 + 7*t + 1. Let v = -4 - -1. Let j(d) = v*q(d) - 2*u(d). Factor j(f).
2*(f + 1)*(f + 2)
Let o(n) be the first derivative of 2*n**3/27 + 2*n**2/3 - 40. Factor o(s).
2*s*(s + 6)/9
Suppose -2*f + 7 = 1. Factor 5 + 3*h - 5 - 6*h**2 + f*h**2.
-3*h*(h - 1)
Let s(t) be the third derivative of t**7/840 + t**6/480 - t**5/80 - t**4/96 + t**3/12 + 19*t**2. Find c, given that s(c) = 0.
-2, -1, 1
Let u(y) be the third derivative of -1/36*y**4 + 1/18*y**3 + 0 + 0*y + 5*y**2 + 1/180*y**5. Suppose u(q) = 0. What is q?
1
Let h(y) = 4*y**2. Let g(o) = o. Let f(z) = 16*g(z) + h(z). Find x, given that f(x) = 0.
-4, 0
Find m, given that -30*m - 9 - 36*m**2 - 55*m**4 + 106*m**4 - 18*m**3 - 54*m**4 = 0.
-3, -1
Factor 2 - 2*c**5 + 4*c**2 + 4*c**3 - 2*c**4 + 0*c**4 - 2*c - 4.
-2*(c - 1)**2*(c + 1)**3
Let u(a) be the second derivative of -a**7/8820 - a**6/2520 - a**4/4 + 4*a. Let p(q) be the third derivative of u(q). Determine i so that p(i) = 0.
-1, 0
Let j(c) = c**5 - 7*c**4 + 3*c**3 + 4*c**2 + 2*c. Let t(p) = 3*p**5 - 15*p**4 + 7*p**3 + 8*p**2 + 4*p. Let u(b) = -7*j(b) + 3*t(b). What is q in u(q) = 0?
-1, 0, 1
Factor i**3 - i**4 + 1/4*i**5 - 5/4*i + 1/2 + 1/2*i**2.
(i - 2)*(i - 1)**3*(i + 1)/4
Let c = 97 + -97. Solve c*p**2 + 0 + 0*p - 2/11*p**3 - 2/11*p**4 = 0 for p.
-1, 0
Let o be (-3)/3 + 1 - (-1)/6. Factor 1/6 + 1/6*i - o*i**3 - 1/6*i**2.
-(i - 1)*(i + 1)**2/6
Let p = -65 + 35. Let w be (-1)/(-3) - 5/p. Find d such that 0 + d - w*d**3 + 1/2*d**2 = 0.
-1, 0, 2
Let q(p) be the first derivative of -p**4/4 - p**3 - 6. Determine s, given that q(s) = 0.
-3, 0
Let i be 3/9 + 20/3. Let o be 3/i - (-133)/(-539). Factor 0 + 2/11*g**4 + 0*g + 0*g**2 - o*g**3.
2*g**3*(g - 1)/11
Let c = 42 + -38. Factor 54/5*k**4 + c*k + 2/5 + 72/5*k**2 +