*r - 3/5*r**5. Factor c(z).
-3*(z + 1)**2*(z + 3)**2
Let l(n) be the second derivative of -n**5/20 - n**4/6 + n**3/6 + n**2 - 4*n. Factor l(x).
-(x - 1)*(x + 1)*(x + 2)
Factor -1/4*t + 1/4*t**2 + 0.
t*(t - 1)/4
Let o = 196 - 119. Factor -2*k**2 - 4*k**3 - k**4 - o - k**4 + 77.
-2*k**2*(k + 1)**2
Factor 5*q**3 + 4*q**2 - 45*q + 25 - 10*q**2 + 6*q**2 + 15*q**2.
5*(q - 1)**2*(q + 5)
Let m = -992/3 - -335. Let j = m - 85/21. Let 2/7*y**2 + 0*y + j*y**3 + 0 = 0. What is y?
-1, 0
Let h(r) be the first derivative of -1/18*r**3 + 1/6*r**2 - 1/6*r - 2. Let h(p) = 0. Calculate p.
1
Suppose -2*l + 3*x = -5, -x = -5*l - 2*x + 21. Suppose 0*d + 0 + 1 + l*d + 1 + 2*d**2 = 0. What is d?
-1
Let x(q) be the third derivative of -q**7/3360 - q**6/480 - q**5/240 + q**3/2 + 4*q**2. Let v(i) be the first derivative of x(i). Factor v(n).
-n*(n + 1)*(n + 2)/4
Suppose 5*h - 4*h = -1. Let o be -3 + (7 - 3) + h. Factor 2/7*n**3 + 4/7*n**2 + o + 2/7*n.
2*n*(n + 1)**2/7
Factor -3*p**2 + 24 + 9*p - 12 + 0.
-3*(p - 4)*(p + 1)
Factor 4/7*i + 2/7*i**4 + 0*i**2 - 2/7 - 4/7*i**3.
2*(i - 1)**3*(i + 1)/7
Let i(v) be the second derivative of -v**6/6 + v**5/4 + 5*v**4/4 - 25*v**3/6 + 5*v**2 + 16*v. Factor i(r).
-5*(r - 1)**3*(r + 2)
Let c(z) be the second derivative of z**5/60 + z**4/18 - z**3/18 - z**2/3 + 2*z - 4. Factor c(f).
(f - 1)*(f + 1)*(f + 2)/3
Let x(v) be the second derivative of -v**5/20 - v**4/2 - v**3/6 - 3*v**2/2 - 4*v. Let f be x(-6). Factor -2/7 - 2/7*u**4 + 4/7*u**2 + 0*u**f + 0*u.
-2*(u - 1)**2*(u + 1)**2/7
Let w(i) = -4*i**3 + i**2 - 13*i - 7. Let s(o) = 5*o**3 - o**2 + 14*o + 6. Let k(b) = -5*s(b) - 6*w(b). Solve k(p) = 0 for p.
-2, 3
Let q = 205/618 - -1/618. Let t be 0 - ((-4)/3 + 1). Factor f - q + t*f**3 - f**2.
(f - 1)**3/3
Let d be (0/(5 - (3 - -1)))/(-2). Let l(z) be the first derivative of 0*z + 3 + 2*z**2 + 2/5*z**5 - 2*z**3 + d*z**4. Factor l(i).
2*i*(i - 1)**2*(i + 2)
Let h(y) be the first derivative of -y**6/12 - 4*y**5/5 - 5*y**4/2 - 5*y**3/3 + 21*y**2/4 + 9*y + 26. Suppose h(s) = 0. What is s?
-3, -2, -1, 1
Find j, given that 12*j**3 + 4*j**4 + 8*j**2 - 76*j + 76*j = 0.
-2, -1, 0
Let r be ((-4)/(-14))/(27/(-42)). Let o = r - -17/18. Factor 1/2*h - 1 + o*h**2.
(h - 1)*(h + 2)/2
Let l(h) = -2*h - 10. Let r = 1 + -8. Let z be l(r). Factor 16*a**2 - 23*a**3 + 2*a + 32*a**z + 71*a**3 + 2*a**2.
2*a*(a + 1)*(4*a + 1)**2
Let r(d) be the second derivative of d**8/36960 + d**7/13860 - d**4/6 + 3*d. Let v(c) be the third derivative of r(c). Let v(n) = 0. Calculate n.
-1, 0
Let w(g) = g**2 - g - 14. Let k be w(0). Let n be 5/(-15) - k/6. Let -3*f**n + 0*f**2 + 5 + 0*f**2 - 2 = 0. What is f?
-1, 1
Let d(m) be the first derivative of m**6/120 + m**5/20 + m**4/8 + 2*m**3/3 + 5. Let q(v) be the third derivative of d(v). Factor q(w).
3*(w + 1)**2
Let i(y) = y**3 + 6*y**2 - 3*y - 4. Let w(x) = x**3 - 1. Let m(d) = -i(d) + 4*w(d). Factor m(f).
3*f*(f - 1)**2
Let f(g) be the first derivative of 4*g**3/3 + 24*g**2 - 52*g - 5. Solve f(o) = 0 for o.
-13, 1
Let j = 12 - 8. Suppose -r - j*r = 15. Let l(b) = 3*b**5 - b**4 - 4*b**3 + 6*b**2 + b - 2. Let f(o) = -o**4. Let i(x) = r*f(x) - l(x). Factor i(y).
-(y - 1)**3*(y + 1)*(3*y + 2)
Let t(w) be the first derivative of 4*w**3/3 + 14*w**2 + 40*w - 31. Let t(l) = 0. What is l?
-5, -2
Let j(c) be the first derivative of -4*c**3/3 + 8*c**2 - 12*c + 5. Factor j(t).
-4*(t - 3)*(t - 1)
Let x(f) = -6*f**3 + 19*f**2 - 16*f - 8. Let r(v) = 18*v**3 - 58*v**2 + 48*v + 24. Let j(k) = -3*r(k) - 8*x(k). Factor j(q).
-2*(q - 2)**2*(3*q + 1)
Suppose -2*d = -d + 3*u - 17, -4*d - u + 112 = 0. Let a = d + -13. What is g in -24*g - a*g**2 - 3 + 6*g**2 - 5 - 8*g**2 = 0?
-2/3
Let q be (-18)/4 + 6/(-12). Let u(c) = 0*c + 11*c - 5*c**2 - 3*c. Let r(j) = 5*j**2 - 8*j + 1. Let s(x) = q*u(x) - 4*r(x). Factor s(t).
(t - 2)*(5*t + 2)
Let o = -1036 + 1995/2. Let j = 39 + o. Find h, given that -j*h**2 + h - h**3 - 1/4 + 3/4*h**4 = 0.
-1, 1/3, 1
Solve 40*w**3 - 3*w**4 + 40*w + 23*w**4 - 20*w + 40*w**2 + 4*w**5 + 4 = 0.
-1
Let w(l) be the third derivative of 1/70*l**5 + 0*l**4 - 1/280*l**6 + 0*l**3 + 0*l + 0 - 6*l**2. Factor w(n).
-3*n**2*(n - 2)/7
Suppose -t - 2*t + 15 = 0, 5*i = 2*t + 50. Factor -11*z**5 + z**4 + i*z**5 + z**4 + z**3.
z**3*(z + 1)**2
Let y = 2226 - 33356/15. Let q = -118/105 + y. Factor q + 2/7*l**2 - 8/7*l.
2*(l - 2)**2/7
Let m = -40/153 - -63/17. Let o = -28/9 + m. Find c, given that -o*c**3 + 0 + 4/3*c**4 + 0*c + 0*c**2 = 0.
0, 1/4
Find j such that 25 + 3*j**5 + 9*j**3 - 12*j + 19*j**4 - 12*j**2 - 7*j**4 - 25 = 0.
-2, -1, 0, 1
Let w(s) = s**2 + s. Let b(i) = -4*i**2 - 7*i - 4. Let g be 87/(-12) - (-2)/8. Let z = g + 9. Let r(k) = z*b(k) + 6*w(k). Factor r(p).
-2*(p + 2)**2
Let l = 7772/11 - 708. Let o = l - -75/44. Factor -s**3 - o*s + s**2 + 0.
-s*(2*s - 1)**2/4
Let r(x) be the first derivative of -x**5/90 + 7*x**4/54 - 5*x**3/9 + x**2 - 3*x - 1. Let o(w) be the first derivative of r(w). Factor o(l).
-2*(l - 3)**2*(l - 1)/9
What is r in 1/3*r**4 - 8/3 - r**3 + 4*r - 2/3*r**2 = 0?
-2, 1, 2
Suppose -32/9 + 64*v**3 - 256/9*v - 18*v**4 - 368/9*v**2 = 0. Calculate v.
-2/9, 2
Let o(z) be the first derivative of z**3/24 - 3*z**2/4 + 9*z/2 + 13. Factor o(b).
(b - 6)**2/8
Let -16/5 - 4/5*l**2 + 16/5*l = 0. What is l?
2
Let c(g) be the first derivative of g**3/24 - g**2/2 + 7*g/8 + 33. Determine t so that c(t) = 0.
1, 7
Find q, given that 11 + 15*q**2 - 1 - 25*q + 0 = 0.
2/3, 1
Suppose -w + 2*d = 8, 3*w - d + 4 = 6*w. Factor -1/5*i**2 + w + 2/5*i.
-i*(i - 2)/5
Let q(g) be the third derivative of g**8/60480 - g**7/15120 - g**6/1080 - g**5/60 - g**2. Let c(w) be the third derivative of q(w). Factor c(f).
(f - 2)*(f + 1)/3
Suppose j - 2 = 2. Let x(a) be the first derivative of 1/5*a**5 - 1/3*a**3 + 0*a + 1/4*a**2 + 0*a**j - 1/12*a**6 + 2. Determine f, given that x(f) = 0.
-1, 0, 1
Find q such that 800/7*q**4 - 250/7*q**5 - 48/7 + 328/7*q + 30/7*q**3 - 92*q**2 = 0.
-1, 2/5, 3
Let r = 13 + -7. Factor -5*t**3 + 6*t + t**4 + 7*t**4 + t**2 - r*t - 4*t**5.
-t**2*(t - 1)*(2*t - 1)**2
Let p = 1 + -7. Let a be p/(-5)*30/9. Solve y - y**5 - 2*y**4 + 10*y**2 - 4*y**2 - a*y**2 = 0.
-1, 0, 1
Determine d so that 2*d**3 + 2*d + 2*d**2 - 6*d**3 - 2 - d**3 + 3*d**3 = 0.
-1, 1
Let s(x) be the first derivative of -x**9/16632 + x**8/4620 - x**7/4620 + 2*x**3/3 - 1. Let t(k) be the third derivative of s(k). Solve t(b) = 0.
0, 1
Let w(f) be the second derivative of f**7/3360 - f**5/480 + 5*f**3/6 - f. Let h(m) be the second derivative of w(m). Suppose h(u) = 0. What is u?
-1, 0, 1
Let s be ((-11)/22*0)/(-2). Find r such that 4/3*r**3 - 4/3*r + 2/3*r**4 + s - 2/3*r**2 = 0.
-2, -1, 0, 1
Let h(g) be the second derivative of 0*g**5 + 1/9*g**4 + 0*g**2 - 1/63*g**7 - 2/45*g**6 + 0 + 1/9*g**3 - 3*g. Factor h(c).
-2*c*(c - 1)*(c + 1)**3/3
Let m(z) be the first derivative of z**5/75 + z**4/40 - z**3/30 + z**2 + 3. Let p(a) be the second derivative of m(a). Suppose p(l) = 0. What is l?
-1, 1/4
Let p = -29 - -29. Factor -1/3*v**5 - 1/3*v**4 + p + 1/3*v**3 + 0*v + 1/3*v**2.
-v**2*(v - 1)*(v + 1)**2/3
Let u = 154 + -1384/9. Determine c so that -2/9 + 4/9*c - u*c**2 = 0.
1
Let g(n) be the third derivative of 0*n + 0*n**4 - n**2 + 0 + 2/3*n**3 - 1/15*n**5. Factor g(j).
-4*(j - 1)*(j + 1)
Suppose 0 = -7*d + 2*d + 20. Let q(p) = -7*p**2 - 12*p - 12. Let a(h) = -6*h**2 - 12*h - 12. Let o(i) = d*a(i) - 3*q(i). Factor o(k).
-3*(k + 2)**2
Let q(a) be the third derivative of a**8/504 + a**7/630 - 24*a**2. Factor q(c).
c**4*(2*c + 1)/3
Let m(u) be the first derivative of u**6/1440 - u**5/80 + 3*u**4/32 - 2*u**3/3 + 2. Let a(g) be the third derivative of m(g). Let a(v) = 0. What is v?
3
Let b(v) be the third derivative of -v**7/1260 - v**6/180 + 5*v**4/24 + v**2. Let f(u) be the second derivative of b(u). Determine p, given that f(p) = 0.
-2, 0
Let r(u) = u**3 + u**2 - u + 1. Let i(m) = m**3 + 5*m**2 - 3*m + 3. Let s(z) = -i(z) + 3*r(z). Factor s(j).
2*j**2*(j - 1)
Factor 0 - 6/7*i**3 + 2/7*i**2 + 6/7*i - 2/7*i**4.
-2*i*(i - 1)*(i + 1)*(i + 3)/7
Let p = -27/7 + 289/35. Factor 32/5*k**2 - 38/5*k**3 - k**5 - 13/5*k + 2/5 + p*k**4.
-(k - 1)**4*(5*k - 2)/5
Let v(c) = -c**2 + 4*c. Suppose 21 = b + b - 5*f, b = 5*f + 18. Let z be v(b). Factor 1/2*o**4 + 0*o + 0*o**z + 0 + 0*o**2 + 1/2*o**5.
o