4/3 - 74*f**3/3 - 233*f**2. Factor l(h).
-4*(h - 37)*(h - 1)
Let a(v) = -5*v**3 + 31*v**2 + 19*v - 45. Let n(x) = 2*x**3 - 10*x**2 - 6*x + 14. Let p(z) = -2*a(z) - 7*n(z). Factor p(j).
-4*(j - 2)*(j - 1)*(j + 1)
Suppose 0 = 2*t + 3*l + 9, 3*t - l - 21 = -18. Let c(p) be the second derivative of t + 4/3*p**3 - 1/3*p**4 + 4*p - 2*p**2. Factor c(a).
-4*(a - 1)**2
Factor 2*q + 0 + 2/7*q**3 - 16/7*q**2.
2*q*(q - 7)*(q - 1)/7
Let j(w) = w**3 + w**2 + w - 2. Let c(p) = 9*p**3 + 6*p**2 - 42*p - 12. Let s(m) = c(m) - 6*j(m). Factor s(g).
3*g*(g - 4)*(g + 4)
Let h(l) = -60*l - 64*l**2 - 17 + 14*l**3 - 7 + 6*l**3. Let r(m) = -m**3 + m**2 + m + 1. Let p(k) = h(k) + 24*r(k). Factor p(c).
-4*c*(c + 1)*(c + 9)
Let g = -6372 - -6377. Factor -3*j**3 - 1/2*j**g - 1/2*j + 0 + 2*j**2 + 2*j**4.
-j*(j - 1)**4/2
Solve 45/2 + 1/2*p**2 - 9*p = 0.
3, 15
Let a be (-250)/20*6/(-5). Suppose -5*p + 8*f = 5*f - a, 0 = -3*p + 5*f + 9. Let -2*r**5 + 2*r**4 - 8*r**4 + 3*r**3 - 2*r**3 - 5*r**p = 0. What is r?
-2, -1, 0
Let v(t) be the first derivative of 2*t**6/3 - 2*t**5/5 - 5*t**4/2 + 2*t**3/3 + 3*t**2 + 329. Solve v(s) = 0 for s.
-1, 0, 1, 3/2
Let q(k) = 4*k**2 + 19*k - 3. Let j be q(-5). Let p(s) be the second derivative of 0 + 0*s**2 + 0*s**3 + 1/20*s**4 + j*s. Find a such that p(a) = 0.
0
Let s(n) = -n**3 + 24*n**2 - n + 27. Let j be s(24). Factor -j*z + 5*z**2 + 2*z - 4*z.
5*z*(z - 1)
Solve -10/3*w**3 + 20/3 + 26/3*w - 2*w**2 + 2/3*w**4 = 0.
-1, 2, 5
Let c(m) be the third derivative of -2*m**7/315 - m**6/36 - m**5/30 + m**4/36 + m**3/9 + 110*m**2. Determine g so that c(g) = 0.
-1, 1/2
Let g(p) = p**3 + 13*p**2 - 14*p + 2. Let m be g(-14). Let 4/23*u**m + 2/23*u**3 - 4/23 - 2/23*u = 0. What is u?
-2, -1, 1
Let o(l) = 92*l**3 + 1146*l**2 + 2020*l + 966. Let t(s) = s**4 + 2*s + 1. Let m(f) = o(f) + 2*t(f). What is z in m(z) = 0?
-22, -1
Suppose 3*f = -2*b + 7*b - 44, -5*b + 5*f = -40. Let q be 2/b - (-8)/60. Suppose 0 - q*l + 1/3*l**2 = 0. Calculate l.
0, 1
Let z be 2/(-5) + 4472/11830. Let c = 164/819 - z. Let c + 2/9*x**2 - 4/9*x = 0. Calculate x.
1
Let g(t) be the second derivative of -t**7/14 - 7*t**6/2 - 99*t**5/10 + t**4/2 + 67*t**3/2 + 99*t**2/2 + 925*t. Factor g(n).
-3*(n - 1)*(n + 1)**3*(n + 33)
Suppose -4*j - 4 = 0, g - 6 = -g - 2*j. Let c(i) be the first derivative of -5 + 1/3*i**6 + 1/2*i**g + 0*i**2 + 0*i**3 + 0*i - 4/5*i**5. Solve c(f) = 0 for f.
0, 1
Let f(m) = 3*m**3 - 271*m**2 - 183*m + 87. Let j(q) = 15*q**3 - 1355*q**2 - 915*q + 433. Let a(o) = -11*f(o) + 2*j(o). Solve a(x) = 0.
-1, 1/3, 91
Find v such that -13/6*v - 5/2 + 1/2*v**2 + 1/6*v**3 = 0.
-5, -1, 3
Let b = 64 - 4. Let s = 64 - b. Factor -1/2*a**3 + 1/2*a**s + 0*a - 1/2*a**2 + 1/2*a**5 + 0.
a**2*(a - 1)*(a + 1)**2/2
Let g be (-2)/((-12)/7 - -2). Let f be (-4)/g*(-49)/(-14). Factor -4*a**3 + 2*a**3 + 3*a**3 + 0*a**2 + 2*a**f.
a**2*(a + 2)
Let i(d) be the second derivative of d**4/60 + d**3/30 - 3*d**2 - 9*d - 12. Find y, given that i(y) = 0.
-6, 5
Let m(v) be the third derivative of -5*v**8/336 + v**7/21 + v**6/24 - v**5/6 - 359*v**2. Let m(n) = 0. Calculate n.
-1, 0, 1, 2
Let r(u) be the third derivative of 0*u**4 + 0*u + 6*u**2 + 2/9*u**3 - 1/180*u**5 + 0. Factor r(f).
-(f - 2)*(f + 2)/3
Let r be ((-209)/(-8))/19 - (-2)/(-16). Let k(g) be the second derivative of 7/2*g**3 + 0 + 3*g**2 - 3*g + r*g**4. Let k(x) = 0. Calculate x.
-1, -2/5
Suppose 253*m = 256*m. Let n(t) be the second derivative of m*t**2 + 0 + 0*t**4 + 1/30*t**5 - 1/45*t**6 + 6*t + 0*t**3. Suppose n(x) = 0. What is x?
0, 1
Let p be (-4)/(-20) - 48/(-10). Suppose 5 - 37 = -4*q + 3*d, 40 = p*q - 3*d. Factor -3 - 25*i + 5 - q - 4 - 5*i**3 - 20*i**2.
-5*(i + 1)**2*(i + 2)
Let j(a) = -2*a**3 + 2*a**2 + 3*a. Let p be j(-2). Suppose p = 4*h + 6. Let 3*g**4 + g**2 + 6*g**3 - g**5 + 0*g**2 - 9*g**h = 0. Calculate g.
0, 1
Let m = 177 + -1055/6. Let l(d) be the third derivative of -4/3*d**3 - m*d**4 + 4/15*d**5 - d**2 + 0*d + 0. Determine j, given that l(j) = 0.
-1/4, 2
Let g be 7 - (87/21 - (-5)/(-35)). Let h be 94/18 - (-6)/(-27). Solve 3*b**5 - b**5 + b**h + b**g - 4*b**3 = 0.
-1, 0, 1
Let f(a) be the third derivative of -a**8/504 - a**7/63 - a**6/20 - 7*a**5/90 - a**4/18 - a**2 + 244*a. Factor f(r).
-2*r*(r + 1)**3*(r + 2)/3
Let q(d) be the third derivative of d**6/30 + d**5 - 8*d**4/3 + 9*d**2 + d. Factor q(n).
4*n*(n - 1)*(n + 16)
Let h(s) be the second derivative of -s**7/231 + 7*s**6/165 - s**5/11 - 10*s**4/33 + 56*s**3/33 - 32*s**2/11 + 13*s + 3. What is o in h(o) = 0?
-2, 1, 2, 4
Let p be (-6)/(720/76) - 6/(-9). Let q(u) be the third derivative of -10*u**2 + 1/525*u**7 + 1/150*u**6 - p*u**4 + 0*u**5 + 0 + 0*u - 1/15*u**3. Factor q(l).
2*(l - 1)*(l + 1)**3/5
Let m(j) be the second derivative of 1/12*j**4 - 35*j + 18*j**2 + 0 + 2*j**3. Factor m(p).
(p + 6)**2
Let q(y) = -8*y**2 - 33*y + 27. Let t(k) = k**2 + 3*k - 2. Let o(c) = -2*q(c) - 18*t(c). Factor o(x).
-2*(x - 3)**2
Let p(k) be the third derivative of -5*k**8/336 + k**7/42 + 29*k**6/24 - 15*k**5/4 - 45*k**4 + 360*k**3 + 140*k**2. Determine m so that p(m) = 0.
-4, 3
Suppose 6*u = 8 + 4. Suppose 2 + 2*p**2 + 9*p + p**u + 2 + 2 = 0. What is p?
-2, -1
Factor 28*b**4 + 2*b**5 - 7 + 1 - 22*b - 28*b**2 - 12*b**3 - 26*b**4.
2*(b - 3)*(b + 1)**4
Let g(l) be the first derivative of -l**5/30 - 5*l**4/24 - l**3/3 - 13. Find j such that g(j) = 0.
-3, -2, 0
Let h = -53 + 65. Factor -5*n**2 - h*n + 4*n**3 + 8*n**2 + 4*n + n**2.
4*n*(n - 1)*(n + 2)
Let r(v) be the third derivative of -v**6/30 + 44*v**5/15 - 242*v**4/3 + 9*v**2 + 6. Determine d so that r(d) = 0.
0, 22
Let w(r) be the first derivative of -9 + 0*r + 10/3*r**3 + 5/4*r**4 + 5/2*r**2. Let w(l) = 0. What is l?
-1, 0
Let x(o) = -2*o**2 + 33*o + 59. Let s be x(18). Suppose 0 = 2*b - f - 6, 4*b + s*f + 4 = b. Factor 8/7*p + 0 - 16/7*p**b - 2/7*p**4 + 10/7*p**3.
-2*p*(p - 2)**2*(p - 1)/7
Solve -1/2*x**4 + x**3 + 0*x - 1/2*x**2 + 0 = 0.
0, 1
Suppose 2/11*u**2 + 0 - 2/11*u**4 - 32/11*u**3 + 32/11*u = 0. What is u?
-16, -1, 0, 1
Let g(o) be the first derivative of o**4/12 + 40*o**3/9 + 77*o**2/6 + 38*o/3 - 251. Factor g(u).
(u + 1)**2*(u + 38)/3
Let l be 2/(-36)*(1 - 2). Let v(w) be the second derivative of 8/9*w**3 + 16/3*w**2 + 0 + l*w**4 + 7*w. Factor v(g).
2*(g + 4)**2/3
Let c(q) = -30*q**5 - 45*q**4 - 20*q**3 + 35*q**2 + 25*q + 10. Let n(f) = f**5 + f**4 - f**2. Suppose 0*w = -2*w - 50. Let b(o) = w*n(o) - c(o). Factor b(a).
5*(a - 1)*(a + 1)**3*(a + 2)
Find c, given that -7/4*c**3 - 34*c - 59/4*c**2 - 12 = 0.
-4, -3/7
Let p(u) be the third derivative of u**8/21 + 32*u**7/105 + 13*u**6/30 + u**5/5 - 5*u**2 - 3*u. Solve p(s) = 0.
-3, -1/2, 0
Let f = 2405 + -2403. Factor 0 + 1/3*y + 1/3*y**f.
y*(y + 1)/3
Suppose -60 = -a - 5*a. Let 4*x**5 - 13*x**4 - 3*x**4 - a - 20*x**3 + 10 = 0. Calculate x.
-1, 0, 5
Let k(i) = -15*i**4 - 60*i**2 - 120*i - 20. Let h(b) = -b**4 - 2*b - 1. Let d(o) = 20*h(o) - k(o). Let d(j) = 0. What is j?
-2, 0, 4
Let w be 1 - (2 - 3)*5. Factor 4 + 12*g**2 - 2*g**3 - 2*g**3 - 18*g + w*g.
-4*(g - 1)**3
Suppose -m + 7 = 4. Factor -20*b + 21*b**2 + 12*b**m + 50*b - 3 - 24*b.
3*(b + 1)**2*(4*b - 1)
Suppose -2*v + 16 = 2*v. Factor 6*l + 3*l**2 + l**v + l**2 - 6*l**3 - 41 + 36.
(l - 5)*(l - 1)**2*(l + 1)
Let y(u) be the second derivative of -u**5/30 - 7*u**4/9 - 25*u**3/9 - 4*u**2 - 4*u - 5. Factor y(d).
-2*(d + 1)**2*(d + 12)/3
Suppose 6*k**4 + 32*k - 13*k**4 + 14*k**2 + 10*k**2 + 5*k**4 + 0*k**4 = 0. What is k?
-2, 0, 4
Let a(f) be the second derivative of -f**9/45360 - f**8/10080 + f**7/7560 + f**6/1080 - 5*f**4/6 + 6*f. Let z(v) be the third derivative of a(v). Factor z(m).
-m*(m - 1)*(m + 1)*(m + 2)/3
Suppose 13*w - 30*w - 12*w + 87 = 0. Factor -2/9*m**w + 2/9*m - 2/3*m**2 + 2/3.
-2*(m - 1)*(m + 1)*(m + 3)/9
Let n(q) be the third derivative of q**5/690 - 37*q**4/46 + 4107*q**3/23 - 343*q**2. Factor n(u).
2*(u - 111)**2/23
Let t(j) = j**4 + j**3. Let c(y) be the first derivative of 3*y**5/5 + y**4 + 6. Let p(x) = -2*c(x) + 7*t(x). Factor p(n).
n**3*(n - 1)
Let c(r) = 3*r**3 - 4*r**2 - 5*r + 5. Let y be c(2). Determine q so that 2/7*q**4 + 0*q**y + 0*q - 10/7*q**2 + 8/7 = 0.
-2, -1, 1, 2
Let t(y) be the third derivative of -3*y**6/80 + 7*y**5/5 - 33*y**4/4 + 16*y**3 + 27*y**2. Suppose t(i) = 0. What is i?
2/3, 2, 16
F