 second derivative of -1/8*k**4 + 3/4*k**2 + 0 + 2*k + 0*k**3. Factor b(y).
-3*(y - 1)*(y + 1)/2
Let q(t) = -t**2 + 8*t + 2. Let d be q(8). Factor 0*s - 3 + 6*s**3 - 3*s**5 - 3*s**4 - 5*s + 5*s**d + 2*s + s**2.
-3*(s - 1)**2*(s + 1)**3
Let d be 1 - 0 - (-1)/(-1). Let o(n) be the second derivative of d*n**6 + 0*n**2 - 1/126*n**7 + 0*n**4 + 0 + 0*n**5 + 0*n**3 + n. Factor o(a).
-a**5/3
Let t(b) be the first derivative of b**4/16 - 5*b**3/12 + 7*b**2/8 - 3*b/4 - 25. Factor t(c).
(c - 3)*(c - 1)**2/4
Let m(g) be the second derivative of 1/30*g**4 + 4*g + 1/15*g**3 + 0*g**2 + 0. Determine f so that m(f) = 0.
-1, 0
Let o(l) be the third derivative of -l**3 - 1/30*l**5 + 0*l + 0 + 7*l**2 + 1/3*l**4. Factor o(q).
-2*(q - 3)*(q - 1)
Let t be ((-1)/(-7))/(384/63 + -6). Suppose -15/4*v - t - 3/4*v**3 - 3*v**2 = 0. What is v?
-2, -1
Let n(c) = 40*c**2 + 92*c + 48. Let m(t) = -13*t**2 - 31*t - 16. Let g(z) = -16*m(z) - 5*n(z). Factor g(v).
4*(v + 4)*(2*v + 1)
Let q(n) = -5*n + 15. Let z(u) = u**2 + 1. Let t(f) = -q(f) + 15*z(f). Let t(l) = 0. What is l?
-1/3, 0
Let c(l) = -4*l**4 + 9*l**3 - l**2 + 7*l. Let r = 43 + -29. Let p(u) = -u**4 + 3*u**3 + 2*u. Let i(k) = r*p(k) - 4*c(k). Factor i(s).
2*s**2*(s + 1)*(s + 2)
Let z(x) = -4*x**3 - 5*x**2 - 4*x - 13. Let t(l) = 3*l**3 + 6*l**2 + 3*l + 12. Let f(w) = 3*t(w) + 2*z(w). Let s be f(-8). Factor -3/2 + 0*j + 3/2*j**s.
3*(j - 1)*(j + 1)/2
Let n = -29 - -41. Let j be (-1)/(-4)*16/n. Factor 0*a**2 - j + 1/3*a**4 - 2/3*a + 2/3*a**3.
(a - 1)*(a + 1)**3/3
Let z(q) be the second derivative of -7*q**4/6 - 8*q**3/5 - 4*q**2/5 - 5*q. Determine s, given that z(s) = 0.
-2/5, -2/7
Let z(y) be the first derivative of -y**5/5 - y**4/4 - 4. Let z(i) = 0. What is i?
-1, 0
Let c(m) be the third derivative of 1/3*m**4 + 1/15*m**5 + 7*m**2 + 0*m + 0 + 2/3*m**3. What is i in c(i) = 0?
-1
Factor 0 - a + 1/3*a**3 + 2/3*a**2.
a*(a - 1)*(a + 3)/3
Let m(v) be the third derivative of -v**4/24 + 2*v**2. Let l(j) = 2*j**2 + 4*j - 4. Let s(c) = l(c) + 2*m(c). Suppose s(a) = 0. Calculate a.
-2, 1
Let p(w) = 3*w**2 - 18*w - 18. Let m(r) = -2*r**2 + 17*r + 17. Let v(k) = 6*m(k) + 5*p(k). Solve v(l) = 0 for l.
-2
Let s(n) = 51*n**5 - 60*n**4 + 21*n**3 + 81*n**2 - 9*n. Let u(l) = 5*l**5 - 6*l**4 + 2*l**3 + 8*l**2 - l. Let o(b) = -2*s(b) + 21*u(b). Factor o(k).
3*k*(k - 1)**3*(k + 1)
Let b(t) be the second derivative of -t**6/80 + 3*t**5/40 - 5*t**4/32 + t**3/8 + 24*t. Factor b(c).
-3*c*(c - 2)*(c - 1)**2/8
Let t(u) = u**3 - 5*u**2 - u. Let y(s) = -10*s**2 + 14*s. Let l(h) = 2*h**2 - 3*h. Let c(z) = -14*l(z) - 3*y(z). Let f(q) = 5*c(q) + 2*t(q). Factor f(p).
2*p*(p - 1)*(p + 1)
Let r(l) be the third derivative of -l**9/181440 + l**7/15120 - l**5/60 + 4*l**2. Let d(z) be the third derivative of r(z). Factor d(y).
-y*(y - 1)*(y + 1)/3
Let m(z) = z**2 + 4*z**2 - 5*z + 2 - 4*z**2. Let h be m(5). What is d in -6 + 2*d + 2 + 0*d + 2*d**h = 0?
-2, 1
Suppose r = -3*r + 3*u + 28, -3*u - 32 = -5*r. Suppose h - 7 = -r. Factor 3*t**5 - 3*t**2 - 6*t**4 + t**4 + 4*t**4 - 3*t**h + 4*t**4.
3*t**2*(t - 1)*(t + 1)**2
Let n = -51 + 103/2. Solve -1/2 - b - n*b**2 = 0 for b.
-1
Let k(u) = -3*u - 6. Let r(g) = g + 1. Let n(m) = k(m) + 4*r(m). Let y be n(5). Let 2*z**4 - 3*z - 2*z**2 - 2*z + 2*z**y + 3*z = 0. Calculate z.
-1, 0, 1
Let g(c) = -16*c**5 + 4*c**4 + 22*c**3 + 2*c**2 + 4*c - 16. Let u(t) = -5*t**5 + t**4 + 7*t**3 + t**2 + t - 5. Let r(m) = -6*g(m) + 20*u(m). Factor r(n).
-4*(n - 1)**2*(n + 1)**3
Let w(a) be the first derivative of 8*a**2 - 14/5*a**5 + 15*a**4 - 1 - 24*a**3 + 0*a. Factor w(g).
-2*g*(g - 2)**2*(7*g - 2)
What is z in 12/5*z - 9/5*z**3 + 3/5*z**5 + 0 - 6/5*z**4 + 12/5*z**2 = 0?
-1, 0, 2
Let w = -27 - -27. Factor -8/3*r + 56/3*r**2 + w - 98/3*r**3.
-2*r*(7*r - 2)**2/3
Let t(v) be the first derivative of -v**8/168 - v**7/105 + v**6/60 + v**5/30 + 2*v**2 - 1. Let i(b) be the second derivative of t(b). Factor i(n).
-2*n**2*(n - 1)*(n + 1)**2
Solve -6/5*y**2 - 6/5*y**3 - 2/5*y - 2/5*y**4 + 0 = 0 for y.
-1, 0
Suppose 2*p - f = -23 - 2, -4*p - 5*f - 85 = 0. Let r = p - -17. Determine s, given that -2/11*s**3 + 2/11*s**r + 0*s + 0 = 0.
0, 1
Let x(v) be the second derivative of 1/9*v**3 - 5*v + 0 - 1/6*v**2 - 1/36*v**4. Factor x(i).
-(i - 1)**2/3
Suppose -4*z + 4*x + 10 = -z, -2 = z + 4*x. Factor 18/5*q**z - 3/5*q**3 - 27/5*q + 0.
-3*q*(q - 3)**2/5
Let t(d) be the first derivative of -1/2*d**3 - 3/2*d**2 + 3/2*d**4 - 3 + 0*d + 9/10*d**5. Suppose t(h) = 0. What is h?
-1, 0, 2/3
Let w(k) be the second derivative of k**5/420 - k**4/168 - k**3/21 + 3*k**2/2 - 5*k. Let i(r) be the first derivative of w(r). Factor i(t).
(t - 2)*(t + 1)/7
Let w(m) be the third derivative of -1/112*m**8 + 0*m + 1/10*m**5 - 1/35*m**7 + 0*m**3 + 0*m**6 + 0 + m**2 + 1/8*m**4. Suppose w(n) = 0. Calculate n.
-1, 0, 1
Let g = 12 + -2. Let p(h) = 18*h**3 + 60*h**2 + 51*h + 16. Let v(w) = -9*w**3 - 30*w**2 - 25*w - 8. Let b(y) = g*v(y) + 6*p(y). Let b(z) = 0. Calculate z.
-2, -2/3
Suppose -2*f - 24 = -3*k - 0*f, 5*f = 4*k - 39. Suppose -4*j = k*l - l - 5, 3*l + 4*j - 3 = 0. Factor 0 - 2*a + 2*a**2 + 3*a**2 - 6*a**2 - l.
-(a + 1)**2
Let l(s) = 5*s**3 - 56*s**2 + 68*s - 18. Let a(c) = -c**3 + c. Let n(r) = -22*a(r) + 2*l(r). Solve n(v) = 0 for v.
3/4, 2
Let u(r) be the third derivative of -r**8/616 - r**7/231 + 7*r**6/660 + 3*r**5/110 - r**4/33 - 4*r**3/33 + 26*r**2. Find p such that u(p) = 0.
-2, -1, -2/3, 1
Factor -3*n**2 - 9/4*n + 3/4.
-3*(n + 1)*(4*n - 1)/4
Let s(p) = 16*p**2 - 20*p - 20. Let o(b) = -b**2 + b + 1. Let k(d) = 20*o(d) + s(d). Suppose k(r) = 0. What is r?
0
Let k(d) be the third derivative of -d**8/1008 + d**7/105 - d**6/30 + 2*d**5/45 + 8*d**2. Factor k(t).
-t**2*(t - 2)**3/3
Let 2/7*c**3 - 72/7 + 48/7*c + 22/7*c**2 = 0. Calculate c.
-6, 1
Suppose -5*l = 5*s + 10, 5*l = 3*s - 4*s + 6. Find o such that 0*o + 1/3*o**l + 0 - 1/3*o**5 + 1/3*o**3 - 1/3*o**4 = 0.
-1, 0, 1
Let k = -226 - -685/3. Suppose -2*d - 16 = 2*g - 6*g, 5*d = -20. Factor 2/3 + 20/3*a**3 + k*a**g - 11/3*a.
(a + 1)*(4*a - 1)*(5*a - 2)/3
Let l = -25/2 + 13. Suppose -3*h + 16 = -4*u, u - 2*u - 4 = -h. Let 0*d + 1/2*d**2 + 0 - l*d**4 + h*d**3 = 0. What is d?
-1, 0, 1
Let t(v) be the first derivative of 0*v**3 + 1/21*v**4 + 0*v**2 + 2 - 2*v + 1/70*v**5. Let o(h) be the first derivative of t(h). Factor o(y).
2*y**2*(y + 2)/7
Let p = -80 + 904/11. Determine k, given that -10/11*k**2 + 18/11*k**4 - 8/11 - 24/11*k + p*k**3 = 0.
-1, -2/3, 1
Let y = 3 - 0. Suppose 0 = -3*d - 5*f - 4, 0*d - y*d - f = -4. Factor -b**5 + 2*b**d + 0*b - 2*b**4 + 2*b - b.
-b*(b - 1)*(b + 1)**3
Let r(b) = 11*b**4 + 29*b**2 - 23. Suppose 68 = -5*a + a. Let f(m) = 4*m**4 + 10*m**2 - 8. Let z(p) = a*f(p) + 6*r(p). What is q in z(q) = 0?
-1, 1
Let l = -300 + 302. Suppose -4/7*c**l - 8/7 + 12/7*c = 0. What is c?
1, 2
Let t = -95 - -97. Solve 1/4*b**3 + 1/4*b**4 + 0*b + 0 + 0*b**t = 0.
-1, 0
Let p be ((-4)/9)/(13/(-39)). Solve -4/3 - p*r - 1/3*r**2 = 0 for r.
-2
Let d(v) be the second derivative of v**4/9 + v**3/27 - 2*v**2/9 + 9*v. Factor d(h).
2*(2*h - 1)*(3*h + 2)/9
Let h(a) be the second derivative of -a**4/42 - 4*a**3/21 - 4*a**2/7 + a. Factor h(k).
-2*(k + 2)**2/7
Determine t, given that -9*t**2 + 0*t**2 - t**3 + 4*t**3 + 3*t**2 = 0.
0, 2
Let g(v) = -5*v**3 - 10*v**2 + 5*v + 4. Let f(m) = m**3 + m**2 - 1. Let k(b) = 6*f(b) + g(b). Factor k(s).
(s - 2)*(s - 1)**2
Let j(z) be the first derivative of 2/5*z**5 + 0*z**3 - 1 + 0*z + 0*z**2 + 0*z**4. Let j(i) = 0. What is i?
0
Suppose -10 = 5*k, -5*k - 16 = -2*a + 4*a. Let j = a + 6. Factor 0*w**3 - w**2 - w**j - 2 + w + 3.
-(w - 1)*(w + 1)**2
Suppose 16 = -3*w - 14. Let r be 12 + -10 + w/6. Suppose -r*f**2 - 4/3*f - 4/3 = 0. What is f?
-2
Suppose -c = -23 + 23. Find b such that c + 2/5*b**2 - 1/5*b**3 + 0*b = 0.
0, 2
Let k(m) be the first derivative of -8*m**5/5 - m**4 + 13*m**3/2 - 17*m**2/4 + m - 24. What is u in k(u) = 0?
-2, 1/4, 1
Let i(b) be the third derivative of b**6/660 - 3*b**2. What is v in i(v) = 0?
0
Let o(p) be the third derivative of p**7/15120 - p**5/720 + p**4/24 - 4*p**2. Let y(v) be the second derivative of o(v). Factor y(g).
(g - 1)*(g + 1)/6
Let y = -78 - -238/3. Let b(o) be the first derivative of -1 - 13/3*o**2 + 14/15*o**5 - 23/6*o**4 + y*o + 6*o**3. Determine j,