*4/20 - 4*a**3/5 + 6*a**2/5 - a. Factor o(m).
3*(m - 1)*(m + 2)*(3*m - 2)/5
Factor -3/2 + 1/3*d**2 + 2/3*d**3 - 2*d - 1/6*d**4.
-(d - 3)**2*(d + 1)**2/6
Let w(h) be the first derivative of 4/3*h**2 - 7/18*h**3 - 1 - 2/3*h. Determine c so that w(c) = 0.
2/7, 2
Let z(k) = 7*k**4 + 6*k**3 - 4*k. Let l(h) = -h**4 + h. Let s(w) = -4*l(w) - z(w). Suppose s(q) = 0. Calculate q.
-2, 0
Let f(r) be the third derivative of r**8/1344 + r**7/210 + r**6/80 + r**5/60 + r**4/96 - 9*r**2. Factor f(v).
v*(v + 1)**4/4
Let j(r) be the third derivative of r**8/504 + r**7/315 - r**6/180 - r**5/90 - 4*r**2. Factor j(a).
2*a**2*(a - 1)*(a + 1)**2/3
Let v(b) be the second derivative of -b**7/840 + b**6/180 - b**3/6 + 10*b. Let h(d) be the second derivative of v(d). Factor h(c).
-c**2*(c - 2)
Factor 0*o**2 - 6*o - 3*o**4 + o**3 + 5*o**3 - o**2 + 4*o**2.
-3*o*(o - 2)*(o - 1)*(o + 1)
Let n = -69 - -277/4. Determine h, given that -n*h**2 - 1/2*h + 0 = 0.
-2, 0
Let r(b) = -b + 8. Let v be r(5). Let q(o) be the third derivative of 0*o - 1/15*o**5 - o**2 + 1/6*o**v + 0 - 1/8*o**4. Suppose q(w) = 0. Calculate w.
-1, 1/4
Let l be (-1)/(-6) - 22/(-12). Determine y so that -8/7 + 4*y - 20/7*y**l = 0.
2/5, 1
Suppose 0 = 2*k + 5*z - 18, -27 = 3*k - 6*k - 5*z. Suppose -q = 0, -3*r = -4*q + 6*q - k. Factor -o + 2 - 2*o**r + 6*o**2 - 3*o - 2*o.
-2*(o - 1)**3
Let s(r) = r**2 + 4*r - 11. Let j be s(-6). Let w be j + 8/20 + -1. Factor -2/5*t + 4/5*t**2 - w*t**3 + 0.
-2*t*(t - 1)**2/5
Factor -6/5*j**3 - 18/5*j**2 + 24/5 + 0*j.
-6*(j - 1)*(j + 2)**2/5
Let u = -17 + 21. Let a(q) be the first derivative of 2/9*q**3 + 1/6*q**u + 1 + 0*q - 2/15*q**5 - 1/3*q**2. Find b, given that a(b) = 0.
-1, 0, 1
Factor 0*f + 0 + 2/7*f**3 + 0*f**2 - 2/7*f**4.
-2*f**3*(f - 1)/7
Let o(m) = -m + 3. Let l be o(-7). Suppose 2*a + 0*w - l = 2*w, 22 = 5*a - 2*w. Solve -r**3 + a - r**3 + 6*r + 0 = 0.
-1, 2
Let f = -126048 + 2647496/21. Let n = f + -68/3. Factor -2/7*b**2 + n*b**3 - 4/7*b + 2/7.
2*(b - 1)*(b + 1)*(2*b - 1)/7
Let j(o) be the first derivative of o**6/42 - 4*o**5/35 + o**4/28 + 2*o**3/3 - 10*o**2/7 + 8*o/7 - 14. Let j(r) = 0. Calculate r.
-2, 1, 2
Let v be -3*((-15)/9)/1. Suppose 0 = 2*w - 3 - v. Factor -8/5*t - 6/5*t**2 + 8/5 + 4/5*t**3 + 2/5*t**w.
2*(t - 1)**2*(t + 2)**2/5
Factor -1/2*f + 1/4*f**2 + 1/4.
(f - 1)**2/4
Factor 4/15*u + 0 + 2/15*u**3 + 2/5*u**2.
2*u*(u + 1)*(u + 2)/15
Let p(w) be the second derivative of -w**5/10 - w**4/8 + 3*w**3/4 - w**2/2 + w - 1. Factor p(q).
-(q - 1)*(q + 2)*(4*q - 1)/2
Let c(a) be the second derivative of 1/30*a**5 - 1/45*a**6 - a + 0*a**2 + 0*a**3 + 0*a**4 + 0. Let c(p) = 0. Calculate p.
0, 1
Let v(b) be the first derivative of -22/3*b**3 - 7*b**2 - 13*b + 2. Let x(a) = -15*a**2 - 9*a - 9. Let o(l) = 5*v(l) - 7*x(l). What is n in o(n) = 0?
-1, -2/5
Factor 27/5*y**2 - 21/5*y - 3*y**3 + 6/5 + 3/5*y**4.
3*(y - 2)*(y - 1)**3/5
Find p such that -2*p**2 - 5*p**2 - 24*p + 11*p**2 + 36 = 0.
3
Suppose 4*y = -5*v, 0 = -6*v + v. Factor 2*z**3 + y*z**2 + 2*z**2 + 0 + 0.
2*z**2*(z + 1)
Let w(u) = -u**4 + 7*u**3 - 5*u**2 - 2*u + 6. Let t(j) = -j**3 + j**2 - 1. Let g(c) = 5*t(c) + w(c). Factor g(l).
-(l - 1)**3*(l + 1)
Suppose 18 = -w + 4*d, 4*d = d + 12. Let q be (7 - w)/(-3) + 6. Solve -6*p**3 + 4*p**3 - 2*p**2 - p - 3*p**3 + 4*p**q = 0 for p.
-1, 0
Let f(t) be the third derivative of 4*t**2 - 1/60*t**5 + 0 - 3/2*t**3 + 0*t + 1/4*t**4. Find g, given that f(g) = 0.
3
Suppose 0*i + 21 = 3*i. Suppose i = 3*v + 1. Let 2/3*u + 1/3 + 1/3*u**v = 0. What is u?
-1
Let n(b) = -b**4 - 7*b**3 - 13*b**2 + 15*b - 6. Let x(q) = -2*q**4 - 20*q**3 - 38*q**2 + 45*q - 18. Let v(g) = -11*n(g) + 4*x(g). Determine l so that v(l) = 0.
-2, 1
Let i(g) be the third derivative of g**6/360 - g**4/24 + g**3/2 - 4*g**2. Let n(d) be the first derivative of i(d). Factor n(s).
(s - 1)*(s + 1)
Determine s so that 1/6*s**3 - 2/3 - 2/3*s + 1/6*s**2 = 0.
-2, -1, 2
Let x(n) = 117*n**4 - 172*n**3 + 68*n**2 - 3*n. Let m(c) = c**4 + c. Let p(d) = -5*m(d) + x(d). Suppose p(l) = 0. What is l?
0, 1/4, 2/7, 1
Let y(o) be the second derivative of o**6/10 - 3*o**5/10 + o**4/4 + 3*o. Factor y(t).
3*t**2*(t - 1)**2
Solve -2*k**2 - 12*k + 9*k**2 - 4*k**3 + 9*k**2 - 4*k**2 + 4 = 0 for k.
1
Let a(j) be the third derivative of -j**6/30 - j**5/15 + j**4/6 + 2*j**3/3 + 4*j**2. Factor a(b).
-4*(b - 1)*(b + 1)**2
Let p(u) be the third derivative of u**7/147 - u**6/35 + 3*u**5/70 - u**4/42 + u**2. Determine d so that p(d) = 0.
0, 2/5, 1
Let x be 5/(-2)*(-4)/5. Suppose p**3 + 2*p**4 - 2 + p**5 + x = 0. What is p?
-1, 0
Let r(v) be the third derivative of -v**8/1344 + v**7/420 - v**6/480 + 11*v**2. Factor r(s).
-s**3*(s - 1)**2/4
Let z(b) = 5*b**2 - 8*b - 15. Let l(r) = 4*r**2 - 8*r - 14. Let i(h) = -7*l(h) + 6*z(h). Factor i(c).
2*(c + 2)**2
Let k(n) be the third derivative of 1/4*n**5 - 2*n**3 + 1/4*n**4 + 0 + 3/80*n**6 + 2*n**2 + 0*n. Determine j, given that k(j) = 0.
-2, 2/3
Let b = -486/55 - -150/11. Let d(m) be the first derivative of -b*m**5 - 1 + 8/3*m**6 + 23/3*m**3 + m - 9/2*m**2 - 7/4*m**4. Let d(k) = 0. What is k?
-1, 1/4, 1
Factor 2/5*v + 8/5*v**2 - 4/15 + 14/15*v**3.
2*(v + 1)**2*(7*v - 2)/15
Let c = -25 + 13. Let g be c/24*(-1)/2. Factor 0 + 1/4*n**2 - g*n.
n*(n - 1)/4
Let g(j) be the third derivative of j**8/2520 + 4*j**7/1575 + j**6/225 - j**5/225 - j**4/36 - 2*j**3/45 - j**2. Determine h so that g(h) = 0.
-2, -1, 1
What is s in -10*s**2 + 8*s - 8 + s**3 + 8*s + s**3 = 0?
1, 2
Factor 14*k**2 + 2/7 + 4*k.
2*(7*k + 1)**2/7
Let m(n) be the second derivative of -5/84*n**7 + 0*n**5 + 0*n**4 + 0*n**2 - 1/30*n**6 + 0*n**3 + 7*n + 0. Factor m(g).
-g**4*(5*g + 2)/2
Let n(l) be the first derivative of -4/9*l**3 + 2/3*l - 1/9*l**6 + 2/15*l**5 + 1/3*l**4 - 1 - 1/3*l**2. Factor n(b).
-2*(b - 1)**3*(b + 1)**2/3
Suppose -2*z + 6*f + 16 = f, 7 = 3*z + f. Let h(b) be the second derivative of -1/3*b**2 + b + 0 - 1/18*b**4 + 2/9*b**z. Let h(m) = 0. What is m?
1
Find d such that 393*d + 221*d + 584*d + 4*d**3 + 830*d + 8788 + 156*d**2 = 0.
-13
Let f(j) be the third derivative of -j**9/60480 + j**8/26880 - j**4/4 + 5*j**2. Let b(r) be the second derivative of f(r). Determine s, given that b(s) = 0.
0, 1
Let q(s) be the third derivative of s**8/3360 - s**7/2520 - s**5/30 - 2*s**2. Let c(f) be the third derivative of q(f). Factor c(p).
2*p*(3*p - 1)
What is p in -8*p**2 + 32*p**2 - 6*p**2 + 16*p - 14*p**2 = 0?
-4, 0
Let p = 29 - 25. Let s(t) be the second derivative of -1/10*t**5 - 5/6*t**p - 4*t**2 - 8/3*t**3 + 0 - 3*t. What is q in s(q) = 0?
-2, -1
Let j be (-2)/(-8) - 14/(-8). Solve q - 4*q - 3 + 5*q + 2*q**j - 1 = 0 for q.
-2, 1
Let l(y) = y - 15. Let q be l(12). Let s be q + 0 + 143/26. What is d in -1/2*d**3 + 1 + 3/2*d**2 - 1/2*d**4 + s*d = 0?
-1, 2
Suppose 0 = -3*w + 5*b - 1, 4*b - 14 = -5*w + 9. Suppose 2*a = h + 5, -3*a + 4*a = 5*h - 2. What is s in 2*s - s**5 + a*s**5 + 1 - 1 - 4*s**w = 0?
-1, 0, 1
Let n = -6/31 + 91/310. Let v(t) be the second derivative of 1/21*t**4 + n*t**5 + 0*t**3 + 0 + t + 1/21*t**6 + 0*t**2. Determine i, given that v(i) = 0.
-1, -2/5, 0
Solve 0 + 0*b**3 + 0*b + 0*b**2 - 1/4*b**5 - 1/4*b**4 = 0 for b.
-1, 0
Let k = 35/6 + -31/6. Let d(h) be the first derivative of 1/3*h**2 + 4/9*h**3 - k*h - 2/15*h**5 + 4 + 1/9*h**6 - 1/3*h**4. Factor d(t).
2*(t - 1)**3*(t + 1)**2/3
Let v(p) be the third derivative of 0*p**4 + 0*p + p**2 + 1/150*p**5 + 0*p**3 + 0 + 1/300*p**6. Factor v(t).
2*t**2*(t + 1)/5
Let u(s) be the third derivative of s**7/189 - 13*s**6/540 - s**5/45 + 40*s**2. Let u(o) = 0. Calculate o.
-2/5, 0, 3
Solve -11 + 13 - 6 + 0*g - 2*g**2 - 6*g = 0 for g.
-2, -1
Let v be 44/(-24)*(-144)/352. Solve 5/4*a**3 + 0 + 0*a + v*a**2 = 0 for a.
-3/5, 0
Let i(r) be the second derivative of r**3/6 - r**2 - 4*r. Let h be i(4). Factor 1/2*t**h + 1/2*t - 1/2*t**3 - 1/2.
-(t - 1)**2*(t + 1)/2
Let x = -270 + 270. Solve 0*h**3 - 3/2*h**4 + 0*h + x + 3/2*h**2 = 0 for h.
-1, 0, 1
Let o(g) = -g**3 + 9*g**2 - 9*g - 9. Let j(k) = k**3 - 5*k**2 + 5*k + 5. Let y(x) = 5*j(x) + 3*o(x). Solve y(c) = 0.
-1, 1
Let u(q) be the first derivative of -7*q**5/5 - 9*q**4/4 + 4*q**3 + 2*q**2 - 35. Let u(x) = 0. Calculate x.
-2, -2/7, 0, 1
Let o(k) be the first derivative of -k**5/10 + k**4/6 - 2*k - 3. Let w(n) be the first derivative of o