2*w + 2*w**3 + u.
2*(w - 1)*(w + 1)*(3*w - 1)/3
Let r = 638/7 + -90. Find w such that 4*w**2 + r*w + 0 = 0.
-2/7, 0
Let f(m) be the third derivative of -m**6/24 - 4*m**5/3 - 40*m**4/3 + 2*m**2 - 46*m. Solve f(c) = 0.
-8, 0
Let g(c) = -c**4 + 19*c**3 + 46*c**2 + 26*c - 6. Let s(a) = 15*a**4 - 265*a**3 - 645*a**2 - 365*a + 85. Let w(l) = 85*g(l) + 6*s(l). Factor w(i).
5*i*(i + 1)*(i + 2)**2
Let i = 8 - 6. Suppose 0*y = -i*y + 8. Factor -7*j**2 + 3*j**2 + j**y + 2 + j**4.
2*(j - 1)**2*(j + 1)**2
Let r(h) be the third derivative of -h**8/672 + h**7/210 + h**6/80 - h**5/30 - h**4/12 + h**2. Factor r(x).
-x*(x - 2)**2*(x + 1)**2/2
Let g(x) be the third derivative of -7*x**6/240 + x**5/10 - x**4/16 - x**3/6 + 9*x**2. Factor g(h).
-(h - 1)**2*(7*h + 2)/2
Let r(b) be the second derivative of -b**7/14 - b**6/5 + b**4/2 + b**3/2 + 19*b. Factor r(y).
-3*y*(y - 1)*(y + 1)**3
Suppose 6*n - 2*t = 3*n + 13, 0 = -3*t + 3. Let y(c) be the first derivative of 3 + 1/15*c**6 + 0*c**n - 1/10*c**4 + 0*c**2 + 0*c**3 + 0*c. Solve y(u) = 0.
-1, 0, 1
Let r(a) = a**2 + a + 6. Let s be r(0). Let n = s - 4. Solve -5*q**2 + n*q + 2*q**3 + 9*q**2 + 0*q**3 = 0 for q.
-1, 0
Let f(a) be the third derivative of a**6/45 + 13*a**5/300 + a**4/30 + a**3 - a**2. Let n(l) be the first derivative of f(l). Suppose n(v) = 0. Calculate v.
-2/5, -1/4
Let w(u) = u**2 + 2*u + 5. Let n be w(-5). Suppose 18*k - 18*k**3 - 6 + n*k**4 - 6*k**4 - 10*k**2 + 2 = 0. What is k?
-1, 2/7, 1
Let q(r) = r. Let k(m) = 4*m**2 - 3*m - 1. Let w(p) = -k(p) - 6*q(p). Let l(f) = -f**2 - f. Let i(y) = 5*l(y) - w(y). Solve i(a) = 0 for a.
-1
Let m be 2 + (-4)/6 + -1. Let s(t) be the first derivative of 0*t**2 - 1/9*t**3 + m*t - 1. Let s(d) = 0. Calculate d.
-1, 1
Suppose -s = -3 - 3. Factor x**2 + 2*x + 0*x**2 + 3*x - s*x.
x*(x - 1)
Let q(g) be the second derivative of g**9/15120 - g**7/1260 + g**5/120 - g**4/6 + 2*g. Let d(v) be the third derivative of q(v). Factor d(a).
(a - 1)**2*(a + 1)**2
Let l(b) be the second derivative of b**4/36 + b**3/18 - b**2/3 + 4*b. Factor l(j).
(j - 1)*(j + 2)/3
Suppose 2*f + 9 = -5*o, -14 = 5*o + 1. Let s = f - 1. Find b, given that -3*b**4 - 4*b**3 + 2*b**3 + 6*b**2 + 8*b + b**4 + 4 + s*b = 0.
-1, 2
Let p(n) be the second derivative of 11*n**4/3 - 40*n**3/3 - 8*n**2 - 2*n - 7. Factor p(r).
4*(r - 2)*(11*r + 2)
Suppose 2/7*r**2 + 0*r - 3/7*r**3 + 1/7*r**5 + 0 + 0*r**4 = 0. Calculate r.
-2, 0, 1
Let r(g) be the third derivative of g**8/10080 + g**7/630 + g**6/90 + g**5/6 + 7*g**2. Let o(a) be the third derivative of r(a). Factor o(h).
2*(h + 2)**2
Let c = 96 + -478/5. Let -c*m**2 + 0*m + 0 + 2/5*m**3 = 0. What is m?
0, 1
Factor 4*c**2 - 2*c - 4*c + c + c.
4*c*(c - 1)
Let s(p) be the first derivative of -p**9/9072 + p**8/5040 + 2*p**3/3 - 5. Let m(z) be the third derivative of s(z). Factor m(f).
-f**4*(f - 1)/3
Let q(w) be the second derivative of w**6/30 - w**4/4 - w**3/3 - 2*w. Factor q(t).
t*(t - 2)*(t + 1)**2
Let r(y) = -2*y**5 - 9*y**4 + 4*y**3 - 3*y**2 - 5. Let h(z) = 3*z**5 + 9*z**4 - 3*z**3 + 3*z**2 + 6. Let l(q) = 5*h(q) + 6*r(q). Factor l(a).
3*a**2*(a - 1)**3
Let p(s) be the first derivative of -s**6/4 + 3*s**5/10 + 3*s**4/8 - s**3/2 + 8. Factor p(r).
-3*r**2*(r - 1)**2*(r + 1)/2
Let q(f) be the first derivative of f**3/3 - f - 11. Factor q(u).
(u - 1)*(u + 1)
Let y(f) = -f**3 - 8*f**2 - 9*f + 2. Let t(g) = -g**2 - g + 1. Let n(m) = 20*t(m) - 5*y(m). Factor n(s).
5*(s + 1)**2*(s + 2)
Let j be -3 - (27/(-12))/((-45)/(-96)). Factor j*x**2 - 2/5*x + 24/5*x**3 + 0 - 112/5*x**4.
-x*(4*x - 1)**2*(7*x + 2)/5
Let c(b) be the third derivative of b**9/5040 - b**7/420 + b**5/40 + b**4/12 - 3*b**2. Let p(o) be the second derivative of c(o). Determine i so that p(i) = 0.
-1, 1
Let n(g) = g**2 - 3*g + 12. Let s(z) = -2*z**2 + 7*z - 23. Let y(a) = -5*n(a) - 3*s(a). Factor y(u).
(u - 3)**2
Let p = -526 - -1055/2. Suppose -3*k**3 + 3*k**4 - 3 + p*k**5 - 21/2*k - 12*k**2 = 0. Calculate k.
-1, 2
Let t be 2 - 6 - (-14)/2. Let r(a) be the third derivative of 0*a**4 + 1/45*a**6 + 0*a + 0 - 2/45*a**5 + 0*a**t + 3*a**2 - 1/315*a**7. Solve r(m) = 0.
0, 2
Let i(s) = s**4 - 4*s**3 + s**2 + 2*s - 2. Let o(d) = -5*d**4 + 17*d**3 - 4*d**2 - 8*d + 9. Let v(q) = 9*i(q) + 2*o(q). Determine h so that v(h) = 0.
-2, -1, 0, 1
Let y(u) = -u - 1. Let x(n) = -n**2 - 15*n - 22. Let d(z) = 5*x(z) - 35*y(z). Let d(a) = 0. Calculate a.
-5, -3
Suppose 0 = -2*x + 5*x. Let y(h) be the third derivative of x*h - 1/240*h**6 + 0*h**4 + 2*h**2 + 0 - 1/120*h**5 + 0*h**3. Factor y(r).
-r**2*(r + 1)/2
Let s be 8 + (-3)/15*0. Suppose 0 = y + 4 - s. Determine o, given that -1/2*o - o**y + 0 + 1/2*o**3 + o**2 = 0.
-1, 0, 1/2, 1
Let f be 0/((-4)/(-6)*(-2 - 1)). Factor -1/4*t**3 + 0*t + f*t**2 + 1/4*t**4 + 0.
t**3*(t - 1)/4
Let k = 3 - 7. Let n = 4 + k. Find o, given that -2/3*o**3 + n - 4/3*o**2 - 2/3*o = 0.
-1, 0
Let d(a) be the second derivative of -a**8/1680 - a**7/280 - a**6/180 + 2*a**3/3 - 3*a. Let w(m) be the second derivative of d(m). Let w(k) = 0. What is k?
-2, -1, 0
Let w(r) = -2*r. Let b be w(-12). Suppose -d + 3*n + 9 = 0, 4*d + 2 = 5*n + b. Factor 2/9*y**2 - 2/9*y**4 + 0 + 0*y + 0*y**d.
-2*y**2*(y - 1)*(y + 1)/9
Determine j, given that -4*j**3 + j**4 - 2*j + 20*j**3 - 14*j**3 - j**2 = 0.
-2, -1, 0, 1
Find g such that 2/7*g**2 - 6/7*g**3 + 0*g + 0 - 10/7*g**5 - 18/7*g**4 = 0.
-1, 0, 1/5
Let z = -196 + 1374/7. Solve 2/7*g + z*g**2 + 0 = 0.
-1, 0
Suppose 0 = -3*q + 14 - 2. Suppose l - 6 - 2 = 0. Suppose -4*u - 10*u**3 + 2*u**3 - 4*u + l*u**2 + 4*u**2 + 2 + 2*u**q = 0. Calculate u.
1
Factor 2/11*u**3 - 2/11*u + 4/11 - 4/11*u**2.
2*(u - 2)*(u - 1)*(u + 1)/11
Suppose -4*u + 5 = -3*u, -5 = 2*p - 3*u. Let l = p - 1. Let 0*h**4 - 2*h**l - 2*h**2 + 11*h**3 - 7*h**3 = 0. Calculate h.
0, 1
Let z(g) = g**4 - g**3 - g. Let a(t) = 21*t**4 - 24*t**3 - 12*t - 3. Let w(k) = a(k) - 18*z(k). Suppose w(l) = 0. What is l?
-1, 1
Let c(y) be the third derivative of y**6/150 - 4*y**5/75 + 2*y**4/15 - 6*y**2. Suppose c(o) = 0. Calculate o.
0, 2
Factor 8*v**2 + 5*v**3 + 4 - 4*v**3 + v**3 + 2*v + 8*v.
2*(v + 1)**2*(v + 2)
Let q(z) = 3*z**5 + z**4 - 5*z**3 - z**2 + 4*z - 1. Let i(s) = s**4 + s**3 - s**2 + s - 1. Let d(l) = -i(l) + q(l). Factor d(f).
3*f*(f - 1)**2*(f + 1)**2
Suppose -4*k + 4*d = -2*k + 24, -4*d = 2*k + 56. Let p = k + 22. Factor -8*q - 75/4*q**3 - 85/4*q**p - 1.
-(3*q + 1)*(5*q + 2)**2/4
Let h(u) be the second derivative of -2025*u**7/7 + 594*u**6 - 2556*u**5/5 + 2152*u**4/9 - 592*u**3/9 + 32*u**2/3 + 27*u. What is n in h(n) = 0?
2/9, 2/5
Let u = -9734/3 + 3217. Let l = u - -28. Suppose -4/3 - 4/3*c - l*c**2 = 0. What is c?
-2
Let o(s) be the third derivative of -s**5/240 + s**4/8 - 3*s**3/2 + 20*s**2. Solve o(b) = 0.
6
Let p = 216 + -2374/11. Let b = 739/11 + -67. Solve b*s**3 + 0 + 0*s**2 - p*s = 0 for s.
-1, 0, 1
Let g be 1/2*(2 - 2). Suppose 0 = -g*i + 3*i. Factor 2/5*z**5 + 0 + 0*z + i*z**3 + 0*z**2 - 2/5*z**4.
2*z**4*(z - 1)/5
Let z be 0/(8 + 0) - -2. Determine w, given that 15/4*w**z - 9/4*w - 3/2 = 0.
-2/5, 1
Suppose 2/5*i**3 - 4/5 - 2/5*i + 4/5*i**2 = 0. Calculate i.
-2, -1, 1
Let y(w) be the third derivative of 4/25*w**5 + 0*w + 0*w**3 - 1/420*w**8 - 2/15*w**4 - 9*w**2 - 13/150*w**6 + 4/175*w**7 + 0. Factor y(z).
-4*z*(z - 2)**2*(z - 1)**2/5
Suppose 0 = 2*u + 2*j - 12 + 4, u - 8 = -3*j. What is l in 0*l + 0 + 1/3*l**3 - 1/3*l**u = 0?
0, 1
Let x(k) be the third derivative of -2*k**5/45 + 5*k**4/36 - k**3/9 + k**2. Factor x(j).
-2*(j - 1)*(4*j - 1)/3
Suppose -z - 2 = -0*z, 5*z = s - 10. Let y(q) be the second derivative of 1/12*q**3 + q + 1/24*q**4 + s - 1/2*q**2. Let y(f) = 0. Calculate f.
-2, 1
Factor -2/3 + 2/15*n**2 + 8/15*n.
2*(n - 1)*(n + 5)/15
Let g(b) be the third derivative of -b**6/360 - b**5/60 + b**4/18 + 11*b**2. Factor g(y).
-y*(y - 1)*(y + 4)/3
Let r(y) = -3*y**3 - 2*y**3 + 2*y**3 - 6*y. Let p(l) = -2*l**3 + 4*l**3 - 5*l - 4*l**3. Let q(j) = 6*p(j) - 5*r(j). Suppose q(x) = 0. What is x?
0
Let w = -7 + 9. Suppose -9*b = -w*b. Find x such that b + 0*x + 1/4*x**2 + 1/4*x**3 = 0.
-1, 0
Let v = 696 + -3478/5. Factor -2/5*j + v*j**4 + 0 - 6/5*j**3 + 6/5*j**2.
2*j*(j - 1)**3/5
Let l be -8 + -5 + (-7 - -22). Factor 1 + 1/2*a**3 - 3/2*a + 0*a**l.
(a - 1)**2*(a + 2)/2
Let l(c) be the second derivative of -c**6/