. Let b(h) be the third derivative of m(h). Factor b(q).
-q*(q - 1)**2*(q + 1)
Let w = 8 - 3. Let 0 - 3 + 5*o**w + 9*o**3 - 12*o**4 - 2*o**2 + 3 = 0. Calculate o.
0, 2/5, 1
Solve -1/5*w**2 + 1/5*w + 0 = 0 for w.
0, 1
Factor 5*l**3 - 3*l - 2*l**3 + 9*l**2 - 12*l**3 + 3*l**4.
3*l*(l - 1)**3
Let d = 11 - 7. Find p, given that 16*p**3 + 9 - 25 + 3*p**4 - 16*p + 12*p**2 + p**d = 0.
-2, -1, 1
Let g = 734/45 - 136/9. Factor 6/5*f**3 + 2/5*f**4 - g*f - 4/5 + 2/5*f**2.
2*(f - 1)*(f + 1)**2*(f + 2)/5
Let o be 80/(-1064) - 8/(-28). Solve -o*x**3 + 0 + 6/19*x**2 + 4/19*x = 0.
-1/2, 0, 2
Let u(o) be the first derivative of 2*o**3/15 - 16*o**2/5 + 128*o/5 + 6. Determine g, given that u(g) = 0.
8
Determine s, given that 2/5*s**2 + 0 + 0*s = 0.
0
Suppose k = 6*k - 2*o - 12, -2*k + 8 = -4*o. Find s such that 2*s + 0*s - 3*s**2 + s**k = 0.
0, 1
Let k(s) = -15*s**4 - 15*s**3 + 45*s**2 + 8*s - 37. Let b(y) = -5*y**4 - 5*y**3 + 15*y**2 + 3*y - 12. Let t(h) = 7*b(h) - 2*k(h). Factor t(l).
-5*(l - 1)**2*(l + 1)*(l + 2)
Let d = -12 + 18. Suppose -5*p + d = -4. What is c in -2/7*c**p + 0 + 2/7*c = 0?
0, 1
Suppose -23*n - 11 = -11. Let r(g) be the third derivative of 1/120*g**6 + 0*g - 1/12*g**4 + 0 + n*g**3 + g**2 - 1/60*g**5. Let r(d) = 0. Calculate d.
-1, 0, 2
Let i(h) = -6*h + 0*h + 1 + 5*h. Let u(b) = -b**3 + 3*b**2 - 5*b + 3. Let j(y) = 4*i(y) - 2*u(y). Factor j(v).
2*(v - 1)**3
Suppose 0 = -4*b + 5*a - 9 + 89, 5*a = 0. Suppose 5*z - b = 3*n, n = z - 3 - 1. Determine x, given that 5*x - 3*x - z + 4 + 2*x**2 = 0.
-1, 0
Factor -12*u - 2*u**3 + 8 + 4*u**2 + u**3 + 4*u**2 - 2*u**2.
-(u - 2)**3
Suppose -5 = -26*y + 25*y. Let n(u) be the second derivative of 0 - 3*u + 3/80*u**y + 0*u**2 + 0*u**3 + 1/16*u**4. Suppose n(m) = 0. Calculate m.
-1, 0
Let t(s) be the second derivative of -2/9*s**3 + 0 - 7*s + 1/3*s**2 + 0*s**4 + 1/15*s**5 - 1/45*s**6. Suppose t(u) = 0. What is u?
-1, 1
Let c(r) = 10*r**3 - 16*r**2 + 6*r + 5. Let x(v) = -v**3 + v**2 + 1. Let j(s) = -c(s) + 5*x(s). Let j(p) = 0. What is p?
0, 2/5, 1
Let x = 19729/7590 + 1/1518. Factor -x*u**3 - 2/5 - 28/5*u**2 - 17/5*u.
-(u + 1)**2*(13*u + 2)/5
Suppose -3*s + 4*m + 4 = -1, -2*s - 4*m + 10 = 0. Factor 3 + 10*b**s - 6 - 1 + 18*b - 24*b**2.
2*(b - 1)**2*(5*b - 2)
Let v = -11/6 + 53/24. Let k(c) be the second derivative of 1/16*c**4 + 0 + c + 3/4*c**2 - v*c**3. Suppose k(o) = 0. Calculate o.
1, 2
Let q(m) = m**2 - 1. Let a(l) = 4*l**2 + 7*l - 15. Let j(f) = a(f) - 5*q(f). Let k(s) = s - 1. Let p(z) = j(z) - k(z). Factor p(y).
-(y - 3)**2
Let z = -2 - -5. Let r(d) be the third derivative of 2*d**2 + 0*d**5 + 0*d**4 + 0*d**z + 1/480*d**6 + 0 + 0*d. Find a such that r(a) = 0.
0
Let l(i) be the third derivative of 1/84*i**8 + 0*i**7 + i**2 + 0*i**5 + 0*i**3 + 0 + 1/6*i**4 - 1/15*i**6 + 0*i. Suppose l(m) = 0. What is m?
-1, 0, 1
Suppose -3*b - 3 = -15. Suppose 5*z = b*z + 2. Factor z*k**3 - 4*k + k**4 + 5*k - k**2 - 3*k**3.
k*(k - 1)**2*(k + 1)
Let h = 2 + 0. Let n be h/4*(-15 + -5). Let o(i) = 4*i**3 + i**2 + 3. Let s(d) = -7*d**3 - 2*d**2 - 5. Let g(r) = n*o(r) - 6*s(r). Suppose g(c) = 0. What is c?
-1, 0
Suppose 2*q + q = 45. Let w = q + -10. Factor 0*r**2 - 4 + r - 2*r**2 + w*r + 0*r**2.
-2*(r - 2)*(r - 1)
Let i = 254/7 + -36. Factor -2/7*u**3 + 0 - 4/7*u**2 - i*u.
-2*u*(u + 1)**2/7
Suppose 5*k - 10*k**4 + 11*k + 0*k - 14*k**2 - 20*k - 2*k**5 - 18*k**3 = 0. What is k?
-2, -1, 0
Let m(k) be the second derivative of -k**6/24 + k**5/10 - k**4/48 - k**3/12 - k. Factor m(t).
-t*(t - 1)**2*(5*t + 2)/4
Factor -9*r**3 + 5 - 3 - 3*r**4 - 2.
-3*r**3*(r + 3)
Let i(f) be the second derivative of -f**5/20 + f**4/9 - f**3/18 + 6*f. Suppose i(l) = 0. What is l?
0, 1/3, 1
Suppose 6*g = -256 + 268. Suppose 2/5*l + 0 + 6/5*l**3 - 2*l**g - 8/5*l**5 + 2*l**4 = 0. What is l?
-1, 0, 1/4, 1
Let 13*p**2 - 6*p**2 - 8 - 11*p**2 + 2*p - 14*p = 0. Calculate p.
-2, -1
Let f(t) = -t. Let v be f(-3). Suppose -2 + 8 = v*k. Determine o so that 4/7*o**4 + 2/7*o**5 + 2/7*o**3 + 0 + 0*o + 0*o**k = 0.
-1, 0
Let k(d) be the third derivative of d**5/20 - d**4/4 - 3*d**3/2 + 6*d**2. Factor k(s).
3*(s - 3)*(s + 1)
Let b(f) be the first derivative of -14*f**6/3 - 24*f**5 - 50*f**4 - 160*f**3/3 - 30*f**2 - 8*f + 1. Let b(d) = 0. Calculate d.
-1, -2/7
Let d = -35/17 + 540/221. Let y = d + -2/39. Factor 0 + y*i - 1/6*i**4 - 1/3*i**3 + 1/6*i**2.
-i*(i - 1)*(i + 1)*(i + 2)/6
Factor 0 + 24/7*w**4 + 0*w**2 + 12/7*w**3 - 15/7*w**5 + 0*w.
-3*w**3*(w - 2)*(5*w + 2)/7
Factor -44/7*i + 96/7*i**2 - 12/7*i**5 - 104/7*i**3 + 8/7 + 8*i**4.
-4*(i - 1)**4*(3*i - 2)/7
Let n = -2 + 5. Suppose -2*f + 4 = -n*y - 0, -3*y - 6 = -3*f. Find p, given that 7/4*p**f - 1/2 - 5/4*p = 0.
-2/7, 1
Let o(h) be the first derivative of h**3/3 + 3*h**2/2 + 1. Solve o(f) = 0.
-3, 0
Let i(g) = -3*g**2 - 5*g + 4. Let o(a) = 5*a**2 + 9*a - 7. Let w(v) = -7*i(v) - 4*o(v). Factor w(y).
y*(y - 1)
Let z(v) be the second derivative of 2*v**6/15 + 40*v. Factor z(w).
4*w**4
Suppose 0 = -3*j + 70 - 70. Factor 0 - 2/7*r**3 + j*r**2 + 2/7*r.
-2*r*(r - 1)*(r + 1)/7
Let a(r) = r**2 + r + 1. Let c(w) = -16*w**3 + 46*w**2 + 14*w + 2. Let d(t) = -2*a(t) + c(t). Determine y, given that d(y) = 0.
-1/4, 0, 3
Let p(t) be the first derivative of -1/4*t**4 + 1/2*t**2 - t + 1/3*t**3 - 7. Let p(s) = 0. Calculate s.
-1, 1
Let i(p) be the third derivative of -p**5/20 + p**3/2 - 5*p**2. Suppose i(v) = 0. Calculate v.
-1, 1
Let l(t) be the first derivative of -2*t**3/9 + 6*t - 37. Factor l(x).
-2*(x - 3)*(x + 3)/3
Factor -2/7*a**3 - 18/7*a - 8/7 - 12/7*a**2.
-2*(a + 1)**2*(a + 4)/7
Solve -25/4*n**4 + 5/2*n + 5/4*n**5 + 45/4*n**3 + 0 - 35/4*n**2 = 0.
0, 1, 2
Let c(z) be the second derivative of -z**6/90 + z**5/15 - z**4/12 - 2*z**3/9 + 2*z**2/3 + 22*z. Let c(q) = 0. What is q?
-1, 1, 2
Let q(c) be the second derivative of 81*c**7/14 + 117*c**6/10 - 123*c**5/20 - 113*c**4/4 - 20*c**3 - 6*c**2 - 12*c. Determine x so that q(x) = 0.
-1, -2/9, 1
Let f(b) = -19*b**5 + 6*b**4 - 7*b**3 - 19*b**2 - 13. Let r(m) = 9*m**5 - 3*m**4 + 3*m**3 + 9*m**2 + 6. Let t(z) = 6*f(z) + 13*r(z). Factor t(j).
3*j**2*(j - 1)**2*(j + 1)
Let l be ((32/(-12))/4)/(2/(-9)). Suppose 1/2*n - 3/4*n**l + 0 + 3/4*n**2 - 1/2*n**4 = 0. Calculate n.
-2, -1/2, 0, 1
Suppose 0 = -114*u + 107*u. Factor 4/3*y**2 - 1/3*y**3 + u - 4/3*y.
-y*(y - 2)**2/3
Suppose -48 = -5*s - 18. Let u(w) be the second derivative of -2*w + 1/75*w**s + 0 + 0*w**2 - 1/25*w**5 + 1/30*w**4 + 0*w**3. Solve u(n) = 0 for n.
0, 1
Suppose -3*q + 3*q + 5*q = 0. Let b(g) be the second derivative of -2/5*g**2 + q - 2/15*g**3 - 1/60*g**4 - g. What is s in b(s) = 0?
-2
Let o(a) be the second derivative of a**2 - 1/2*a**3 + 0 + 1/20*a**5 + 3*a + 0*a**4. Factor o(p).
(p - 1)**2*(p + 2)
Let p = 6 + -1. Suppose -p*v = -v. Find w such that 0*w**2 + 0 + 1/2*w + v*w**4 - w**3 + 1/2*w**5 = 0.
-1, 0, 1
Let x(f) = f**3 + 9*f**2 - 15*f + 5. Let p(l) = -2*l**3 - 8*l**2 + 14*l - 4. Let g(r) = -3*p(r) - 4*x(r). Suppose g(t) = 0. What is t?
1, 4
Let z = 160 - 160. Factor 2/7*w**2 + 2/7*w + z.
2*w*(w + 1)/7
Let d(x) be the second derivative of 15*x**7/77 + x**6/55 - 3*x**5/55 - 22*x. Factor d(b).
6*b**3*(3*b - 1)*(5*b + 2)/11
Let h(k) be the first derivative of 3*k**5/35 + 2*k**4/7 + k**3/3 + k**2/7 + 2. Factor h(f).
f*(f + 1)**2*(3*f + 2)/7
Let o(r) be the first derivative of r**7/105 - r**6/25 + 2*r**4/15 - 8*r + 6. Let v(p) be the first derivative of o(p). Determine n so that v(n) = 0.
-1, 0, 2
Let w(q) = -6*q - 6. Let s be w(-1). Factor -2*t**3 + 0*t + 4/3*t**2 + s + 2/3*t**4.
2*t**2*(t - 2)*(t - 1)/3
Suppose 65 - 71 = -3*t + 3*p, -5*p = -3*t + 10. Factor 3*r + t - 3/2*r**2.
-3*r*(r - 2)/2
Let z(y) be the second derivative of -7*y**4/102 + 3*y**3/17 - 2*y**2/17 + 4*y. Factor z(f).
-2*(f - 1)*(7*f - 2)/17
Factor 2/7 + 4/7*b**3 - 2/7*b**5 + 2/7*b**4 - 4/7*b**2 - 2/7*b.
-2*(b - 1)**3*(b + 1)**2/7
Let x(i) = -i**2. Let q(m) = -18*m**2 + 15*m - 12. Let o(z) = q(z) - 15*x(z). Factor o(f).
-3*(f - 4)*(f - 1)
Let r(b) be the third derivative of -b**6/24 - b**5/6 + b**2. Factor r(s).
-5*s**2*(s + 2)
Determine k so that 1/3 - 1/9*k + 5/9*k**3 - 7/9*k**2 = 0.
-3/5, 1
Let q(r) be the first derivative of -r**4/48 + r**3/12 - r**2/8 - 7*r - 5. Let v(l) be the first derivative of q(l). Factor v(i).
-(i - 1)**2/4
Let u = 284 -