Let x(m) = -6*m**5 - 16*m**4 + 34*m**3 - 12*m**2 - 16*m. Let w(z) = 2*z**5 + 5*z**4 - 11*z**3 + 4*z**2 + 5*z. Let v(f) = -16*w(f) - 5*x(f). Factor v(b).
-2*b**2*(b - 1)**2*(b + 2)
Let b(i) = -97*i**3 - 304*i**2 - 169*i + 192. Let q(f) = -24*f**3 - 76*f**2 - 42*f + 48. Let n(g) = 4*b(g) - 18*q(g). Factor n(j).
4*(j + 2)**2*(11*j - 6)
Let w(v) be the third derivative of -1/60*v**6 - v**2 + 0*v**5 + 0*v + 1/4*v**4 + 2/3*v**3 + 0. Factor w(p).
-2*(p - 2)*(p + 1)**2
Solve -a**2 - a**3 + a**4 + 3*a + 0*a**2 - 2*a = 0 for a.
-1, 0, 1
Let h(o) be the third derivative of -o**6/30 + o**5/15 + o**4/3 + 23*o**2. Factor h(w).
-4*w*(w - 2)*(w + 1)
Let k(t) be the third derivative of 3*t**2 + 0 + 0*t - 1/10*t**5 + 1/3*t**3 + 1/6*t**4. Factor k(r).
-2*(r - 1)*(3*r + 1)
Factor -46*y**3 + 14*y - 150*y**3 - 7 + 23 - 142*y + 308*y**2.
-4*(y - 1)*(7*y - 2)**2
Let s be 6/(-5)*5/(-2). Let c(z) = z**2 + 7*z + 3. Let m be c(-7). Determine d so that d + d - m*d + d**s = 0.
-1, 0, 1
Let v = 9 - 7. Let g = 4 - 2. Factor 2 - v*a**g - 2*a - 2.
-2*a*(a + 1)
Let o be (-17)/(-5) + (-4)/10. Let n(k) be the second derivative of -2*k + 2/9*k**o + 0 + 1/36*k**4 + 2/3*k**2. Find g such that n(g) = 0.
-2
Factor 3*u**2 - 12*u**4 + 3*u**3 - 3*u**5 + 6*u**4 + 3*u**4.
-3*u**2*(u - 1)*(u + 1)**2
Let g(p) = -20*p**3 + 20*p**2 + 85*p - 15. Let d(a) = 3*a**3 - 3*a**2 - 12*a + 2. Let y(u) = 15*d(u) + 2*g(u). Factor y(w).
5*w*(w - 2)*(w + 1)
Let k(p) = -2*p - 2. Let i be k(-3). Let a be (-3)/2 + i + -2. Solve 0 + t - a*t**2 = 0.
0, 2
What is i in 0*i**3 + 0 + 2/3*i**2 - 4/9*i - 2/9*i**4 = 0?
-2, 0, 1
Let w(p) be the third derivative of 8/27*p**3 - 1/135*p**5 - 1/540*p**6 + 1/27*p**4 + 0*p + 0 + 2*p**2. Factor w(o).
-2*(o - 2)*(o + 2)**2/9
Let l(d) be the third derivative of -2*d**7/525 + 7*d**6/75 - 4*d**5/5 + 12*d**4/5 + 32*d**2. Find i, given that l(i) = 0.
0, 2, 6
Determine v, given that -7 + 5 - 4*v**2 - 14 - 16*v = 0.
-2
Let c(n) be the first derivative of -n**4/2 + 2*n**3/3 + 4*n**2 - 8*n - 7. Solve c(l) = 0.
-2, 1, 2
Solve -8/3 - 2/3*h**2 + 8/3*h = 0 for h.
2
Factor 2 - 2*q**3 + 0 + 7*q**4 - 2 - 7*q**2 + 2*q.
q*(q - 1)*(q + 1)*(7*q - 2)
Let p(c) = 2*c**2 - 5*c + 4. Let f be p(3). Let g(w) = 8 - f - w + 6*w**2 + 6. Let b(l) = 5*l**2 - l + 6. Let x(y) = 7*b(y) - 6*g(y). Let x(n) = 0. Calculate n.
-1, 0
Suppose p = -0*p. Suppose p = -s + 5*s - 28. Determine g so that -s + g + 2 + 3 + g**2 = 0.
-2, 1
Let x(v) = 2*v**2. Let h be x(1). Factor w**3 - 2*w**4 + 5*w**3 - w**3 + 2*w**2 - 3*w**3 - h*w.
-2*w*(w - 1)**2*(w + 1)
Let u = 2/21 - -5/21. Let t(s) = -s**3 + 8*s**2 + 8*s + 12. Let c be t(9). Find y, given that 1/3*y**4 - 1/3*y**2 + u*y - 1/3*y**c + 0 = 0.
-1, 0, 1
Factor 4*s**3 + 10*s + 6*s - 19*s**2 + 35*s**2.
4*s*(s + 2)**2
Let s = 25 - 18. Suppose 11 = -2*z + 6*z - r, 0 = 3*z + 4*r + 6. Solve -s - g**3 + 9 - g**2 + 5*g + 4*g**z - g**4 = 0 for g.
-1, 2
Let p be (-264)/(-32) + -1 + -7. Factor 1/8 - 1/8*i**5 - 1/8*i + 1/8*i**4 - 1/4*i**2 + p*i**3.
-(i - 1)**3*(i + 1)**2/8
Let y(g) be the first derivative of 2/15*g**5 + 0*g**3 - 1/3*g**4 + 4 + 2/3*g**2 - 2/3*g. Factor y(u).
2*(u - 1)**3*(u + 1)/3
Solve 8 + 3*n + 28*n**3 - 33*n + 12*n**2 + 2*n - 20*n**4 = 0 for n.
-1, 2/5, 1
Let m(v) be the first derivative of -54*v**6 + 792*v**5/5 - 76*v**4 + 32*v**3/3 - 6. Factor m(h).
-4*h**2*(h - 2)*(9*h - 2)**2
Let h = 3879/910 + 3/130. Factor -30/7*l**2 - 3/7 - 15/7*l**4 + 15/7*l + h*l**3 + 3/7*l**5.
3*(l - 1)**5/7
Let j(b) be the second derivative of b**8/840 + 3*b**2/2 - 2*b. Let t(h) be the first derivative of j(h). Factor t(o).
2*o**5/5
Suppose -336*q**3 + 432/5 + 4296/5*q**2 + 147/5*q**4 + 576*q = 0. What is q?
-2/7, 6
Let p(r) be the second derivative of r**6/40 - 3*r**5/80 - r**4/16 + r**3/8 + 8*r. Let p(f) = 0. Calculate f.
-1, 0, 1
Let n(g) be the second derivative of -g**4/78 + 5*g**3/39 - 4*g**2/13 + 21*g. Determine q so that n(q) = 0.
1, 4
Determine w, given that -27*w**2 + 11*w**5 - 24*w**3 + 21*w**4 + 4*w**5 + 15*w**2 = 0.
-2, -2/5, 0, 1
Suppose o = -4*o + 45. Let l be (-6)/9*o/(-2). Suppose -6*t**3 + 3*t**5 - 2*t**4 + 2*t**2 + l*t**3 + t**4 - t**2 = 0. What is t?
-1, 0, 1/3, 1
Let f(h) = 5*h - 50. Let r be f(10). Let z(m) be the first derivative of 1/12*m**3 + r*m - 1/16*m**4 - 1 + 0*m**2. Factor z(n).
-n**2*(n - 1)/4
Let j(p) be the first derivative of -p**7/1260 + p**5/120 - p**4/72 + 9*p**2/2 - 9. Let a(b) be the second derivative of j(b). Factor a(i).
-i*(i - 1)**2*(i + 2)/6
Suppose 5*u + 2 = -3. Let k be u/1 - (-28)/21. Factor 1/3*g**2 + k - 2/3*g.
(g - 1)**2/3
Let p(o) be the first derivative of -2*o**3 + 3/2*o**2 + 1 + 6*o - 3/4*o**4. Factor p(a).
-3*(a - 1)*(a + 1)*(a + 2)
Let v be (-17)/(-30) + 24/(-144). Let p = -3 - -6. Factor 0*b**2 - v*b + 2/5*b**p + 0.
2*b*(b - 1)*(b + 1)/5
Let c(y) be the second derivative of 6*y + 2/5*y**4 - 2/25*y**6 - 2/25*y**5 + 2/15*y**3 + 0 - 6/5*y**2 + 2/105*y**7. Find b such that c(b) = 0.
-1, 1, 3
Let j(m) be the third derivative of -3*m**2 + 0*m**7 + 0*m**4 + 0*m**6 + 0*m**3 + 0 + 0*m**5 + 0*m - 1/224*m**8. Determine o, given that j(o) = 0.
0
Solve r**2 - 2 - 2/3*r**3 + 11/3*r = 0.
-2, 1/2, 3
Let k = 443 + -441. Find g, given that 2 + 7/4*g**3 + 5*g - 13/2*g**k = 0.
-2/7, 2
Let s = 20 + -45. Let l = s - -35. Solve 4*q**4 - 3*q**2 - l*q**5 - 3*q**2 + 15*q**3 + 5*q**3 + 4 - 10*q - 2*q**2 = 0 for q.
-1, 2/5, 1
Let n(v) be the first derivative of -v**7/280 - v**6/40 - 3*v**5/40 - v**4/8 - v**3 + 3. Let q(w) be the third derivative of n(w). Find a, given that q(a) = 0.
-1
Let f(r) be the third derivative of -5*r**8/168 - r**7/6 + r**6/8 + 17*r**5/12 - 25*r**4/24 - 5*r**3 + 3*r**2 + 2. Solve f(j) = 0 for j.
-3, -2, -1/2, 1
Let h(x) be the third derivative of -x**8/4032 - x**7/1080 - x**6/1080 - 7*x**4/24 + 6*x**2. Let d(z) be the second derivative of h(z). Solve d(u) = 0 for u.
-1, -2/5, 0
Let t(k) = -3*k**5 + 3*k**4 - 4*k**3 + 9*k**2 + 7*k - 2. Let s(w) = -2*w**5 + 2*w**4 - 2*w**3 + 5*w**2 + 4*w - 1. Let x(m) = -10*s(m) + 6*t(m). Factor x(b).
2*(b - 1)**3*(b + 1)**2
Let w(q) be the second derivative of 1/4*q**4 - 3*q + 0*q**3 + 0 - 3/2*q**2. Factor w(i).
3*(i - 1)*(i + 1)
Let d(n) be the third derivative of n**9/272160 - n**7/7560 + n**6/1620 + n**5/15 - 5*n**2. Let l(q) be the third derivative of d(q). Factor l(s).
2*(s - 1)**2*(s + 2)/9
Factor 33/2*n - 3/2*n**2 - 15.
-3*(n - 10)*(n - 1)/2
Let g be 2/(-14) + 78/154. Solve -6/11*w**3 - 4/11*w**2 + g + 6/11*w = 0 for w.
-1, -2/3, 1
Suppose -1 + 9 = 4*c. Find v, given that 1/4*v**3 - 1/4*v**4 - 1/2 + 3/4*v**c - 1/4*v = 0.
-1, 1, 2
Let i(v) be the third derivative of -v**6/100 - v**5/6 + 53*v**4/180 - v**3/5 - 28*v**2. Factor i(b).
-2*(b + 9)*(3*b - 1)**2/15
Let q(j) = j**3 - 4*j**2 - 5*j + 2. Let c be q(5). Factor 1 - c - 2 + k**2 - 2*k.
(k - 3)*(k + 1)
Let m(o) be the first derivative of o**6/30 + 2*o**5/25 - o**4/10 - 8*o**3/15 - 7*o**2/10 - 2*o/5 - 5. Factor m(k).
(k - 2)*(k + 1)**4/5
Let r(y) be the second derivative of y**9/34020 - y**8/30240 + y**4/6 - 9*y. Let o(v) be the third derivative of r(v). Let o(a) = 0. What is a?
0, 1/2
Let r be 39/65*(6 - 1). Factor 2*v**2 + 4*v**3 + 6*v**r - 12*v**3.
-2*v**2*(v - 1)
Factor -t**2 + 2*t**2 + 2*t**2 + t**2 + 48*t + 144.
4*(t + 6)**2
Let d be 4/(-30)*(-10 + 121/22). Let d*f**3 - 3/5*f - 1/5*f**2 + 2/5 - 1/5*f**4 = 0. Calculate f.
-1, 1, 2
Find c such that -2*c**2 + 0*c**2 - 14 + 12 + 3*c**2 + c = 0.
-2, 1
Suppose -4*t**2 + t + 6*t**3 + 0*t**5 + 2*t**5 + 2*t**5 - 4*t**4 - 3*t**5 = 0. Calculate t.
0, 1
Factor -3 + 9/2*j + 0*j**2 - 3/2*j**3.
-3*(j - 1)**2*(j + 2)/2
Let a = -1318/163 - -187189/25428. Let r = -3/52 - a. Solve -r*m**2 + 0 - 2/3*m = 0 for m.
-1, 0
Factor -2*t**3 + 5*t**2 + 5*t**4 - 10 + 11*t**3 - 15*t + 6*t**3.
5*(t - 1)*(t + 1)**2*(t + 2)
Let r(f) be the third derivative of f**8/10080 - f**7/630 + f**6/90 - f**5/20 - 3*f**2. Let a(m) be the third derivative of r(m). Suppose a(g) = 0. What is g?
2
Let s(r) = r**2 + 10*r + 12. Let t be s(-9). Let k(d) = d - 3. Let a be k(6). Solve -9*x**5 - 5*x**4 + 5*x**5 + x + t*x**a + 5*x**2 + 0*x**5 = 0.
-1, -1/4, 0, 1
Let l(d) be the second derivative of 1/100*d**5 + 0*d**3 - 3*d + 0 + 0*d**4 + 0*d**2. Solve l(k) = 0 for k.
0
Let c(x) be the first derivative of -x**4/28 - 5*x**3/7 - 75*x**2/14 - 125*x/7