 2. Let f(o) = -6*o**2 - 4*o. Let h(l) = j*f(l) + 4*w(l). Factor h(c).
-2*c**2
Suppose z + 24 = -3*o, -4*z + 0*o - 3*o = 51. Let n be z/(-6)*32/24. Factor -2/5*p**3 + 0 + 0*p - 4/5*p**n.
-2*p**2*(p + 2)/5
Suppose 2*z = 2*y + 4, -z = y + z - 13. Let b(h) be the third derivative of 1/20*h**5 + 0*h + h**2 + 0*h**4 - 1/2*h**y + 0. Determine l, given that b(l) = 0.
-1, 1
Factor 14*b + 28*b**2 + 15 + 64*b + 42*b + 17.
4*(b + 4)*(7*b + 2)
Let h(r) be the second derivative of -r**4/42 + r**3/21 + 3*r. Factor h(v).
-2*v*(v - 1)/7
Let j(p) = p**3 + 9*p**2 + 8*p + 3. Let r be j(-8). Suppose -7 = 2*v - 3, -r*y + 8 = -4*v. Factor 1/2*q**2 + 0 + y*q.
q**2/2
Let u(b) be the first derivative of b**4/24 + b**3/18 - b**2/6 - 20. Solve u(r) = 0 for r.
-2, 0, 1
Let k be (1 + 2)*1/3. Find o such that -k + 0 - o**2 + 2 = 0.
-1, 1
Suppose 1/3*j**4 - 72*j + 36*j**2 - 6*j**3 + 0 = 0. What is j?
0, 6
Let b(k) = 39*k**2 + 33*k + 1. Let g(m) = -19*m**2 - 17*m - 1. Let x(n) = -3*b(n) - 7*g(n). Factor x(w).
4*(w + 1)*(4*w + 1)
Let l be (-16 + -3)*4/165. Let d = -2/33 - l. Factor -6/5*b**3 - d*b + 2/5*b**4 + 6/5*b**2 + 0.
2*b*(b - 1)**3/5
Let o(y) be the second derivative of -2*y**6/15 - 19*y**5/60 + 4*y**4/9 + 13*y**3/18 + y**2/3 + 14*y. Solve o(b) = 0 for b.
-2, -1/3, -1/4, 1
Let 4/7*c - 4/7*c**2 + 0 = 0. Calculate c.
0, 1
Suppose 0 = 3*j + 104 - 32. Let l be (4/j)/((-2)/8). Factor -4/9*o**3 + l*o**4 + 2/3*o - 2/9 - 4/9*o**2 - 2/9*o**5.
-2*(o - 1)**4*(o + 1)/9
Let a(c) be the third derivative of -c**8/43680 - c**7/16380 + 3*c**4/8 + c**2. Let d(w) be the second derivative of a(w). Factor d(z).
-2*z**2*(z + 1)/13
Let i(m) be the first derivative of m**4 + 4*m**3/3 - 10*m**2 + 12*m + 35. Find p, given that i(p) = 0.
-3, 1
Let p(z) be the third derivative of -z**5/120 - z**4/24 + 23*z**2. Suppose p(f) = 0. Calculate f.
-2, 0
Let z = 116/3 - 38. Let j(k) = -k**3 - 3*k**2 - k + 2. Let s be j(-3). Determine g, given that 2/3*g**s + 4*g**3 + z*g - 8/3*g**4 - 8/3*g**2 + 0 = 0.
0, 1
Suppose 45 = -5*x + 5*f, 2*x - 2*f + 3 = 3*f. Let k be (-8)/x*42/12. Factor 0 + 10/7*z**5 - 2*z**4 + 0*z**k + 0*z + 4/7*z**3.
2*z**3*(z - 1)*(5*z - 2)/7
Let c = 5 - 3. Let b(r) = -r - 2. Let y be b(-7). Determine s, given that 10*s**2 + 7*s + y*s**3 + 4*s**4 - s**2 + c - 3*s**4 = 0.
-2, -1
Let b(t) = t**2. Let s(y) = y**3 + 13*y**2 + 11*y - 13. Let x be s(-12). Let q(z) = 5*z**2 + 4*z. Let i(u) = x*q(u) + 3*b(u). Factor i(k).
-2*k*(k + 2)
Let c(i) = 4*i**2 + 4*i - 3. Let v = 5 + 0. Let w(y) = 8*y - v*y - 1 - 1 + 3*y**2. Let q(r) = 2*c(r) - 3*w(r). Let q(t) = 0. Calculate t.
-1, 0
Find f such that 96/5*f + 147/5*f**3 - 12/5 - 231/5*f**2 = 0.
2/7, 1
Let d(g) be the third derivative of g**6/24 - g**5/4 + 10*g**3/3 - 6*g**2. Let d(m) = 0. Calculate m.
-1, 2
Suppose q + o + 12 = 4*q, 8 = 2*q + 5*o. Let 2*n**2 + n**4 - 3*n**4 - 2*n**3 + 2*n + 0*n**q + 0*n**3 = 0. Calculate n.
-1, 0, 1
Let x(w) be the third derivative of -w**8/252 - w**7/63 + w**5/18 + w**4/18 - 26*w**2. Determine k so that x(k) = 0.
-2, -1, -1/2, 0, 1
Factor 8/5 + 8/5*p + 2/5*p**2.
2*(p + 2)**2/5
What is n in 0*n**2 + 13 - 5 - 3*n**2 - 6*n + 1 = 0?
-3, 1
Let l(r) be the third derivative of -r**8/1344 + r**7/840 + r**6/480 - r**5/240 - 12*r**2. Suppose l(o) = 0. Calculate o.
-1, 0, 1
Let g(z) be the second derivative of 2*z**7/105 + 6*z**6/25 + 26*z**5/25 + 34*z**4/15 + 14*z**3/5 + 2*z**2 + 30*z. Let g(y) = 0. What is y?
-5, -1
Let v(n) be the second derivative of -n**8/5040 + n**7/2520 + n**6/1080 - n**5/360 - n**3/6 - n. Let g(k) be the second derivative of v(k). Factor g(l).
-l*(l - 1)**2*(l + 1)/3
Let l(w) be the second derivative of w**6/6 - w**5/2 + 5*w**3/3 - 5*w**2/2 - 25*w. Suppose l(u) = 0. What is u?
-1, 1
Let p = 71 - 69. Factor 0 + 1/5*m - 1/5*m**p.
-m*(m - 1)/5
Let m = -13 + 13. Let u be 2 - m/(9/3). Find r, given that 2/5*r**5 + 0*r**u + 0*r - 4/5*r**4 + 0 + 2/5*r**3 = 0.
0, 1
Factor w**2 + 5*w - 4*w + 0*w**2 - 2*w**2.
-w*(w - 1)
Let k be (-1 + 0)*0*19/57. Factor k + 3/2*p + 9/2*p**3 + 6*p**2.
3*p*(p + 1)*(3*p + 1)/2
Let b(l) be the first derivative of l**3 + 15/14*l**2 + 3/7*l + 9/28*l**4 + 5. Find f, given that b(f) = 0.
-1, -1/3
Factor -1/5*d**3 - 8/5 - 12/5*d - 6/5*d**2.
-(d + 2)**3/5
Determine u so that -81/4 - 27/4*u**2 - 3/4*u**3 - 81/4*u = 0.
-3
Let l = -4 + 4. Let a(p) be the second derivative of l - 1/9*p**4 + 0*p**2 + 1/45*p**6 - p + 0*p**3 + 1/30*p**5. Factor a(q).
2*q**2*(q - 1)*(q + 2)/3
Suppose 30 = 3*q - 0*q. Suppose -2*c + q = -2*i, -i - 4*c + 11 = -9. Let i*j**3 + 0 - 1/4*j**5 + 0*j + 0*j**4 + 0*j**2 = 0. What is j?
0
Let f(q) be the first derivative of 2*q**5/5 + 4*q**4 + 16*q**3 + 32*q**2 + 32*q + 10. Factor f(o).
2*(o + 2)**4
Factor -4/3*r**4 + 0*r + 0 + 0*r**2 - 1/3*r**5 - 4/3*r**3.
-r**3*(r + 2)**2/3
Let d(h) be the third derivative of 2*h**2 + 4/27*h**3 + 1/540*h**6 + 0*h**4 + 0 - 1/90*h**5 + 0*h. Factor d(s).
2*(s - 2)**2*(s + 1)/9
Let y = 83/316 - 1/79. Let r(l) be the first derivative of 1/6*l**2 + y*l**4 + 1/15*l**5 + 1/3*l**3 - 2 + 0*l. Find t, given that r(t) = 0.
-1, 0
Let s(b) = -b**5 + b**2 + b. Let x(d) = -14*d**5 - 16*d**4 - 16*d**3 + 18*d**2 + 30*d + 8. Let g(h) = -10*s(h) + x(h). Let g(z) = 0. Calculate z.
-2, -1, 1
Find l, given that -8 + 2*l**2 - 11*l + 42*l**4 + 10*l - 20*l - 11*l + 68*l**3 = 0.
-1, -2/7, 2/3
Suppose -2*t = 3*t - 15. Let p = t + -1. Find l such that l - p*l**2 - l**2 + 4*l**2 = 0.
-1, 0
Let g(n) be the first derivative of 1/5*n**2 + 1 + 0*n + 2/15*n**3. Factor g(s).
2*s*(s + 1)/5
What is n in 12/5*n - 3/5 + 3/5*n**2 - 12/5*n**3 = 0?
-1, 1/4, 1
Let c(w) = w**3 + 4*w**2 + 4*w - 3. Let z(t) = 1. Let x(o) = c(o) + 3*z(o). What is p in x(p) = 0?
-2, 0
Factor -t - 2 + t**2 - 2 + 2 + 2*t.
(t - 1)*(t + 2)
Let w(r) be the second derivative of r**7/126 - 11*r**6/90 + 43*r**5/60 - 73*r**4/36 + 28*r**3/9 - 8*r**2/3 - 11*r. Suppose w(u) = 0. What is u?
1, 4
Suppose -72 = 3*h - 6. Let k = -16 - h. Factor 6*w**4 + 4*w**3 + 3*w - k*w**2 - 3*w - 4*w.
2*w*(w - 1)*(w + 1)*(3*w + 2)
Let a(u) be the first derivative of u**3/3 - 23*u**2/2 + 7*u + 5. Let h(v) = v**2 - 35*v + 10. Let s(o) = -8*a(o) + 5*h(o). Solve s(i) = 0.
1, 2
Let v(m) be the second derivative of 2/5*m**5 - m + 0 + m**2 + 3/2*m**4 + 2*m**3. Suppose v(o) = 0. What is o?
-1, -1/4
Let s = -33242/15 + 2217. Let h = 6/5 - s. Solve -h - 5/3*i + 3*i**3 - i**2 = 0.
-1/3, 1
Let h(g) be the second derivative of -3*g - 1/6*g**3 + 0*g**2 + 1/6*g**4 - 1/20*g**5 + 0. Factor h(a).
-a*(a - 1)**2
Factor -5*q**2 + 44*q - 5 - 10 - 24*q.
-5*(q - 3)*(q - 1)
Suppose -6 = -3*y + 2*c, -8 = -7*y + 3*y - 2*c. Suppose 3 - 4*n - 1 + n**y + 2 = 0. What is n?
2
Find h such that 0*h + 0 + 1/8*h**2 - 1/8*h**3 = 0.
0, 1
Let l(i) = 7*i**2 - i. Let c(g) = -g**2 + 5*g. Let r be c(4). Let u(w) = -r - w**2 + 2 + 2. Let h(z) = -l(z) - 6*u(z). What is q in h(q) = 0?
0, 1
Find d, given that -5*d**4 + 0*d - 7*d - 15*d**3 - 4*d - 15*d**2 + 6*d = 0.
-1, 0
Factor -588*l - 1344 - 11*l**2 - 31*l**2 - 5*l**3 - 1400 + 4*l**3.
-(l + 14)**3
Let f(y) be the first derivative of 1/4*y**2 - 1/6*y**3 + 0*y + 5. Factor f(k).
-k*(k - 1)/2
Let y(c) be the second derivative of -c**5/120 + c**4/48 + 5*c**2/2 + c. Let q(z) be the first derivative of y(z). What is h in q(h) = 0?
0, 1
Let u(n) be the first derivative of 10*n**4 - 34*n**3/3 - 5*n**2 + 4*n - 6. What is d in u(d) = 0?
-2/5, 1/4, 1
Let y(m) be the first derivative of -m**4/6 + 34. Determine a, given that y(a) = 0.
0
Let r(g) be the third derivative of -g**8/84 + 2*g**7/105 + g**6/30 - g**5/15 - 5*g**2. Factor r(b).
-4*b**2*(b - 1)**2*(b + 1)
Factor 1/4*g**5 - 3/4*g**2 - 1/2*g + 3/4*g**4 + 1/4*g**3 + 0.
g*(g - 1)*(g + 1)**2*(g + 2)/4
Let d(j) be the first derivative of -j**4/4 + j**3/3 + 2*j**2 - 4*j + 20. Determine o so that d(o) = 0.
-2, 1, 2
Suppose 0 = -3*k - 40 + 49. Solve 5/4*x**4 - 5/4*x**2 - 1/2*x + 1/2*x**k + 0 = 0 for x.
-1, -2/5, 0, 1
Let k(h) = 2 + 4 + 1 - h + 2. Let s be k(7). Determine f so that 1/2*f**3 - 5/2*f**4 + s*f**5 + 0*f + 0 + 0*f**2 = 0.
0, 1/4, 1
Let o = -35 + 14. Let b be (-214)/(-14) - (-6)/o. Factor -12*y - 3*y**3 - 3*y**2 + b*y + 2 + 3*y**4 - 2.
3*y*(y - 1)**2*(y + 1)
Let d = -1343/6 - -225. Let k(a) be the second derivative of 3*a - 1/4*a**4 + 0 + d*a**3 - a**2. Factor k(u).
-(u - 2)*(3*u - 1)