
Let o(g) be the first derivative of -3/4*g**4 - 3*g - 9/2*g**2 - 3*g**3 - 2. Factor o(f).
-3*(f + 1)**3
Let o(x) = 4*x - 2. Let y be o(1). Let u(l) be the second derivative of -1/3*l**3 + 1/10*l**5 + 0*l**2 + 0 + 1/6*l**4 - 1/15*l**6 + y*l. Factor u(d).
-2*d*(d - 1)**2*(d + 1)
Suppose -4*m + 14*m**5 - 24*m**4 - 2*m**2 - 15*m**3 - 14*m**4 + 45*m**3 = 0. Calculate m.
-2/7, 0, 1
Factor -17*b + 2*b**2 - 6*b**2 + 6*b - 8 - b.
-4*(b + 1)*(b + 2)
Let b(h) be the third derivative of -h**8/210 + 13*h**7/525 - h**6/20 + 7*h**5/150 - h**4/60 + 7*h**2. Determine u, given that b(u) = 0.
0, 1/4, 1
Solve -1/5*l**2 - 3/5 + 4/5*l = 0.
1, 3
Find l, given that 0 + 6/5*l**2 - 3/5*l - 3/5*l**3 = 0.
0, 1
Let g = -12/19 + 211/304. Let j(q) be the second derivative of -g*q**4 + 0 + 0*q**3 + 2*q + 1/80*q**5 + 1/2*q**2. Solve j(r) = 0.
-1, 2
Let o(h) = -h**3 - h**2 - h + 1. Let g(w) = 7*w**3 - 13*w**2 + 12*w - 2. Let n(m) = g(m) + 2*o(m). Factor n(f).
5*f*(f - 2)*(f - 1)
Let v(l) = l**2 + 7*l - 1. Let g be v(-8). Solve h**3 - g*h**2 - 2*h**3 + 9*h**2 = 0 for h.
0, 2
Let k(c) be the first derivative of -2*c**3/27 + 4*c**2/9 - 8*c/9 + 11. Factor k(m).
-2*(m - 2)**2/9
Let y(i) = -i**2 - 12*i - 14. Let v be y(-10). Let b(o) = 8*o**2 + 6*o. Let w(d) = -15*d**2 - 12*d. Let r(j) = v*w(j) + 11*b(j). What is x in r(x) = 0?
-3, 0
Let t(h) = 77*h**3 - 56*h**2 - 160*h - 37. Let j(r) = 115*r**3 - 84*r**2 - 240*r - 55. Let a(o) = 5*j(o) - 7*t(o). Factor a(l).
4*(l - 2)*(l + 1)*(9*l + 2)
Let j(t) = 3*t**4 + 7*t**3 + t**2 - 3*t. Let w = -16 + 25. Let q(x) = -6*x**4 - 15*x**3 - 3*x**2 + 6*x. Let k(c) = w*j(c) + 4*q(c). Factor k(i).
3*i*(i - 1)*(i + 1)**2
Let p be -2 + (2 - (1 + 1)). Let o = p + 2. Factor -5 + 7*k**2 + 1 - 3*k**3 + o.
-(k - 2)*(k - 1)*(3*k + 2)
Let o(x) be the third derivative of x**7/1785 + x**6/102 + 11*x**5/170 + 10*x**4/51 + 16*x**3/51 + 23*x**2. Suppose o(n) = 0. Calculate n.
-4, -1
Let f be (4 + -6)*194/6. Let y = 66 + f. What is x in y*x**2 - 1/3*x**5 + 0 - 1/3*x + 4/3*x**4 - 2*x**3 = 0?
0, 1
Let m(k) be the third derivative of 0 - 3/10*k**5 - 3/2*k**4 - 4*k**3 + 0*k - 5*k**2 - 1/40*k**6. Solve m(l) = 0 for l.
-2
Let f(q) be the second derivative of -5*q**6/6 + 13*q**5/4 - 5*q**4/3 - 10*q**3/3 + 8*q. Factor f(o).
-5*o*(o - 2)*(o - 1)*(5*o + 2)
Suppose -5*l = -0*l - 25. Suppose -4*w = -l*w. Factor 2/5*t**5 + 0*t + w + 6/5*t**4 + 6/5*t**3 + 2/5*t**2.
2*t**2*(t + 1)**3/5
Factor -2/5*t**4 - 24/5*t**2 + 12/5*t**3 + 0 + 16/5*t.
-2*t*(t - 2)**3/5
Let x(t) be the second derivative of -1/9*t**3 + 1/18*t**4 + 1/30*t**5 - 1/45*t**6 + 0*t**2 - t + 0. Factor x(g).
-2*g*(g - 1)**2*(g + 1)/3
Let f(r) be the second derivative of -r**9/16632 + r**7/2310 - r**5/660 - r**3/2 - 3*r. Let v(x) be the second derivative of f(x). What is n in v(n) = 0?
-1, 0, 1
Factor 0 + 8/7*d + 4/7*d**2 - 4/7*d**3.
-4*d*(d - 2)*(d + 1)/7
Let j = -33 - -56. Let v = j + -23. Determine m, given that 0 - 2/7*m + 2/7*m**3 + v*m**2 = 0.
-1, 0, 1
Factor -2*r**4 + 3*r**2 + 4*r**3 - 8*r + 2*r**3 + 2*r - r**4.
-3*r*(r - 2)*(r - 1)*(r + 1)
Let j(c) = -c**5 - c**4 - c**3 + c**2 + c. Let q(z) = 8*z**5 - 4*z**4 - 61*z**3 + z**2 + 40*z + 12. Let v(d) = 4*j(d) - q(d). Suppose v(g) = 0. Calculate g.
-2, -1/2, 1, 2
Let d(u) be the third derivative of -1/12*u**5 + 0*u - 7/24*u**4 + u**2 + 0 - 1/3*u**3. Solve d(h) = 0 for h.
-1, -2/5
Let b(d) = -2*d**2 - 4*d - 4. Let f(l) be the first derivative of 15/2*l**2 + 8/3*l**3 - 1 + 16*l. Let u(h) = -9*b(h) - 2*f(h). Factor u(n).
2*(n + 1)*(n + 2)
Let c be (-12)/(-18) - 64/13. Let o = -38/13 - c. Factor 2/3 - o*s + 2/3*s**2.
2*(s - 1)**2/3
Let o(y) be the first derivative of y**4/14 - 10*y**3/21 + 4*y**2/7 - 12. Determine r so that o(r) = 0.
0, 1, 4
Factor 2*u**3 + 3 - 6 - 16*u + 10*u - 1.
2*(u - 2)*(u + 1)**2
Let u = -136 + 410/3. Factor 0 + 2/3*j + u*j**2.
2*j*(j + 1)/3
Let 1/3 + m**2 - m - 1/3*m**3 = 0. What is m?
1
Let a(j) = 4*j**2 + 13*j - 3. Let r(c) = -8*c**2 - 25*c + 7. Let l(q) = -7*a(q) - 3*r(q). Factor l(g).
-4*g*(g + 4)
Let q be (-4)/(-18)*(-4 - -7). Let y(l) be the first derivative of 2*l**2 + q*l**3 + 2*l - 1. Factor y(t).
2*(t + 1)**2
Suppose u = -3*u - 12, -6 = 5*y + 2*u. Suppose -2/5*t**4 + y + 0*t**2 - 8/5*t + 6/5*t**3 = 0. What is t?
-1, 0, 2
Let g(a) be the third derivative of a**6/30 - 2*a**5/15 - a**4/6 + 4*a**3/3 + 10*a**2. Factor g(x).
4*(x - 2)*(x - 1)*(x + 1)
Let t(w) be the second derivative of -w**5/100 - w**4/60 + w**3/30 + w**2/10 + 3*w. Suppose t(n) = 0. Calculate n.
-1, 1
Let d(b) be the second derivative of 3*b**7/28 + b**6/10 - 21*b**5/40 + b**4/4 - 2*b. Suppose d(v) = 0. What is v?
-2, 0, 1/3, 1
Let a(l) = -l**2 - 6*l - 1. Let z be a(-3). Factor o**2 + 0*o**2 - 8 - o + z.
o*(o - 1)
Let u = -22 - -32. Factor 4*q**2 - 7*q + 21*q - u*q.
4*q*(q + 1)
Let h = 29/10 + -21/10. Determine q so that -h - 6/5*q - 2/5*q**2 = 0.
-2, -1
Let l(n) = -n**3 + 18*n - 12. Let b(r) = -9*r + 6. Let s(y) = 5*b(y) + 3*l(y). Suppose s(o) = 0. What is o?
-2, 1
Let f(d) be the second derivative of 5*d**7/42 - d**6/6 + d**5/15 + d**2/2 + 8*d. Let w(g) be the first derivative of f(g). Let w(b) = 0. What is b?
0, 2/5
Let b(f) = -24*f**5 - 45*f**4 - 9*f**3 + 12*f**2 + 9*f. Let x(n) = 6*n**5 + 11*n**4 + 2*n**3 - 3*n**2 - 2*n. Let g(r) = 2*b(r) + 9*x(r). Factor g(y).
3*y**2*(y + 1)**2*(2*y - 1)
Let z = 29 - 27. Let w = -29 + 29. Factor w - i - 5/2*i**z.
-i*(5*i + 2)/2
Let j(l) be the first derivative of 75*l**4/4 - 30*l**3 - 54*l**2 - 24*l - 11. Factor j(t).
3*(t - 2)*(5*t + 2)**2
Let v(w) be the third derivative of w**6/60 + w**5/75 - w**4/12 - 2*w**3/15 + 13*w**2. Factor v(a).
2*(a - 1)*(a + 1)*(5*a + 2)/5
Let f = 6 - 4. Find s such that -2*s**2 - s**2 + 3*s**2 + f*s**2 = 0.
0
Let r(w) be the third derivative of -w**7/150 - 2*w**6/75 - 11*w**5/300 - w**4/60 - 38*w**2. Find v such that r(v) = 0.
-1, -2/7, 0
What is u in 9*u**2 - u**3 - 2*u**3 - 6*u**2 = 0?
0, 1
Let b(t) = -4*t**2 + 5*t + 3. Let k(h) = 2 - 5 - 9*h - 2 + 7*h**2. Let u(q) = -5*b(q) - 3*k(q). Determine l so that u(l) = 0.
0, 2
Let i(n) = n + 11. Let o be i(-6). Factor 1/2*p**o + 5/2*p**2 - 1/2*p**4 + 0 - p - 3/2*p**3.
p*(p - 1)**3*(p + 2)/2
Suppose -2 = -s - 0*s. Suppose -i = -5*p - 20, s*i = 3*i - 2*p - 8. Factor m - 2*m + i*m - m**2 - m.
-m*(m + 2)
Let c(a) be the third derivative of a**6/2340 - a**5/390 + a**4/156 - a**3/3 + 3*a**2. Let y(i) be the first derivative of c(i). Factor y(v).
2*(v - 1)**2/13
Suppose -z = -1 - 6. Suppose z = 5*w - 3. Solve w*j**3 + 3*j**3 - 2*j**5 - 7*j**3 + 4*j**4 = 0.
0, 1
Suppose 2*v = -2*v + 8. Factor 6*s**4 + 3*s**3 + s**5 - v*s**4 - s**4 + s**2.
s**2*(s + 1)**3
Let w be 6/8 - 6/8. Solve -4*c**4 + w*c**2 + 2*c**2 + 2*c**4 = 0 for c.
-1, 0, 1
Let j(b) be the second derivative of -2*b**6/15 + b**5/5 + b**4/3 - 2*b**3/3 - 27*b. Factor j(p).
-4*p*(p - 1)**2*(p + 1)
Let a(u) be the first derivative of -1/4*u**4 - 1 - u + 1/2*u**2 + 1/3*u**3. Let a(y) = 0. What is y?
-1, 1
Let f = 5 - 3. Let z be (1 - 1)/((-2)/f). Factor z*a + 2*a**4 - 2*a**2 + 0*a**2 + a - a**5.
-a*(a - 1)**3*(a + 1)
Let r(t) be the first derivative of -2*t**5/5 - t**4/4 + t**3 + t**2/2 - t - 2. Determine z so that r(z) = 0.
-1, 1/2, 1
Let k(l) = 5*l**2 - 11*l - 13. Let j(q) = q**2 - q - 1. Let s(p) = -6*j(p) + 2*k(p). Suppose s(x) = 0. What is x?
-1, 5
Let q be (2/9)/(15/((-495)/(-2))). Solve -4/3 + i**3 + 8/3*i + q*i**2 = 0.
-2, 1/3
Let d(w) be the third derivative of w**7/42 - w**5/12 - 8*w**2. Factor d(n).
5*n**2*(n - 1)*(n + 1)
Let j(l) = -9*l**4 + 11*l**3 - 11*l**2 + 11*l + 11. Let i(h) = -3*h**4 + 4*h**3 - 4*h**2 + 4*h + 4. Let v(n) = 11*i(n) - 4*j(n). Solve v(o) = 0 for o.
0
Let n(c) = c + 4. Let b be n(8). Suppose -u = -5*u + b. Let r**u - r - r**2 + r = 0. What is r?
0, 1
Let w(k) be the second derivative of 1/84*k**7 + 0*k**3 + 0*k**2 + 0 - 1/40*k**5 + 2*k + 1/24*k**4 - 1/60*k**6. Factor w(x).
x**2*(x - 1)**2*(x + 1)/2
Suppose 2*h = -2*h - 12. Let b be (h + 1)*-1*1. Factor 25/3*f**b + 20/3*f + 4/3.
(5*f + 2)**2/3
Factor 0*v**2 - 3/7*v**5 + 0*v**4 + 0 + 6/7*v**3 - 3/7*v.
-3*v*(v - 1)**2*(v + 1)**2/7
Suppose 4*u = -3*v - 1 + 30, 5*v = u - 13. Let x be 0 + -2 + u - 3. Solve 0*s + 0 + 1/6*s**x - 1/6*s**2 = 0.
0, 1
Let x(n) = -48*n**3 - 33*n**2 + 48*n. Let a(b) = 3*b**3 + 2*b**2 - 3*b. Suppose 5*m + 8 = m.