
-1, 0
Let t(o) be the third derivative of -o**8/10080 + o**7/7560 - o**5/30 + 2*o**2. Let g(f) be the third derivative of t(f). Factor g(m).
-2*m*(3*m - 1)/3
Let z = 1 - -2. Suppose k + 3*k + 8 = 4*y, z*k + 2*y = 19. Factor -3*t**2 + 2*t - t**k - 1 - 4*t - t.
-(t + 1)**3
Suppose -q - 9 = 2*q. Let b be (-2 - 2/(-2))/q. Factor -4/3*u**3 + 0 + 0*u + b*u**4 + 4/3*u**2.
u**2*(u - 2)**2/3
Let o(w) = w**2 - 7*w - 8. Let b be o(6). Let p = b - -16. Suppose 1/2*d**p + 1/2*d + 0 = 0. What is d?
-1, 0
Suppose 2*q = -d + 9, q + 3*q - 22 = 2*d. Determine s, given that -q*s + 27*s**4 - 24*s**4 - s + 9*s**3 - 3*s**2 - 3*s**5 = 0.
-1, 0, 1, 2
Suppose 0 = -m - 1, 3*p + 4*m = -m + 1. Suppose 0 = p*d + 3*k - 6, -3*d + 2*k + k = -9. Let r**4 - 3*r**3 + 5*r**d + 0*r**4 + 0*r**4 = 0. What is r?
-2, 0
Let p(j) = j. Let n(x) = -2*x**2 + 4*x - 4. Suppose 2*f + i = -10 + 27, -5*f - 3*i = -41. Let q(v) = f*p(v) - n(v). Let q(z) = 0. Calculate z.
-2, -1
Let f(u) be the third derivative of -u**5/12 + 5*u**3/6 - 6*u**2. Factor f(c).
-5*(c - 1)*(c + 1)
Suppose -6 = -3*l + 24. Suppose -3*u = -8*u + l. Factor -g**2 - 3*g**2 - 6 + u*g**2 + 4 - 4*g.
-2*(g + 1)**2
Let j be (-12)/(-234)*(-58)/4. Let u = -1/13 - j. Factor -1/3*h**2 + h - u.
-(h - 2)*(h - 1)/3
Let r = -15 - -19. Factor -a**2 - 3*a**r + 3*a**2 + a**4.
-2*a**2*(a - 1)*(a + 1)
Factor -2/3 - q - 1/3*q**2.
-(q + 1)*(q + 2)/3
Suppose 0 = -3*z + 26 - 14. Find i, given that 0*i**z - 1/4*i**5 + 0 + 1/4*i**3 + 0*i + 0*i**2 = 0.
-1, 0, 1
Let s be 54/(-21)*(-28)/(-6). Let z be (4/(-12))/(2/s). Suppose 0 - 1/2*p**3 - p**z - 1/2*p = 0. Calculate p.
-1, 0
Let q = 30 + -30. Let d(g) be the second derivative of 3*g + 0*g**3 + q - 1/20*g**5 + 0*g**4 + 0*g**2 - 1/60*g**6. Factor d(s).
-s**3*(s + 2)/2
Solve 6/11 - 2/11*p**2 + 4/11*p = 0.
-1, 3
Let b(m) be the first derivative of -6 + 0*m + 0*m**3 - 1/5*m**5 + 0*m**2 + 0*m**4 + 1/12*m**6. Solve b(z) = 0 for z.
0, 2
Let u(c) = 28*c**5 + 10*c**2 + 46*c**4 - 4*c**2 + c + 1 - 2*c**4 + 20*c**3 - 3*c**2. Let o(w) = w**5 - w**4 - w**3 + w + 1. Let n(h) = o(h) - u(h). Factor n(d).
-3*d**2*(d + 1)*(3*d + 1)**2
Let c be -1 + -3 + (3 - (3 + -4)). Solve -1/2*s**5 + 0 + c*s**3 + s**2 + 1/2*s - s**4 = 0 for s.
-1, 0, 1
Let m(q) be the first derivative of -q**6/9 + q**4/3 - q**2/3 + 6. Let m(j) = 0. What is j?
-1, 0, 1
Let d(c) be the third derivative of 1/105*c**7 + 1/30*c**6 + 0 - 1/168*c**8 + 0*c**5 + 0*c**4 - 7*c**2 + 0*c**3 + 0*c. Determine p so that d(p) = 0.
-1, 0, 2
What is o in 0 + 2/7*o**3 - 2/7*o**5 - 2/7*o**2 + 0*o + 2/7*o**4 = 0?
-1, 0, 1
Let v(a) be the first derivative of a**4 + 4*a**3/9 - 3. Let v(n) = 0. What is n?
-1/3, 0
Let 0*g**3 + 1/3*g**4 - g**2 + 0 + 2/3*g = 0. What is g?
-2, 0, 1
Factor 2/3*j**2 - 4/3*j + 1/3*j**3 - 8/3.
(j - 2)*(j + 2)**2/3
Let -2/11*n + 0 + 0*n**2 + 2/11*n**3 = 0. What is n?
-1, 0, 1
Let l(h) be the third derivative of -h**6/360 + h**5/90 + 7*h**2. Factor l(o).
-o**2*(o - 2)/3
Let i(u) be the second derivative of -2*u**6/15 + 2*u**5/5 + u**4/3 - 4*u**3/3 + 3*u. Suppose i(j) = 0. What is j?
-1, 0, 1, 2
Let w be (3*4/72)/2. Let g(o) be the first derivative of 0*o**2 + 0*o + w*o**3 - 1 - 1/16*o**4. Let g(l) = 0. Calculate l.
0, 1
Suppose 3*b = -0*b. Let r(q) be the first derivative of 1 - 1/9*q**3 + b*q + 1/3*q**2. Factor r(t).
-t*(t - 2)/3
Let 28*c**4 - 51*c**4 + 19*c**4 - 2*c**5 = 0. Calculate c.
-2, 0
Solve 4*m**2 + 1 + 8*m + 5 - 2 = 0 for m.
-1
Find q such that 4*q**5 + 8/3*q**2 + 0*q - 4*q**3 - 8/3*q**4 + 0 = 0.
-1, 0, 2/3, 1
Let j be (-6)/10 + (-168)/(-30). Let q(y) be the third derivative of 0*y + 1/24*y**4 - 1/180*y**j - 1/9*y**3 + y**2 + 0. Factor q(l).
-(l - 2)*(l - 1)/3
Let c(w) be the second derivative of 2*w**7/147 - 8*w**6/35 + 48*w**5/35 - 64*w**4/21 - 13*w. Factor c(m).
4*m**2*(m - 4)**3/7
Let l(j) = -9*j**2 + 8*j - 9. Let p(v) = -4*v**2 + 4*v - 4. Let a(m) = -2*l(m) + 5*p(m). Determine t so that a(t) = 0.
1
Let t(k) = k**4 + k**2 - k + 1. Let l(c) = -2*c**4 + 8*c**3 - 6*c**2 + 8*c - 8. Let q(b) = l(b) + 8*t(b). Factor q(d).
2*d**2*(d + 1)*(3*d + 1)
Let a(y) be the second derivative of y**4/12 - 11*y**3/42 + 2*y**2/7 - 7*y. Factor a(r).
(r - 1)*(7*r - 4)/7
Let p(x) be the first derivative of -x**5/10 + x**3/3 - 2*x - 3. Let k(u) be the first derivative of p(u). Factor k(o).
-2*o*(o - 1)*(o + 1)
Find m such that -2/5*m + 0 + 2/5*m**2 = 0.
0, 1
Let f = 391169/39 + -10029. Let y = f - 4/13. Factor 0*i + 0 + y*i**2.
2*i**2/3
Let x(f) be the third derivative of 0*f - 1/630*f**7 + 0*f**4 - 1/180*f**5 + 0*f**3 - 3*f**2 + 1/180*f**6 + 0. Find h such that x(h) = 0.
0, 1
Let s(d) be the third derivative of -5*d**8/1176 - 17*d**7/735 - d**6/20 - 11*d**5/210 - d**4/42 - 8*d**2. Let s(f) = 0. What is f?
-1, -2/5, 0
Suppose -3*p - v = -22, 3*p = -2*p + 2*v + 22. Let q be (9/(-6))/((-3)/4). Factor -36*c + 2 + p*c**q + 3*c**3 - c**3 + 42*c.
2*(c + 1)**3
Suppose 2*w = -2*d - 8, 3*w = 5*d + 2*w + 8. Let q be (-2 + 4)/(3 + d). Factor 1/4*r**3 + 0 + 1/4*r - 1/2*r**q.
r*(r - 1)**2/4
Let q(r) be the second derivative of r**7/21 + r**6/3 + 7*r**5/10 - r**4/6 - 8*r**3/3 - 4*r**2 - 2*r + 14. Let q(z) = 0. What is z?
-2, -1, 1
Determine k, given that 2/15*k**3 - 2/3*k**2 - 14/15 - 26/15*k = 0.
-1, 7
Let u(a) = -4*a**2 - a - 7. Let m(t) = -t**2 - 1. Let z(b) = b - 2 + 1 + 0*b. Let x be z(0). Let j(p) = x*u(p) + 5*m(p). Determine f, given that j(f) = 0.
-1, 2
Factor -4*s**3 - 341 + s**3 - 885 - 576*s - 310 - 72*s**2.
-3*(s + 8)**3
Let j(z) be the first derivative of z**5 + 5*z**4/4 - 43. Suppose j(r) = 0. What is r?
-1, 0
Let m(l) be the first derivative of -2*l**5/25 - 3*l**4/10 - 4*l**3/15 + 5. Factor m(d).
-2*d**2*(d + 1)*(d + 2)/5
Let y(z) be the third derivative of -z**6/180 - z**5/30 - z**4/18 + 17*z**2. Factor y(f).
-2*f*(f + 1)*(f + 2)/3
Suppose -2*q + 7 = -3*b + 6*b, -4*b = 4*q - 12. Let w(r) be the first derivative of -1/2*r - b - 1/8*r**4 + 1/6*r**3 + 1/4*r**2. Factor w(o).
-(o - 1)**2*(o + 1)/2
Let v(g) be the first derivative of -g**7/4200 + g**5/600 - 2*g**3 + 5. Let i(r) be the third derivative of v(r). What is o in i(o) = 0?
-1, 0, 1
Let w(t) be the first derivative of -t**3/6 + t**2 - 8. Determine g, given that w(g) = 0.
0, 4
Let u(w) be the third derivative of w**7/840 + w**6/480 - w**5/240 - w**4/96 - 6*w**2. Find s, given that u(s) = 0.
-1, 0, 1
Let p(m) be the second derivative of m**7/840 - m**6/120 + m**5/40 - m**4/24 - m**3/3 + m. Let k(r) be the second derivative of p(r). Factor k(z).
(z - 1)**3
Factor -3*i**2 + 3*i**3 + i**2 - i**3.
2*i**2*(i - 1)
Let x(i) be the first derivative of 2 + 10*i**2 - 8*i - i**4 + 4/5*i**5 - 4*i**3. Factor x(r).
4*(r - 1)**3*(r + 2)
Suppose 0 = 2*w + 3*n - 1, 5*n = 2*n - 3. Let k = 40 + -22. Factor -5*t**w - 3*t - 12*t**4 - 5*t**2 - k*t**3 + t**2 - 3*t**2 - 3*t**5.
-3*t*(t + 1)**4
Let t(w) be the second derivative of w**4/16 + w**3/4 + 3*w**2/8 + 10*w. Factor t(l).
3*(l + 1)**2/4
Let t(h) be the first derivative of -h**4/24 + h**3/9 - h**2/12 + 4*h - 1. Let i(f) be the first derivative of t(f). Let i(r) = 0. What is r?
1/3, 1
Let y(u) = -6*u**2 - 10*u - 4. Let h(d) = 5*d**2 + 9*d + 4. Let l(o) = -4*h(o) - 3*y(o). Factor l(v).
-2*(v + 1)*(v + 2)
Suppose 15 = 3*m + 2*m. Suppose 0 = m*t - 7*t. What is f in -3*f**4 + f**3 + t*f**3 + 6*f**2 - 4*f**2 = 0?
-2/3, 0, 1
Suppose 0*l - 3/4*l**2 - 7/4*l**3 - 5/4*l**4 - 1/4*l**5 + 0 = 0. Calculate l.
-3, -1, 0
Let t(h) be the first derivative of -4*h**3/3 + 6*h**2 + 16*h - 11. Solve t(j) = 0.
-1, 4
Let s(r) be the first derivative of -3*r**4/8 - 4. Factor s(k).
-3*k**3/2
Let b(u) be the third derivative of u**7/5040 - u**6/1440 + u**4/6 + 10*u**2. Let p(q) be the second derivative of b(q). Solve p(o) = 0 for o.
0, 1
Let r(p) = 4*p**2 + p - 1. Let u be r(1). Suppose 6 + 10 = u*y. Find f such that 400*f**3 + 128*f + 182*f**2 + 344*f**2 + 125*f**y + 16 - 166*f**2 = 0.
-2, -2/5
Let y be ((-24)/(-2)*1)/2. Factor 6*x + 6*x + 2*x + 0*x**2 + 4 + y*x**2.
2*(x + 2)*(3*x + 1)
Let n = 14 + -9. Suppose -1 + n = 3*d + 5*j, 0 = -3*j - 3. Find u, given that -4*u**d - 5*u**3 + 6*u**3 + u**3 + 6*u**2 - 6*u + 2 = 0.
1
What is z in -8/9*z - 2/9 - 8/9*z**3 - 4/3*z**2 - 2/9*z**4 = 0?
-1
Suppose -2*m + 1 = -3. Solve m*t**2 + 0*t**3 - 2*t**3 + 2*t**2 = 0 for t.
0, 2
Factor 0*b + 0 + 4/7*b**3 - 4/7*b