
Solve 5*r**2 + 2*r - r**2 + 20*r**3 - 18*r**3 = 0.
-1, 0
Let j be -1*(1/(-1) - -1). Let w(z) = z**3 - 4*z**2 - 2*z - 6. Let m be w(5). Let j - 9*g**3 + 3*g**2 - 1/3*g + m*g**4 = 0. Calculate g.
0, 1/3
Let w(a) be the first derivative of 2*a**3/15 - 2*a**2 + 18*a/5 - 23. Suppose w(t) = 0. Calculate t.
1, 9
Let l(v) = 6*v - 31. Let y be l(6). Let o(a) be the third derivative of -2*a**2 + 0*a**3 + 0*a**4 + 0*a + 0 - 1/30*a**y. Factor o(s).
-2*s**2
Suppose 11 = 2*p + 1. Factor 4*d**p - 4*d**3 + 2 + 3*d**2 - 9*d**2 + 6*d**4 - 2*d**2.
2*(d - 1)*(d + 1)**3*(2*d - 1)
Let x(z) be the first derivative of z**3/7 - 3*z**2/14 - 18*z/7 - 44. Suppose x(m) = 0. What is m?
-2, 3
Let w = 18 + -11. Find y, given that -3*y**4 - 6*y**2 - w*y**3 + 9*y**3 + 7*y**3 = 0.
0, 1, 2
Let g(r) be the third derivative of 1/180*r**5 + 0*r**3 + 1/1008*r**8 - 1/630*r**7 + r**2 - 1/360*r**6 + 0*r + 0*r**4 + 0. Determine m so that g(m) = 0.
-1, 0, 1
Let t(h) be the third derivative of -h**8/28 - 3*h**7/70 + h**6/8 + 3*h**5/20 - h**4/8 + 8*h**2. Determine p, given that t(p) = 0.
-1, 0, 1/4, 1
Suppose 2 - 2/3*g**2 + 4/3*g = 0. What is g?
-1, 3
Factor -8*x**2 - 8*x**2 + 5*x - 2*x + 13*x**2.
-3*x*(x - 1)
Let p(z) be the second derivative of -2/7*z**2 + 2/21*z**4 + 0 + 3/70*z**5 + 6*z - 1/21*z**3. Factor p(r).
2*(r + 1)**2*(3*r - 2)/7
Let n(c) = c**3 + 3*c - 2*c**4 + c + 5*c**2 + 7 + 0*c**4. Let f(d) = -3*d**4 + d**3 + 7*d**2 + 6*d + 10. Let t(m) = -5*f(m) + 7*n(m). Factor t(o).
(o - 1)*(o + 1)**3
Let z(v) be the second derivative of v**4/12 - 5*v**3/6 + 2*v**2 - 4*v. What is b in z(b) = 0?
1, 4
Let a = -14 - -16. Solve 2/7*g**a - 2/7 + 0*g = 0 for g.
-1, 1
Let m be (-4)/(-7) - (-72)/21. Find y, given that 20*y**m - 48*y + 48*y**3 - 2 - 1 - 13 - 4*y**2 = 0.
-2, -1, -2/5, 1
Let x(m) = -20*m**3 + 33*m**2 - 3*m + 5. Let c(v) = -60*v**3 + 100*v**2 - 8*v + 16. Let q(l) = 5*c(l) - 16*x(l). Factor q(z).
4*z*(z - 1)*(5*z - 2)
Suppose 1 = 6*h - 17. Let y(m) be the third derivative of 0*m + 0*m**h + 1/480*m**6 + 1/120*m**5 + 0 - 1/280*m**7 + 2*m**2 + 0*m**4. What is x in y(x) = 0?
-2/3, 0, 1
Suppose -2/9 + 4/9*o**3 + 2/3*o**4 - 2/3*o + 2/9*o**5 - 4/9*o**2 = 0. Calculate o.
-1, 1
Let f(x) be the third derivative of -x**6/540 + x**5/135 + 7*x**4/108 + 4*x**3/27 - 5*x**2. Factor f(r).
-2*(r - 4)*(r + 1)**2/9
Let r = 8/23 + -10/161. Let u = -1/28 + r. Determine y so that 1/4*y**2 - 1/4 - 1/4*y + u*y**3 = 0.
-1, 1
Let j = 1 + 1. Find y such that 11*y**j + 3 + 0*y**2 - 3*y**3 - 15*y + y**2 + 3 = 0.
1, 2
Suppose 16 = -4*z + 6*z. Suppose w = 5*w - z. Factor 3/4*u**w + 3/4 - 3/2*u.
3*(u - 1)**2/4
Let h(j) = -j**2 - 6*j + 5. Let i be h(-7). Let l(d) = 3*d**3 - 24*d**2 - 27*d + 9. Let q(p) = p**3 - 6*p**2 - 7*p + 2. Let z(m) = i*l(m) + 9*q(m). Factor z(u).
3*u*(u - 3)*(u + 1)
Suppose 2*n = 2*r - 2*n + 12, 3*n = 2*r + 12. Let g(o) = 2*o**2 + 3. Let q(p) = 3*p**2 + 5. Let h(l) = r*q(l) + 10*g(l). Factor h(z).
2*z**2
Let o(d) be the first derivative of -d**6/24 + 3*d**4/16 + d**3/6 + 7. Solve o(b) = 0 for b.
-1, 0, 2
Let k(t) be the third derivative of -t**6/180 - t**5/15 - t**4/3 + t**3/3 + 2*t**2. Let u(d) be the first derivative of k(d). What is z in u(z) = 0?
-2
Let h = 4 + -3/2. Let r = -58 + 60. Solve -5/2*m**5 - 1 + 5*m**3 + 2*m**r - m**4 - h*m = 0.
-1, -2/5, 1
Let h(k) be the third derivative of 1/1800*k**6 + 1/6*k**3 - 1/600*k**5 + 2*k**2 + 0*k**4 + 0 + 0*k. Let o(v) be the first derivative of h(v). Solve o(c) = 0.
0, 1
Let p be -3 - (-2 + -4) - -1. Factor 23*y**3 + 99*y**2 - 60*y**3 - 6*y**3 + 48*y**p + 3 - 77*y**3 - 30*y.
3*(y - 1)**2*(4*y - 1)**2
Let j(r) be the first derivative of 3*r**5/5 - 9*r**4/4 + r**3 + 9*r**2/2 - 6*r + 46. Factor j(z).
3*(z - 2)*(z - 1)**2*(z + 1)
Suppose 22*i = 20*i. Let n(g) be the second derivative of -3*g + 0 + 1/60*g**6 + 0*g**2 + i*g**3 + 1/24*g**4 - 1/20*g**5. Solve n(y) = 0.
0, 1
Let v(m) be the second derivative of -5*m**7/42 - m**6/2 - 3*m**5/4 - 5*m**4/12 + 16*m. Let v(i) = 0. What is i?
-1, 0
Suppose 0*h**2 + 1/2 + 1/4*h**3 - 3/4*h = 0. What is h?
-2, 1
Let h be (-2)/(-7 + 3)*0. Let w(i) be the first derivative of 2 + h*i**2 + 1/6*i**3 - 1/2*i. Factor w(y).
(y - 1)*(y + 1)/2
Suppose 2*t - 6 + 50 = 0. Let v be (-4)/(-6)*(-24)/t. Factor 2/11*i**3 - v*i**2 + 10/11*i - 4/11.
2*(i - 2)*(i - 1)**2/11
Let u(f) be the first derivative of f**3 - 3*f**2/2 - 6*f - 6. Let u(a) = 0. What is a?
-1, 2
Factor 1/5 - q + 6/5*q**2 + 3/5*q**5 - 7/5*q**4 + 2/5*q**3.
(q - 1)**3*(q + 1)*(3*q - 1)/5
Let z = -1 - -3. Suppose 3*y = z*y + 3. Factor 0*n**2 + 6*n**y - 4*n**2 - 4*n**3 + 2*n.
2*n*(n - 1)**2
Let k(x) = -x - 4. Let n be k(-6). Let b be 120/(-20) + (-60)/(-9). Factor -4/3*z**n + 2/3*z + 0 + b*z**3.
2*z*(z - 1)**2/3
Let d(q) = q + 8. Let r be d(-5). Find o, given that -3 + o**3 + 15*o**2 - 1 + 3*o**r + 12*o = 0.
-2, 1/4
Let a(h) be the third derivative of -1/15*h**4 + 0*h + 2*h**2 - 4/75*h**5 + 3/20*h**6 + 0*h**3 + 0. Suppose a(z) = 0. Calculate z.
-2/9, 0, 2/5
Let i(p) be the third derivative of p**6/56 + 11*p**5/20 + 25*p**4/14 + 2*p**3 + 19*p**2. Let i(u) = 0. What is u?
-14, -1, -2/5
Let v = 11 - 8. Suppose v*o + 11 = 5*j, 5*j = -4*o + 2*j + 24. Factor -6*k + 2*k**4 - 2 - 8*k**2 + 3*k + k**5 - 4*k - 2*k**o.
(k - 2)*(k + 1)**4
Determine n so that 0*n - 2/7*n**3 + 2/7*n**4 + 0 + 0*n**2 = 0.
0, 1
Suppose -18 = -3*n - 0. Let c(d) be the first derivative of -4/5*d**5 + 0*d - 1/3*d**n + d**2 + 1 + 4/3*d**3 + 0*d**4. Suppose c(j) = 0. Calculate j.
-1, 0, 1
Factor 2 + 0 + 9*h + 2*h**2 - 5*h.
2*(h + 1)**2
Let h be (-5)/(-15) + (-28)/(-6). Let g = -1 + 3. Suppose 3*r**2 - 3*r**3 + 0*r**g + 3*r - 8 + h = 0. What is r?
-1, 1
Let t(r) = -38*r - 378. Let u be t(-10). Factor 2/7*j**u + 8/7 + 8/7*j.
2*(j + 2)**2/7
Let b be 14/(-16)*8/(-28). Find s, given that b*s + 1/4*s**3 + 0 + 1/2*s**2 = 0.
-1, 0
Let l(p) = 5*p**4 + 13*p**3 - 32*p**2 - 56*p + 8. Let z(g) = -2*g**4 - 4*g**3 + 11*g**2 + 19*g - 3. Let r(s) = -3*l(s) - 8*z(s). Factor r(m).
m*(m - 4)**2*(m + 1)
Suppose 8*i = 6*i + 6. Let c(m) be the third derivative of -9/175*m**7 + 9/25*m**6 + i*m**2 - 24/25*m**5 - 16/15*m**3 + 4/3*m**4 + 0*m + 0. Factor c(k).
-2*(k - 2)*(3*k - 2)**3/5
Let s(v) = -v**2 + v + 1. Let o(d) = 4*d**3 + 7*d**2 - 12*d - 7. Let u(k) = 5*o(k) + 40*s(k). Determine h, given that u(h) = 0.
-1, 1/4, 1
Let g(s) = -3*s - 15. Let p be g(-5). Find h such that 0 - 2/13*h**2 + 2/13*h**4 + 0*h**3 + p*h = 0.
-1, 0, 1
Suppose -170*a**4 - 21*a + 6*a**2 + 20*a**2 + 5*a + 14*a**2 - 100*a**5 + 84*a**3 = 0. Calculate a.
-2, -1/2, 0, 2/5
Suppose 0 = -4*d - 4*p - 8, 2*d + 4*p + 8 = 3*d. Determine t so that d - 1/2*t**2 + 1/4*t**3 + 1/4*t = 0.
0, 1
Let b(l) be the third derivative of 0 - 1/120*l**5 + 4*l**2 + 0*l + 0*l**4 - 1/240*l**6 + 0*l**3. Suppose b(h) = 0. What is h?
-1, 0
Let y = 1/47 + 137/188. Factor 9/4*g**3 + y*g**4 - 3/2 + 3/4*g**2 - 9/4*g.
3*(g - 1)*(g + 1)**2*(g + 2)/4
Suppose -2*a - 2*n = -6*a, 0 = -5*a + 2*n. Let x(g) be the first derivative of a*g + 2/9*g**3 - 2/3*g**2 + 1. Determine w, given that x(w) = 0.
0, 2
Let u(x) be the third derivative of -x**5/6 + x**4/24 + x**3/3 - 5*x**2. Let u(r) = 0. What is r?
-2/5, 1/2
Let i(w) = -26*w**5 - 14*w**4 + 24*w**3 + 2*w - 14. Let q(y) = -9*y**5 - 5*y**4 + 8*y**3 + y - 5. Let a(v) = 5*i(v) - 14*q(v). Suppose a(u) = 0. Calculate u.
-1, 0, 1
Let z(n) = -11*n - 25*n + 4 + 46*n - 5*n**2. Let w(a) = -2*a**2 + 5*a + 2. Let c = -22 + 31. Let x(l) = c*w(l) - 4*z(l). Solve x(o) = 0 for o.
-2, -1/2
Let a(w) = -2*w - 15. Let p be a(-14). Suppose -2 = -s + 3*l + p, 5 = -s - l. What is n in s + 1/3*n**3 + 0*n**2 - 1/3*n = 0?
-1, 0, 1
Let q(f) be the first derivative of -f**3/3 - 10. Factor q(h).
-h**2
Let k(v) = 6 - 2*v + 3*v + 0*v. Let a be k(-4). Factor c - 2 - 2*c**2 + 2*c**2 + 3*c**a.
(c + 1)*(3*c - 2)
Suppose -5*m = 64 - 84. Suppose 0*b = -4*b. Factor 0 + 0*g + 2/7*g**5 + 0*g**m + b*g**2 - 2/7*g**3.
2*g**3*(g - 1)*(g + 1)/7
Let q(g) = -13*g**4 - 5*g - 5. Let w(n) = 6*n**4 + 2*n + 2. Let x(t) = 2*q(t) + 5*w(t). Solve x(c) = 0 for c.
0
Suppose -c + 1 = 0, -c = 3*t + c - 11. Suppose -i - 4*i = -3*j + 54, 0 = -t*i. Factor 0 - 2/3*w**4 + 6*w**3 - 18*w**2 + j*w.
-2*w*(w - 3)**3/3
Let n be ((-4)/30 - 0)*(-2)/8. Let c(m) be the third derivative of 0*m**3 - n*m**5 - 1/6*m**4 - m**2 + 1/60