q**3 + 0 + 32/9*q**2 - 14/9*q**4 = 0. What is q?
-2, 0, 2/7, 1
Let 3*r**3 + 20*r - 20*r**2 - 3 + r + 5*r**2 - 6 = 0. What is r?
1, 3
Suppose -2*m = -5*q + 18, 3*q = -q + 3*m + 20. Determine h, given that 3/2*h**2 - 3*h + q - 1/4*h**3 = 0.
2
Let h(p) = p**3 + 13*p**2 + 19*p + 87. Let o be h(-12). Determine t so that -1/4*t**o + 1/2 - 1/2*t**2 + 1/4*t = 0.
-2, -1, 1
Find m such that 3/7*m**4 + 0*m + 0 + 6/7*m**3 + 3/7*m**2 = 0.
-1, 0
Factor -18 + 16 + 18*x - 3*x**2 + 23.
-3*(x - 7)*(x + 1)
Let b = 0 + 5. Let h(c) be the first derivative of 8/5*c**b - 3*c**2 + 3/2*c**4 + 3 + 2*c - 10/3*c**3. Let h(t) = 0. Calculate t.
-1, 1/4, 1
Let w(i) be the second derivative of 3/20*i**5 + 0 - 3*i - 1/2*i**3 - 1/4*i**4 + 1/10*i**6 + 0*i**2. Determine g, given that w(g) = 0.
-1, 0, 1
Let i be 13*(-12)/42 + 4 + 0. Factor i*q**3 - 2/7*q + 2/7*q**4 + 0 - 2/7*q**2.
2*q*(q - 1)*(q + 1)**2/7
Suppose -5*t - a - 4 = 0, t - 12 = -3*t + 3*a. Let q be (1 + -2)*(2 + -2). Suppose t + 1/3*v**2 - 1/3*v**4 + q*v**3 + 0*v = 0. Calculate v.
-1, 0, 1
Let g = -28 - -34. Let h(t) be the third derivative of 0*t**5 + 0*t**3 + 0 - t**2 - 1/36*t**4 + 1/180*t**g + 0*t. Let h(l) = 0. What is l?
-1, 0, 1
Let p(d) = d**2 + d - 4. Suppose 0 = -4*n - 3*l - 18, -2*n + l - 10 = 3*l. Let m be p(n). Solve -2/3*y**4 + 0*y**3 + 0 + 0*y**m + 2/3*y**5 + 0*y = 0 for y.
0, 1
Let r(t) = 8*t**3 - 40*t**2 - 150*t - 260. Let x(o) = o**3 - o**2 - 1. Let g(v) = r(v) - 10*x(v). Factor g(y).
-2*(y + 5)**3
Factor -71*w**3 + 75*w**3 + w**2 + 3*w**2.
4*w**2*(w + 1)
Let u = -24 + 17. Let f be (-26)/(-56) - 2/u. Let -f*o + 0 + 9/4*o**2 = 0. Calculate o.
0, 1/3
Let o(u) = 5*u + 6. Let t be o(-3). Let z(q) = -q**3 - 8*q**2 + 10*q + 9. Let x be z(t). Factor x*a - 3/5*a**4 + 3/5*a**2 + 0 + 3/5*a**3 - 3/5*a**5.
-3*a**2*(a - 1)*(a + 1)**2/5
Let l(y) = -9*y**4 - 18*y**3 - 6*y**2 + 9*y + 6. Let r(i) = 18*i**4 + 37*i**3 + 13*i**2 - 18*i - 12. Let b(u) = 5*l(u) + 3*r(u). Factor b(s).
3*(s + 1)**3*(3*s - 2)
Let w(a) = -a**2 + 3*a + 3. Suppose 0*l + l - 3 = 0. Let d be w(l). Factor 4*m**d - 1 - 3*m**3 - 2*m + m**2 + m.
(m - 1)*(m + 1)**2
Let a be (-2)/12 + (-88)/(-495). Let h(c) be the third derivative of 0*c - a*c**5 + c**2 + 0*c**4 + 0 + 1/9*c**3. Factor h(g).
-2*(g - 1)*(g + 1)/3
Let n(o) = -o**4 + o**2 + o + 1. Let v(d) = -7*d**4 + 7*d**3 + d**2 + 2*d + 3. Let m(w) = 6*n(w) - 2*v(w). Find g, given that m(g) = 0.
-1/4, 0, 1
Let o(q) be the first derivative of 4*q**3/9 - 2*q**2/3 - 8*q + 12. Solve o(s) = 0.
-2, 3
Let h = -241/6 - -491/12. Determine a, given that 1/2*a + 1/4 - h*a**2 = 0.
-1/3, 1
Determine r, given that 44/5*r + 8/5 - 52/5*r**2 = 0.
-2/13, 1
Solve -2/7*p**3 + 0 - 4/7*p + 6/7*p**2 = 0.
0, 1, 2
Let t(a) be the third derivative of 0 + 1/900*a**6 + 4*a**2 - 1/450*a**5 - 1/2520*a**8 + 0*a**3 + 0*a + 0*a**4 + 1/1575*a**7. Suppose t(l) = 0. Calculate l.
-1, 0, 1
Suppose -3*v + 20 = 2*v. Suppose v*i - 5*i = -3, 2*p + 3*i = 13. Find y such that 3/4*y**p + y**3 - 9/4*y + 1/2 = 0.
-2, 1/4, 1
Let t = 10229 - 583030/57. Let y = 5/19 + t. Suppose -2/3*z + 0 - y*z**2 = 0. What is z?
-1, 0
Let v(p) = p**2 - p. Let b(z) = -6*z**3 - 15*z**2 - 5*z + 1. Let f(g) = b(g) + 3*v(g). Let o(y) be the first derivative of f(y). Find n, given that o(n) = 0.
-2/3
Suppose 3*x + 3*d = -0*d - 6, 2*d + 10 = 0. Let k(z) = -73*z**2 - 152*z + 36. Let s(r) = 24*r**2 + 51*r - 12. Let n(p) = x*k(p) + 8*s(p). Factor n(v).
-3*(v + 2)*(9*v - 2)
Let -28*u + u**3 - 22 - 1 - 8*u**2 + 3*u**3 + 7 = 0. What is u?
-1, 4
Let k(b) = 5*b**2 + 17*b + 18. Let u(f) = f - 1. Let h(l) = k(l) + 3*u(l). Suppose h(c) = 0. What is c?
-3, -1
Let -6/7*w**2 + 2/7*w**3 + 6/7*w - 2/7 = 0. What is w?
1
Solve -7*s**4 + 28*s**4 - 16*s**4 = 0.
0
Let a(z) be the first derivative of -2*z**3/9 + 4*z**2/3 - 8*z/3 - 4. Factor a(y).
-2*(y - 2)**2/3
Let r = 7 + -5. Suppose -2*k + 18 = r. Let -k*f + 6*f**2 + 2 + 4*f**5 + 4*f**3 + 2*f**2 - 10*f**4 + 0 = 0. What is f?
-1, 1/2, 1
Let z(k) be the second derivative of 0 - 1/4*k**4 + 6*k + 1/2*k**3 + 0*k**2. Factor z(v).
-3*v*(v - 1)
Let n(j) = j + 1. Let m be n(-6). Let p = m - -4. Let l(q) = q**3 - 2*q**2 + 2*q + 2. Let b(c) = -c**3 + c**2 - c - 1. Let w(h) = p*l(h) - 2*b(h). Factor w(r).
r**3
Let a(g) be the third derivative of -g**5/90 - 11*g**4/36 - 10*g**3/9 - 22*g**2. Factor a(w).
-2*(w + 1)*(w + 10)/3
Let c(j) = -8*j**2 - 8*j + 4. Let r(a) = -15*a**2 - 17*a + 7. Let s(u) = -7*c(u) + 4*r(u). Solve s(d) = 0 for d.
-3, 0
Factor 4/11*m**2 + 2/11*m**3 + 2/11*m + 0.
2*m*(m + 1)**2/11
Let b(m) be the second derivative of 0*m**2 - 1/6*m**4 + 1/15*m**5 + 0 + 6*m + 1/9*m**3. Factor b(d).
2*d*(d - 1)*(2*d - 1)/3
Let c be 2/(0 + 4/10). Suppose c*j = -4*z - 0 + 36, 3*j + 2*z - 20 = 0. Solve -4 + 4 - r**j + r**2 = 0 for r.
-1, 0, 1
Factor 3*d**5 - 8*d**2 - 20*d - 3*d**5 - 3 - 5 + 16*d**3 + 4*d**5 + 16*d**4.
4*(d - 1)*(d + 1)**3*(d + 2)
Let q be ((-4)/9)/((-19)/((-285)/(-20))). Factor -1/3 - 1/3*n + 1/3*n**2 + q*n**3.
(n - 1)*(n + 1)**2/3
Let r = -44/225 + 16/25. Factor -2/9*n**2 + 0 - r*n.
-2*n*(n + 2)/9
Let x(z) = 7*z**2 - 3*z. Let l(y) = -15*y**2 + 6*y. Let f(c) = 4*l(c) + 9*x(c). Factor f(w).
3*w*(w - 1)
Let r(o) be the second derivative of -o**5/20 - 5*o**4/6 - o**3/6 - 4*o**2 + 3*o. Let q be r(-10). Find k such that 4*k - q + 1 + 3 + 2*k**2 = 0.
-1
Let p(m) = -5*m**2 + 2*m + 1. Let z(t) be the first derivative of -2*t**3 + t**2 + t - 9. Let r = -9 - -2. Let c(x) = r*p(x) + 6*z(x). Factor c(q).
-(q + 1)**2
Factor 0 - 12/5*r**2 - 4/5*r**3 + 8*r.
-4*r*(r - 2)*(r + 5)/5
Suppose -2*q = 5*m - 4*q - 14, -29 = -5*m - 3*q. Suppose 11 = 2*z - 5*w, 0 = m*z - 4*w - 20 + 4. Factor -2/5*g**4 + 4/5*g**z + 2/5 - 4/5*g + 0*g**2.
-2*(g - 1)**3*(g + 1)/5
Let a = 5689/48 + -237/2. Let j(f) be the second derivative of 0 - 2*f + 0*f**2 + 1/80*f**5 - a*f**4 + 0*f**3. Let j(q) = 0. Calculate q.
0, 1
Let r(s) = -s**2 - 5*s - 6. Suppose 5*a + 0*b + 14 = b, 0 = -2*a + 4*b - 20. Let g be r(a). Determine l so that 1/4*l**2 + g + 1/4*l = 0.
-1, 0
Let i(f) be the third derivative of -f**5/60 - f**4/6 + 3*f**2. Let d be i(-4). Factor -8*t**3 - 1/2*t + 4*t**2 + d.
-t*(4*t - 1)**2/2
Let x(g) = g + 7. Let p be x(-5). Let a(c) be the second derivative of c + 1/50*c**5 + 0 + 1/75*c**6 - 2/5*c**p - 1/10*c**4 - 1/3*c**3. Factor a(d).
2*(d - 2)*(d + 1)**3/5
Let n be (-1)/(-4) + (-39)/(-4). Suppose -5*r + n*r - 10 = 0. Suppose -10/7*d**4 + 2/7*d**5 - 20/7*d**r + 20/7*d**3 - 2/7 + 10/7*d = 0. Calculate d.
1
What is l in 9 - 3*l**4 - 6*l**3 - 9 + 0 = 0?
-2, 0
Factor -1/3*g**2 + 2/3*g + 0.
-g*(g - 2)/3
Let d(f) be the first derivative of -1/25*f**5 - 4/15*f**3 + 1/5*f**4 + 0*f**2 - 3 + 0*f. Solve d(u) = 0.
0, 2
Find q such that -25/3*q - 20/3 - 5/3*q**2 = 0.
-4, -1
Let u(x) = -10*x**3 - 50*x**2 + 42*x + 18. Let w(o) = 3*o**3 + 17*o**2 - 14*o - 6. Let f(t) = -3*u(t) - 8*w(t). Factor f(g).
2*(g - 1)*(g + 3)*(3*g + 1)
Let a(r) = -3*r**4 + 17*r**3 - 24*r**2 + 12*r. Let k(b) be the first derivative of -b**4/4 + 6. Let u(d) = a(d) + 2*k(d). Factor u(n).
-3*n*(n - 2)**2*(n - 1)
Suppose 3*l + 5 = 5*z - 6, 2*l + 3*z = -1. Let g be (-46)/(-10) - l/5. Determine f, given that g*f + 5*f**3 - 4*f**2 - 2 + 0*f - 4*f**3 = 0.
1, 2
Let s(m) be the first derivative of -m**6/14 - m**5/35 + m**4/14 + 1. Find r, given that s(r) = 0.
-1, 0, 2/3
Let w(z) = 4*z**2 + 5*z + 1. Let a(o) = 2*o + 3. Let b = -3 - -1. Let d be a(b). Let i(y) = -y**2 - y. Let x(r) = d*w(r) - 3*i(r). Let x(t) = 0. What is t?
-1
Let t(g) be the first derivative of 1 + g + 1/2*g**4 + 1/15*g**6 - 3/10*g**5 - 1/3*g**3 + 0*g**2. Let z(h) be the first derivative of t(h). Factor z(y).
2*y*(y - 1)**3
Let g(x) be the third derivative of x**9/20160 - x**8/3360 - x**5/12 + 6*x**2. Let u(l) be the third derivative of g(l). Factor u(k).
3*k**2*(k - 2)
Let o(w) = -w**3 + 3*w**2 + 6*w - 5. Suppose -2*i - 2*i + 16 = 0. Let d be o(i). What is b in 3*b**2 - 4*b**2 - b**3 - b + d*b = 0?
-2, 0, 1
Let j be -2 + 3/30 + 2. Let h(c) be the first derivative of -1/8*c**4 - 1/6*c**3 + j*c**5 + 1/4*c**2 + 0*c + 2. Solve h(q) = 0 for q.
-1, 0, 1
Let j(f) be the third derivative of -f**5/90 + 7*f**4/18 - 49*f**3/9 - 16*f**2. Factor j(p).
-2*(p - 7)**2/3
Factor -2/5*d + 4/5*d**2 - 2/5*d**4 + 4/5*d**3 - 2/5*d**5 - 2/5.
-2*(d - 1)**2*(d + 1)**3/5
Let y(w) be the