5*b + 11. Suppose -s*m = 2*m. Factor -2/3*i + 2*i**2 + m + 2/3*i**4 - 2*i**3.
2*i*(i - 1)**3/3
Let j(t) = -t**2 - 10*t + 14. Let q be j(-11). Let i be q/10*50/60. Let -1/4 + i*k**2 + 0*k = 0. Calculate k.
-1, 1
Let a(h) be the second derivative of -2*h**6/3 - 4*h**5 - 65*h**4/12 - 5*h**3/2 - 8*h. Factor a(u).
-5*u*(u + 3)*(2*u + 1)**2
Factor -37*s**4 - 3*s**2 + 6*s - 32*s**2 + 29*s**3 + 30*s**3 + 7*s**5.
s*(s - 3)*(s - 1)**2*(7*s - 2)
Let i = -4 - -3. Let u be (-2 - -2)*i/2. Factor 3/4*w**3 + u + 1/4*w**4 + 3/4*w**2 + 1/4*w.
w*(w + 1)**3/4
Let k(r) be the first derivative of -4*r**5/25 - 2*r**4/5 + 4*r**2/5 + 4*r/5 - 3. Let k(x) = 0. What is x?
-1, 1
Let v(y) = y - 3. Let z be v(7). Let x(h) be the second derivative of 0 + 4*h**2 + 3*h + 1/6*h**z - 4/3*h**3. Factor x(u).
2*(u - 2)**2
Let g = -57/11 - -421/77. Factor 0*j - 2/7*j**5 + 2/7*j**3 - 2/7*j**4 + g*j**2 + 0.
-2*j**2*(j - 1)*(j + 1)**2/7
Suppose -4 = h - 7. Let f(o) = -3*o**2 + 12*o**h - 1 - 3*o + 4*o**2 - 9*o**3. Let p(y) = -y**3 + y. Let x(m) = -3*f(m) - 6*p(m). Solve x(c) = 0 for c.
-1, 1
Let t(l) = -l. Let n be t(-2). Let f = 5 + -3. Factor -2*s**n - 2*s**3 + 4*s + s + 0*s**2 + f - 3*s.
-2*(s - 1)*(s + 1)**2
Let c be (-9)/18 + (-1)/(-2). Let z(b) be the first derivative of 5*b**2 + c*b**2 - 4 + 12*b + 2*b**2 - b**2 + b**3. Factor z(d).
3*(d + 2)**2
Let v(p) = -9*p**2 - 19*p - 31. Let s(f) = -5*f**2 - 9*f - 15. Let u(q) = 10*s(q) - 6*v(q). Factor u(d).
4*(d + 3)**2
Suppose 0 = -3*q - 0*q - 3. Let i(j) = j. Suppose 4*b - 5*b = 6. Let x(p) = p**2 - 4*p + 1. Let z(r) = b*i(r) + q*x(r). Factor z(s).
-(s + 1)**2
Let m(j) be the second derivative of j**5/40 + j**4/24 - j**3/12 - j**2/4 - 11*j. Factor m(c).
(c - 1)*(c + 1)**2/2
Let s(v) = -4*v**2 - 5*v + 1. Let k(z) = -6*z - 3*z**2 - 9 - 2*z**2 + 11. Let t(n) = -2*k(n) + 3*s(n). Suppose t(j) = 0. Calculate j.
-1, -1/2
Let s(m) = -m**3 + 10*m**2 + 2*m - 20. Let p be s(10). Factor 2/5*c**4 - 2/5*c**2 + 0*c**3 + 0*c + p.
2*c**2*(c - 1)*(c + 1)/5
Let i(z) = -9*z**3 + 18*z**2 + 8*z - 17. Let q(p) = 3*p**3 - 6*p**2 - 3*p + 6. Let h(g) = -6*i(g) - 17*q(g). What is m in h(m) = 0?
0, 1
Suppose 0 = -4*j - 3*a - 3, -j - 4*a - 7 = -2*a. Factor 2/7*r**j + 0 + 0*r**2 - 2/7*r.
2*r*(r - 1)*(r + 1)/7
Let n(u) be the third derivative of -1/40*u**5 + 1/160*u**6 + 0*u - 4*u**2 + 0 + 0*u**3 + 1/32*u**4. Determine w so that n(w) = 0.
0, 1
Let q(w) be the third derivative of w**6/30 - 4*w**5/15 - 15*w**2. Let q(r) = 0. Calculate r.
0, 4
Factor -8/13*c**3 - 8/13*c - 2/13 - 2/13*c**4 - 12/13*c**2.
-2*(c + 1)**4/13
Let o = 4 + -4. Let t(b) be the third derivative of 1/12*b**4 + 1/168*b**8 + 0 + 1/10*b**6 + 2/15*b**5 - 2*b**2 + o*b**3 + 4/105*b**7 + 0*b. Factor t(y).
2*y*(y + 1)**4
Let q = 8 - 6. Let n(t) = -2*t - 2. Let f be n(-2). Solve -4*d + 0*d**f + d**q + 3*d = 0.
0, 1
Let -95*b - 16 + 5*b**3 + 32 - 7 + 40*b**2 + 41 = 0. Calculate b.
-10, 1
Let j be 4/924 - (3 - (-3 - -6)). Let a(h) be the second derivative of -j*h**7 + 4/165*h**6 - 3*h + 2/33*h**4 - 1/33*h**3 - 3/55*h**5 + 0 + 0*h**2. Factor a(n).
-2*n*(n - 1)**4/11
Let j be (-1383)/36 + (-1)/3. Let o = j - -39. Determine a so that a**4 + 0 - 3/2*a**3 - o*a**5 + a**2 - 1/4*a = 0.
0, 1
Let u be (-156)/(-135) + (-11)/(385/(-14)). Factor 0*j + 0 - 4/9*j**2 - 16/9*j**4 + 2/3*j**5 + u*j**3.
2*j**2*(j - 1)**2*(3*j - 2)/9
Let z(i) be the second derivative of i**4/48 + i**3/12 - 6*i. Factor z(k).
k*(k + 2)/4
Let w(m) be the second derivative of m**4/22 - 5*m**3/33 + 2*m**2/11 - 13*m. Let w(s) = 0. Calculate s.
2/3, 1
Let c(i) = 2*i**2 - i - 2. Let n(m) = m**3 - m**2 + 1. Let y = -1 - -2. Suppose -2*g + g = y. Let x(a) = g*n(a) - c(a). Factor x(k).
-(k - 1)*(k + 1)**2
Let b(j) be the third derivative of j**8/336 + j**7/35 + 7*j**6/60 + 4*j**5/15 + 3*j**4/8 + j**3/3 + 25*j**2. Factor b(y).
(y + 1)**4*(y + 2)
Let q be (-9)/12 + 27/4. Let d = 9 - q. Let 0*i - 2/7*i**4 + 2/7*i**d + 0 + 2/7*i**2 - 2/7*i**5 = 0. What is i?
-1, 0, 1
Factor 2/5*b - 2/5*b**2 + 0.
-2*b*(b - 1)/5
Let z(d) be the second derivative of 1/15*d**5 - 9*d + 0 - 2/63*d**7 + 1/9*d**4 - 2/45*d**6 + 0*d**3 + 0*d**2. Let z(i) = 0. Calculate i.
-1, 0, 1
Find z, given that 13*z**4 + 0*z**2 - z**4 - 12*z**2 - 4*z**5 + 8*z - 4*z**3 = 0.
-1, 0, 1, 2
Let p(d) be the third derivative of 1/15*d**5 + 8/3*d**3 + 0 - 2/3*d**4 + 0*d + 8*d**2. Find x such that p(x) = 0.
2
Determine k, given that -12*k**3 - 9*k**4 + 9/2*k**5 + 16/3 + 40/3*k**2 + 56/3*k = 0.
-2/3, 2
Let w(o) = 2*o**4 + 7*o**2 - 3*o + 3. Let g(i) = i**4 + i**3 + 6*i**2 - 2*i + 2. Let v(d) = -3*g(d) + 2*w(d). Factor v(b).
b**2*(b - 4)*(b + 1)
Solve 8*k**2 - 14*k**4 - 14*k**5 + 0*k**3 - 8*k**3 - 24*k**4 - 8*k**3 = 0.
-2, -1, 0, 2/7
Let b(z) be the first derivative of 2*z**5/5 - 4*z**3/3 + 2*z + 2. Find r such that b(r) = 0.
-1, 1
Let r = 27 + -25. Suppose -r*v = -3*v + 5*q + 3, 4*v = 5*q + 12. Determine g, given that 4/3*g**2 - 2/3*g + 2*g**v + 0 = 0.
-1, 0, 1/3
Let f(s) = 32*s**3 - 65*s**2 + 48*s - 15. Let p(t) = -16*t**3 + 32*t**2 - 24*t + 8. Let o(b) = -4*f(b) - 7*p(b). Factor o(y).
-4*(y - 1)**2*(4*y - 1)
Factor -20*c + 5/2*c**3 - 5/2*c**2 + 30.
5*(c - 2)**2*(c + 3)/2
Let z = 5 + -5. Let 4*j**3 + z*j**2 - 3*j**3 + j**2 + 0*j**3 = 0. What is j?
-1, 0
Let y(w) be the third derivative of w**6/1080 + w**5/270 - w**4/216 - w**3/27 + 21*w**2. Find n, given that y(n) = 0.
-2, -1, 1
Determine q, given that 0*q**2 + 1/7*q**3 + 1/7*q**4 + 0 + 0*q = 0.
-1, 0
Find t such that -1 + 2/3*t**2 + 1/3*t**4 - 4/3*t**3 + 4/3*t = 0.
-1, 1, 3
Let s = -271/4 - -68. Let -1/4*w + s - 17/4*w**2 + 9*w**4 + 21/4*w**3 = 0. What is w?
-1, -1/4, 1/3
Let c(o) be the third derivative of 27*o**7/455 - 3*o**6/65 + 2*o**5/195 + 8*o**2. Solve c(v) = 0 for v.
0, 2/9
Let k(r) = -8*r**2 - 9*r + 5. Let p(g) = 15*g**2 + 18*g - 11. Let i(j) = 7*k(j) + 3*p(j). Factor i(f).
-(f + 1)*(11*f - 2)
Let h(p) be the second derivative of -10*p**7/189 + 2*p**6/45 + 17*p**5/45 - 19*p**4/27 + 8*p**2/9 - 2*p + 17. Determine u so that h(u) = 0.
-2, -2/5, 1
Factor 0*j**2 + 3/4*j**3 - j + 0 - 1/4*j**4.
-j*(j - 2)**2*(j + 1)/4
Let q(d) be the first derivative of 3/2*d**4 - 3 - 3*d**2 - 4*d + 4/3*d**3. Solve q(z) = 0.
-1, -2/3, 1
Let f(g) be the third derivative of g**8/16800 - g**7/25200 - g**6/3600 + g**5/30 + 3*g**2. Let j(l) be the third derivative of f(l). Factor j(x).
(2*x - 1)*(3*x + 1)/5
Let c(d) be the second derivative of -d**7/14 - 17*d. Determine m, given that c(m) = 0.
0
Let h = 26 + -76/3. Find s, given that 10/9*s**2 + h*s - 4/9 = 0.
-1, 2/5
Let w(r) be the third derivative of r**3 + 0 + 0*r + 3/4*r**4 + 1/140*r**7 - 6*r**2 + 13/40*r**5 + 3/40*r**6. Determine z so that w(z) = 0.
-2, -1
Suppose 0 = 2*s - g - 3, -2*g - 6 = 2*s - 0*s. Let q(v) be the first derivative of 0*v**3 + s*v - 1 - 1/2*v**4 + v**2. Factor q(o).
-2*o*(o - 1)*(o + 1)
Factor 2/3*h**2 + 0 + h**3 + 0*h.
h**2*(3*h + 2)/3
Let h(b) be the second derivative of -b**6/360 - b**5/60 - b**4/24 + 5*b**3/6 - 4*b. Let i(g) be the second derivative of h(g). Solve i(j) = 0.
-1
Let b(c) be the third derivative of -c**6/480 - c**5/60 - 5*c**4/96 - c**3/12 - 4*c**2. Let b(i) = 0. Calculate i.
-2, -1
Let x(u) be the second derivative of 0 - 6*u + 0*u**3 - 1/4*u**4 + 6*u**2. Factor x(a).
-3*(a - 2)*(a + 2)
Let r = 240 - 240. Factor -6/5*s - 3/5*s**2 + 3/5*s**3 + r.
3*s*(s - 2)*(s + 1)/5
Let n(f) be the first derivative of f**4 - 26*f**3/3 + 6*f**2 + 12. Factor n(h).
2*h*(h - 6)*(2*h - 1)
Factor -1/4*h + h**2 + 1/4*h**3 - h**4 + 0.
-h*(h - 1)*(h + 1)*(4*h - 1)/4
Let n(z) be the second derivative of -z**4/4 + z**3/2 + 3*z**2 - 6*z. Let n(k) = 0. Calculate k.
-1, 2
Factor -6*u**3 + 3*u - 2*u**4 + 4*u - u + 2*u.
-2*u*(u - 1)*(u + 2)**2
Suppose -2*r - u = -2, 2*r - 9 = -5*u - 23. Let -2/9*c**2 - 2/9*c**r + 2/9*c + 2/9 = 0. What is c?
-1, 1
Suppose 0 = 3*v - 2*p - 9 - 15, 5*v - p = 33. Factor -2*u**4 + 5 - 6*u**2 - 5 + 0*u + v*u**3 + 2*u.
-2*u*(u - 1)**3
Let s(h) = 2*h**2 - h**2 + 21*h - 15*h + 5. Let w be s(-5). Factor 1/3*x**3 - 1/3*x**5 + 1/3*x**4 + w + 0*x - 1/3*x**2.
-x**2*(x - 1)**2*(x + 1)/3
Let z(s) be the second derivative of -3*s**7/161 + 5*s**6/23 - 116*s**5/115 + 164*s**4/69 - 208*s**3/69 + 48*s**2/23 - 9*s. What is k in z(k) = 0?
2/3, 2, 3
Let h(q) = -q**4 - q**3 - q + 1. Let s(i) = i**5 - 5