*2 + 22*s - 31. Let i(x) = g(x) + 4*o(x). Find h such that i(h) = 0.
3
Let i(d) be the second derivative of 1/5*d**4 - 3/25*d**5 - 2/15*d**3 + 0*d**2 + 0 - 4*d + 2/75*d**6. Factor i(b).
4*b*(b - 1)**3/5
Let n = 57 - 23. Let z = -34 + n. Determine a, given that -1/2*a + 1/4*a**2 + z + 1/4*a**3 = 0.
-2, 0, 1
Factor -3/5*r**3 + 3/5*r**2 + 0 + 1/5*r**4 - 1/5*r.
r*(r - 1)**3/5
Suppose -13 = -4*z + 3. Let g be z*((-20)/(-18) + -1). Factor 0 - 2*r**2 - g*r - 14/9*r**3.
-2*r*(r + 1)*(7*r + 2)/9
Factor 1/2*d**2 + 0*d - 2.
(d - 2)*(d + 2)/2
Suppose m**4 + m**3 - 3*m - m + 0*m - 4*m**2 + 0*m**3 = 0. Calculate m.
-2, -1, 0, 2
Let t be 5 - 8/(8/5). Factor 0 + 2/11*a**5 + 2/11*a**2 + 6/11*a**4 + 6/11*a**3 + t*a.
2*a**2*(a + 1)**3/11
Solve 4*n - 2*n**2 - 4*n**3 + 0 + 4 - 2*n**2 = 0.
-1, 1
Let r be 5/(75/2)*50/15. Determine y, given that 0*y**2 + 2/9*y**4 - 4/9*y + r*y**3 - 2/9 = 0.
-1, 1
Suppose 0 = s - 3*s. Factor 2*n**2 + 2*n**3 + s*n**3 + 2 + 6*n**2 + 10*n + 2.
2*(n + 1)**2*(n + 2)
Let d(y) be the first derivative of -y**6/40 - y**5/10 - y**4/8 - 5*y**2/2 - 2. Let s(u) be the second derivative of d(u). Suppose s(h) = 0. Calculate h.
-1, 0
Factor -6*g**3 + 8*g**4 - 4*g**2 + 5*g**4 - 15*g**4.
-2*g**2*(g + 1)*(g + 2)
Let m(u) = -19*u**5 + 7*u**4 + 13*u**3 - 13*u**2 - 13*u + 13. Let a(b) = 9*b**5 - 3*b**4 - 6*b**3 + 6*b**2 + 6*b - 6. Let k(w) = -13*a(w) - 6*m(w). Factor k(n).
-3*n**4*(n + 1)
Let a(s) be the second derivative of 7*s**4/48 - 3*s**3/8 + s**2/4 + 3*s. What is w in a(w) = 0?
2/7, 1
Let c(s) be the second derivative of 0 + 0*s**3 - 11*s - 1/24*s**4 - 1/80*s**5 + 0*s**2. Factor c(p).
-p**2*(p + 2)/4
Let x(s) be the third derivative of -s**7/1050 - s**6/200 - s**5/150 - 12*s**2. Factor x(y).
-y**2*(y + 1)*(y + 2)/5
Let n = 151 + -7247/48. Let m(j) be the third derivative of 2*j**2 + 1/120*j**5 - 1/420*j**7 + 0 + n*j**4 + 0*j + 0*j**3 - 1/240*j**6. Factor m(k).
-k*(k - 1)*(k + 1)**2/2
Let l(s) be the third derivative of -s**7/42 - s**6/8 + 3*s**2. Suppose l(u) = 0. What is u?
-3, 0
Let d(p) be the third derivative of p**7/8820 - p**5/420 + p**4/3 - 9*p**2. Let a(f) be the second derivative of d(f). Let a(u) = 0. What is u?
-1, 1
Let x(v) = -14*v**2 - 6*v. Let i(w) = -45*w**2 - 16*w. Let k(b) = 11*b**2 + 4*b. Let l(z) = 2*i(z) + 9*k(z). Let m(c) = -8*l(c) - 5*x(c). Factor m(n).
-2*n*(n + 1)
Let m(g) be the third derivative of g**7/14 - 13*g**6/24 + 7*g**5/6 + 5*g**4/6 - 20*g**3/3 + 6*g**2. What is s in m(s) = 0?
-2/3, 1, 2
Let m = 30313/30615 + 48/785. Let t = -5/13 + m. Factor 2/3*r**3 + 2/3*r**4 - t*r**2 + 0 - 2/3*r.
2*r*(r - 1)*(r + 1)**2/3
Factor -t**3 + 0*t**3 - t**3 + 4*t**3 + 2*t**2.
2*t**2*(t + 1)
Let r be (5/(50/45) - 5)*-1. Find a such that 0 + r*a**2 - 1/2*a = 0.
0, 1
Let d(a) be the first derivative of -a**8/168 - 2*a**7/105 + a**5/15 + a**4/12 - 3*a**2/2 + 3. Let j(w) be the second derivative of d(w). Factor j(u).
-2*u*(u - 1)*(u + 1)**3
Let f(p) = p**2 - 9*p + 12. Let l be f(8). Factor 5*r**4 - r**3 - r**3 + r**l.
2*r**3*(3*r - 1)
Let v be 28/49 + 146/14. Let j be v/9 + (-21)/21. Find k such that 0 + 0*k - 2/9*k**2 + j*k**3 = 0.
0, 1
Suppose 3*z = h + 17, 4*z - h - 4*h = 19. Let q = z + -2. Let -5/4*y**q + 0 + 1/2*y - 1/2*y**3 + 5/4*y**2 = 0. Calculate y.
-1, -2/5, 0, 1
Let s(x) be the first derivative of 2 + 1/12*x**3 + 1/4*x**2 + 0*x. Factor s(o).
o*(o + 2)/4
Let d = -11 - -18. Suppose 0 = 2*c - d*c. Factor 0*q + c - 1/4*q**2.
-q**2/4
Let q(f) = -2 - 7*f**3 + 6 - 3*f + 8*f**3 - 3*f**2. Let u be q(4). What is p in p**2 - 2*p**2 + 4*p**2 + u*p - 2*p = 0?
-2, 0
Let m(c) = -2*c + 3. Let i be m(-4). Suppose 0 = 4*z - u - 13, z + i = -z - 3*u. Let 1 + 2*k**2 + 4*k**3 - 3*k - 2*k**z = 0. Calculate k.
-1, 1/2
Let b(n) be the first derivative of -n**6/240 - n**5/30 - n**4/12 - n**2/2 + 2. Let t(p) be the second derivative of b(p). Factor t(i).
-i*(i + 2)**2/2
Let k(r) be the second derivative of -r**8/6720 + r**6/720 + 7*r**4/12 - 3*r. Let w(u) be the third derivative of k(u). Solve w(i) = 0.
-1, 0, 1
Let i(s) = -s**5 - s**4 + s**3 - 7*s**2. Let h(t) = -6*t**2. Let f(w) = 4*h(w) - 3*i(w). Find n, given that f(n) = 0.
-1, 0, 1
Let j(v) = -6*v - 9. Let h be j(-2). Let t be (-18)/(-8) - 1/4. Factor -4*o**2 - h*o - o**2 + o + 3*o**t.
-2*o*(o + 1)
Suppose 0*s = 3*s + 15, -2*w + 3*s + 15 = 0. Factor -4/5*c**4 + w + 0*c + c**3 - 1/5*c**2.
-c**2*(c - 1)*(4*c - 1)/5
Suppose -3 - 6 = -3*v. Suppose 0 = -5*k + v*m + 11, -22 = -3*k - k - 2*m. Solve -3*a**4 + 2*a**2 - 3*a**4 + 4*a**k = 0 for a.
-1, 0, 1
Suppose 0*s**2 + 2/17*s**5 + 4/17*s**3 + 0 - 6/17*s**4 + 0*s = 0. Calculate s.
0, 1, 2
Solve -2/15*z**2 - 4/15*z - 2/15 = 0.
-1
Let m be 0 + 24 - (-15)/(-5). Find t, given that -t**2 - 21 + m = 0.
0
Suppose -8 = 3*g + 7. Let b = -5 - g. Factor b + 4/3*t + 2/3*t**2.
2*t*(t + 2)/3
Suppose 5*w = -o + 227, 0 = -3*w - 5*o + 34 + 111. Let c be (-36)/162 - (-64)/w. Determine i so that -14/5*i**3 + c*i**4 + 0 - 2/5*i + 2*i**2 = 0.
0, 1/3, 1
Let u(w) = 2*w + 1. Let t be u(2). Find y, given that 2 - y**4 + 9*y**4 + 4*y**3 - 14*y**4 + 4*y**2 - 6*y + 2*y**t = 0.
-1, 1
Let h = 71/4 + -65/4. Factor -h*c**2 + 0 + 3*c.
-3*c*(c - 2)/2
Let n(j) be the first derivative of j**7/14 + 3*j**6/10 + j**5/5 + 3*j**2/2 - 7. Let t(v) be the second derivative of n(v). Factor t(l).
3*l**2*(l + 2)*(5*l + 2)
Suppose -2*c - 16 = -2*f, -f - 2*c = -0*f + 7. Suppose -f*a - 15 = -0*i + i, 4*i = 3*a + 15. What is z in 4/3*z**2 - 2*z**3 + i - 2/9*z = 0?
0, 1/3
Factor 0 + 3/7*z**4 + 0*z + 6/7*z**3 + 3/7*z**2.
3*z**2*(z + 1)**2/7
Let w(o) be the third derivative of 0*o**3 + 0 + 1/240*o**5 - 1/480*o**6 + 1/96*o**4 + 0*o - 1/840*o**7 - 3*o**2. Let w(p) = 0. Calculate p.
-1, 0, 1
Solve 6/7*q**2 + 0 + 2/7*q**3 + 0*q = 0.
-3, 0
Let b(o) be the second derivative of -1/60*o**4 + 5*o + 0 + 1/15*o**3 + 0*o**2. Find a, given that b(a) = 0.
0, 2
Let i = 44095 - 1983869/45. Let b = i - 44/5. Factor 0*w**3 - 4/9*w**4 + b*w - 2/9*w**5 + 4/9*w**2 + 0.
-2*w*(w - 1)*(w + 1)**3/9
Let t(y) = -6*y**2 - 3*y. Suppose a + 2 = -4*a - 3*v, 2*a = v + 8. Suppose -6*l = -a*l + 20. Let f(u) = -u**2 - u. Let b(x) = l*f(x) + t(x). Factor b(k).
-k*(k - 2)
Let s(u) be the second derivative of -1/3*u**3 + 0 + 1/12*u**4 + 0*u**2 + u. Factor s(w).
w*(w - 2)
Let b(h) be the third derivative of h**5/360 - h**4/144 - h**3/6 - 20*h**2. Factor b(w).
(w - 3)*(w + 2)/6
Suppose 0*r + 3*f + 6 = 5*r, -4*r - 8 = 4*f. Solve r + 1/6*k**3 + 0*k**2 - 1/6*k = 0.
-1, 0, 1
Let a(n) be the first derivative of -1/42*n**4 - 2*n - 2/21*n**3 - 1 + 0*n**2. Let i(p) be the first derivative of a(p). Factor i(q).
-2*q*(q + 2)/7
Suppose -5*p = -5 - 5. Let q(d) be the second derivative of d**2 + p*d - d**3 - 1/10*d**5 + 0 + 1/2*d**4. Factor q(v).
-2*(v - 1)**3
Suppose -d**2 + 42 - d + 3*d - 42 = 0. What is d?
0, 2
Factor -3*v + 3/5*v**3 - 3/5*v**2 - 9/5.
3*(v - 3)*(v + 1)**2/5
Let g(n) = -n**2 + 6*n - 2. Let i(k) = 2*k**2 - 12*k + 5. Let l(o) = -10*g(o) - 6*i(o). Factor l(v).
-2*(v - 5)*(v - 1)
Let a(d) be the second derivative of -3*d**5/100 - 3*d**4/20 - d**3/5 + 3*d. What is b in a(b) = 0?
-2, -1, 0
Let q(d) be the second derivative of -d**4/48 + d**3/12 + 3*d. Factor q(o).
-o*(o - 2)/4
Suppose 2*g**4 - 2*g**3 + 49 - 49 - 2*g**2 + 2*g = 0. What is g?
-1, 0, 1
Let b = -2 - -7. Suppose -26 = -4*c - 2*u, 3*c + b*u - 50 = -13. Let -8*z**c - 3*z**2 - 5*z**2 + 3*z**5 - z**5 + 2*z + 12*z**3 = 0. What is z?
0, 1
Determine i so that 9*i**3 - 110*i**2 - 5*i**4 - 208*i - 49*i**3 - 45 + 88*i = 0.
-3, -1
Factor 0 - 3/5*i**3 - 24/5*i**2 - 9*i.
-3*i*(i + 3)*(i + 5)/5
Let j(b) be the first derivative of b**6/2 + 27*b**5/20 + 9*b**4/8 + b**3/4 - 42. Factor j(v).
3*v**2*(v + 1)**2*(4*v + 1)/4
Let k(i) be the third derivative of -i**6/120 - i**5/15 + i**4/4 + 7*i**3/6 - 2*i**2. Let f be k(-5). Factor 0 + 2/9*b**3 + 8/9*b**f + 8/9*b.
2*b*(b + 2)**2/9
Let z be (-4)/(-2) - (-2 - 6). Suppose 6 + z*g + 66*g**2 + 28*g + 16*g**3 + 2*g**3 = 0. What is g?
-3, -1/3
Suppose 3*q = 2*k + 8, -k = 3*q - 2*k - 4. Factor -s**2 + 3/2*s**3 - 1/2*s**4 + q*s + 0.
-s**2*(s - 2)*(s - 1)/2
Suppose 4*x + 30 + 0 = 5*d, -2*d + 2*x + 14 = 0. Factor 2/3*c + 0 + 5/3*c**d - 7/3*c**3.
-c*(c - 1)*(7*c + 2)/3
Let s(p) be the second derivative of -5*p**4/12 - 5*p**3/3 - 5*p**2/2 + 4*p. Factor s(b).
-5*(b + 1)