**5/100 + o**4/30 + o**3/30 - 3*o - 2. Let x(g) be the first derivative of u(g). Factor x(b).
b*(b + 1)**2/5
Let p(w) be the first derivative of -w**6/27 - 4*w**5/45 + w**4/9 + 16*w**3/27 + 7*w**2/9 + 4*w/9 + 7. Suppose p(v) = 0. What is v?
-1, 2
Let v(h) be the third derivative of 0*h + 1/105*h**7 + 0*h**3 + 1/168*h**8 - 3*h**2 + 0 + 0*h**4 - 1/60*h**6 - 1/30*h**5. Factor v(l).
2*l**2*(l - 1)*(l + 1)**2
Suppose 0 = 2*o - 3 - 1. Let 16 + b**o + b - 9*b + 0*b + 0*b = 0. Calculate b.
4
Let o = -21119/120 - -176. Let t(v) be the second derivative of -1/8*v**2 + 1/40*v**5 - v + o*v**6 - 1/12*v**3 + 0 + 0*v**4. Find q, given that t(q) = 0.
-1, 1
Let f(z) = -9*z**3 + 2*z**2 + 5*z - 2. Let j(s) = s**3. Let y = -1 - -3. Suppose 5*i - 2*w + 8 = -4, -12 = -y*i + 5*w. Let p(x) = i*j(x) - f(x). Factor p(h).
(h - 1)*(h + 1)*(5*h - 2)
Factor 7/8*v**2 + v - 2 + 1/8*v**3.
(v - 1)*(v + 4)**2/8
Let r(u) be the third derivative of -u**7/3780 - u**6/540 - u**4/8 - 4*u**2. Let c(o) be the second derivative of r(o). Let c(m) = 0. What is m?
-2, 0
Let m be 2/(-8)*0/(-5). Factor -2/9*q + m + 2/9*q**2.
2*q*(q - 1)/9
Factor 20/11*o**2 + 2/11*o**5 + 24/11*o**3 + 6/11*o + 12/11*o**4 + 0.
2*o*(o + 1)**3*(o + 3)/11
Let y = 18 + -15. Let g(w) be the second derivative of 0 + 2/7*w**2 - 1/7*w**y + 1/42*w**4 + w. Suppose g(c) = 0. What is c?
1, 2
Let -1/2*x**2 + 5/4*x**3 - 5*x + 2 = 0. Calculate x.
-2, 2/5, 2
Suppose -30 = -y - 9*y. Suppose 0*w = -w + 2. Factor -2/5 - 12/5*k**w - 2/5*k**4 - 8/5*k - 8/5*k**y.
-2*(k + 1)**4/5
Suppose -2*t + 6*t = 0, -20 = -4*u + 5*t. Factor 4*n**2 - 3*n**2 - 2 + 0 + 6*n**2 - u*n.
(n - 1)*(7*n + 2)
Let y = 27/185 + -511/3552. Let x(o) be the third derivative of 0*o**4 + 0*o**3 + 0*o**5 - y*o**6 + 2*o**2 + 0*o + 0. Let x(u) = 0. What is u?
0
Let m(w) be the first derivative of w**3/12 - w**2/4 + w/4 + 3. Determine a so that m(a) = 0.
1
Factor -2*w**3 - 1/2*w**5 - 7/4*w**4 - 3/4*w**2 + 0 + 0*w.
-w**2*(w + 1)**2*(2*w + 3)/4
Let r(g) be the first derivative of -g**6/15 + g**4/10 - 6. Factor r(l).
-2*l**3*(l - 1)*(l + 1)/5
Suppose 0 = 2*k + 6, 7*k + 14 = m + 3*k. Solve -6*w**4 + 3*w**3 + 6*w**2 - 6*w**m = 0 for w.
0, 1/2
Let a be (-2)/6*(-35 - -33). Determine f, given that a*f**2 + 0 + 0*f = 0.
0
Let g(d) = -d**2 + 7*d + 5. Let h be g(7). Let w(f) be the second derivative of -f + 1/12*f**4 + 3/80*f**h - 1/24*f**3 - 1/4*f**2 + 0. Solve w(s) = 0 for s.
-1, 2/3
Suppose h = -4*h - 140. Let a be 4*(-1)/h*2. Suppose 2/7*c**3 + 2/7*c**4 + 4/7 - 6/7*c**2 - a*c = 0. Calculate c.
-2, -1, 1
Let h(k) = -7*k**4 + 7*k**3 + 5*k**2 - 5. Let n(p) = 3*p**4 - 3*p**3 - 2*p**2 + 2. Suppose -3*i - 6 + 21 = 0. Let b(s) = i*n(s) + 2*h(s). Factor b(t).
t**3*(t - 1)
Let l be ((-19)/(-38))/((-2)/(-12)). Suppose 5*p = l*p. Find m, given that 4/9*m**2 + 0*m**3 - 2/9 - 2/9*m**4 + p*m = 0.
-1, 1
Let j be 122/(-504) - (-2)/8. Let m(u) be the second derivative of 0*u**4 + j*u**7 - u + 1/45*u**6 + 1/60*u**5 + 0*u**2 + 0*u**3 + 0. Factor m(l).
l**3*(l + 1)**2/3
Let i(w) be the second derivative of 2*w**6/5 - 147*w**5/20 + 51*w**4 - 152*w**3 + 96*w**2 - 17*w. Factor i(l).
3*(l - 4)**3*(4*l - 1)
Let i(c) be the first derivative of c**6/6 - c**5/5 - c**4/4 + c**3/3 - 15. Factor i(k).
k**2*(k - 1)**2*(k + 1)
Factor 2*p + 191*p**3 + 0*p - 6*p**2 - 199*p**3.
-2*p*(p + 1)*(4*p - 1)
Let c(x) = x**2 + 7*x + 7. Let b be c(-5). Let t = -1 - b. Suppose -i**2 - 2*i**3 + t*i**2 + 3*i**3 = 0. Calculate i.
-1, 0
Suppose -3*s + 10 = m, -7 + 21 = 5*m + 3*s. Let w(r) = r**2 + 1. Let d be w(m). Factor 0*y - 2*y**4 + 3*y - y**5 - d*y + 2*y**2.
-y*(y - 1)*(y + 1)**3
Let v(z) = -30*z**3 + 72*z**2 + 209*z - 103. Let n(f) = 10*f**3 - 24*f**2 - 70*f + 34. Let u(x) = -7*n(x) - 2*v(x). Factor u(g).
-2*(g - 4)*(g + 2)*(5*g - 2)
Let i(o) = -7*o**4 - 9*o**3 - 3*o**2 - o. Let p(t) be the first derivative of 8*t**5/5 + 5*t**4/2 + t**3 + t**2/2 - 2. Let r(y) = 7*i(y) + 6*p(y). Factor r(d).
-d*(d + 1)**3
Let j(n) be the second derivative of 0 + 0*n**4 + n**2 - 1/80*n**5 - 4*n + 1/8*n**3. Let h(f) be the first derivative of j(f). Factor h(g).
-3*(g - 1)*(g + 1)/4
Suppose 3*r + 0 = 15. Suppose -k + 0*k + 5 = j, 4*j - 12 = 0. Find u such that -u**3 + 0*u**4 - u**k + 0*u**4 + u**r + u**4 + 0*u**5 = 0.
-1, 0, 1
Let x(m) be the second derivative of m**4/8 + m**3/2 - 6*m**2 - 20*m. Let x(y) = 0. Calculate y.
-4, 2
Let s(g) = -5*g**2 + 15*g + 45. Let r(l) = l**2 - 4*l - 11. Let k(b) = 18*r(b) + 4*s(b). Suppose k(p) = 0. What is p?
-3
Let x(s) be the first derivative of s**5 - 11*s**4/3 + 14*s**3/3 - 2*s**2 - 3*s - 5. Let r(k) be the first derivative of x(k). Factor r(v).
4*(v - 1)**2*(5*v - 1)
Let t(k) be the third derivative of 0*k - 3*k**2 - 1/12*k**5 + 0 + 2/9*k**3 - 1/6*k**4 - 1/90*k**6. Factor t(v).
-(v + 2)**2*(4*v - 1)/3
Factor -w**4 + w**2 + 4*w**3 - 9*w + 3*w - w**5 + 4*w - w**3.
-w*(w - 1)**2*(w + 1)*(w + 2)
Let p(c) be the second derivative of -81*c**5/55 + 21*c**4/44 + 10*c**3/33 - 2*c**2/11 - 48*c. Factor p(f).
-(4*f + 1)*(9*f - 2)**2/11
Let f(h) be the first derivative of -5/6*h**5 + 0*h - 5/24*h**4 + 1 + 8/9*h**3 - 1/3*h**2. Factor f(u).
-u*(u + 1)*(5*u - 2)**2/6
Let l be (-45)/(-50) - 1/2. Let q(d) be the first derivative of 0*d**2 - 1 - 2/3*d**3 - l*d**5 + d**4 + 0*d. Factor q(g).
-2*g**2*(g - 1)**2
Let r be (-48)/(-27) - (-4)/18. Suppose -3*c**4 - r*c**2 - 3*c**3 + 0*c**4 + 5*c**2 + 3*c**5 = 0. What is c?
-1, 0, 1
Let p be (-116)/(-14) - (-4)/(-14). Determine m, given that -p*m + 8*m - 2*m**3 + 2*m**2 = 0.
0, 1
Factor 8/3*l + 2/3*l**2 + 0.
2*l*(l + 4)/3
Let o(g) = 3*g**3 + 3*g**2 + 12*g - 6. Let n(w) = -2*w**3 - 2*w**2 - 11*w + 5. Let s(l) = -6*n(l) - 5*o(l). Solve s(u) = 0 for u.
-2, 0, 1
Let y(g) = 11*g**4 - 17*g**3 - 2*g**2 + 8*g - 8. Let x(s) = -4*s**4 + 6*s**3 + s**2 - 3*s + 3. Let n(o) = -8*x(o) - 3*y(o). Determine k so that n(k) = 0.
0, 1, 2
Factor 1/2*l**3 - 1/2*l - l**2 + 1.
(l - 2)*(l - 1)*(l + 1)/2
Let g be (-3)/2*20/(-15). Factor b - 2*b**2 + g*b**2 - 3*b + 2*b**3.
2*b*(b - 1)*(b + 1)
Let l(z) be the first derivative of -z**6/27 + 4*z**5/45 + z**4/6 - 8*z**3/27 - 4*z**2/9 - 19. Let l(r) = 0. What is r?
-1, 0, 2
Determine m, given that -4/9 - 2/3*m - 2/9*m**2 = 0.
-2, -1
Let r(w) be the second derivative of w**9/83160 + w**4/3 - 4*w. Let q(a) be the third derivative of r(a). Solve q(d) = 0.
0
Let h(z) be the third derivative of -z**10/7560 + z**9/3780 - z**4/4 + 5*z**2. Let w(s) be the second derivative of h(s). Factor w(y).
-4*y**4*(y - 1)
Let s(q) = -q**2 - q. Let z(f) = 16*f**2 + 22*f - 2. Let j(r) = -36*s(r) - 2*z(r). Suppose j(x) = 0. What is x?
1
Let x(h) = h**4 - h**2 + h + 1. Let q(l) = 2*l**5 - 5*l**4 + 6*l**3 + 5*l**2 - 5*l + 3. Let a(s) = q(s) - 3*x(s). Solve a(r) = 0 for r.
-1, 0, 1, 2
Let f(k) = -k**3 - 2*k**2 + 7*k + 6. Let d be f(-4). Let c be (8/14)/(d/7). Factor 0*x + 0*x**2 + c*x**3 - 2/5*x**4 + 0.
-2*x**3*(x - 1)/5
Let x(h) be the second derivative of -1/60*h**5 + 2/45*h**6 + 0*h**2 - 1/9*h**4 + h + 0 + 1/18*h**3. Suppose x(m) = 0. What is m?
-1, 0, 1/4, 1
Suppose -6*d = -2*d - 3*b - 220, -3*d + 165 = -4*b. Let w be (-10)/d - (-38)/88. Factor -w*a**2 + 0*a + 1/4.
-(a - 1)*(a + 1)/4
Let z(w) = -w**3 + w. Let h(x) = 10*x**3 + 5*x**2 - 6*x - 9. Let p(r) = 4*h(r) + 36*z(r). Factor p(o).
4*(o - 1)*(o + 3)**2
Factor 2*n**3 + n**2 + 4*n**2 - 4*n**4 + 2*n**3 + 3*n**2.
-4*n**2*(n - 2)*(n + 1)
Find f, given that -2/17*f**3 + 12/17*f**2 + 12/17 - 22/17*f = 0.
1, 2, 3
Let i(q) be the third derivative of 1/45*q**7 - 1/30*q**5 + 0*q**3 - 1/84*q**8 - 1/36*q**4 + 0 + 1/60*q**6 + 0*q + 3*q**2. Suppose i(w) = 0. What is w?
-1/2, -1/3, 0, 1
Let g be 9/15 + 20/(-75). Factor -2/3*d**2 - g*d**5 + 0*d**3 + 1/3*d + 2/3*d**4 + 0.
-d*(d - 1)**3*(d + 1)/3
Let c(z) be the first derivative of 2/3*z - 1/9*z**6 - 5/3*z**4 + 1 - 5/3*z**2 + 20/9*z**3 + 2/3*z**5. Find q, given that c(q) = 0.
1
Factor 3/4*q + 1/4*q**2 + 0.
q*(q + 3)/4
Let h(a) be the third derivative of -2*a**5/45 - 5*a**4/36 - a**3/9 + 7*a**2. Factor h(m).
-2*(m + 1)*(4*m + 1)/3
Suppose 0 = 2*l - 5 - 1. Suppose -25 = -j - 4*r, 0 = -0*r - 4*r + 20. Factor 2*w**2 - j*w**l - w + 4*w**3 - 4*w**2.
-w*(w + 1)**2
Let v be (-76)/(-18) + 12/(-54). Solve h**2 - 4*h**2 + v*h + h**2 + 3*h**2 + 4 = 0 for h.
-2
Let u be (-3)/4 - 45/(-30). Suppose 3*v + 2*v