ative of o**9/3024 - o**8/5040 + o**5/60 + 3*o**2. Let h(g) be the third derivative of p(g). Factor h(w).
4*w**2*(5*w - 1)
Determine g so that 50*g**5 + 8*g**3 + 14*g**4 - 3*g**4 + 29*g**4 = 0.
-2/5, 0
Let q = -1 + 4. Factor 4*f**3 + q + 8*f**2 + 10*f - 2*f**3 + 1.
2*(f + 1)**2*(f + 2)
Let w(v) = v**3 + v + 1. Let h(f) = 15*f**4 + 31*f**3 + 10*f**2 - 4*f - 4. Let n(q) = h(q) + 4*w(q). Factor n(d).
5*d**2*(d + 2)*(3*d + 1)
Let k = 18 + -13. Let d be 1/k - (-45)/25. Factor -2*z - 3 - 7*z**3 - 6*z - d*z**3 - 7*z - 21*z**2.
-3*(z + 1)**2*(3*z + 1)
Let m be 23/6 - (-9)/54. Factor 10*d**2 + d**5 - 3*d**3 + 0*d**5 - 2*d + 0*d**4 - 5*d**2 - d**m.
d*(d - 1)**3*(d + 2)
Let s(n) = 6*n**3 + 12*n**2 - 23*n + 5. Let a(t) = -3*t**3 - 6*t**2 + 11*t - 2. Let u(m) = 5*a(m) + 2*s(m). Factor u(j).
-3*j*(j - 1)*(j + 3)
Let r(i) be the third derivative of -1/75*i**6 + 0*i + 0 - 1/15*i**3 + 4*i**2 - 1/25*i**5 - 1/525*i**7 - 1/15*i**4. Find a, given that r(a) = 0.
-1
Determine v so that 3/5*v**3 + 1/5*v + 0 + 4/5*v**2 = 0.
-1, -1/3, 0
Let a(x) be the second derivative of 0 - 11/27*x**3 - 2/9*x**2 - 8/27*x**4 - 7/90*x**5 - 4*x. Let a(d) = 0. Calculate d.
-1, -2/7
Let t be (-9)/((-81)/(-24)) - 3/(-1). Solve u**3 - 1/3*u**5 + 0 - 1/3*u**4 - 2/3*u + t*u**2 = 0 for u.
-2, -1, 0, 1
Let w(o) be the third derivative of o**6/30 + o**5/3 + 4*o**4/3 + 8*o**3/3 - 3*o**2. Factor w(n).
4*(n + 1)*(n + 2)**2
Let y(t) be the second derivative of t**8/3360 - t**7/1260 - t**4/6 - 3*t. Let z(r) be the third derivative of y(r). Factor z(g).
2*g**2*(g - 1)
Let -a + 1/3*a**2 + 2/3 = 0. Calculate a.
1, 2
Factor 5/9*g**2 + 10/9 - 3*g.
(g - 5)*(5*g - 2)/9
Factor 0 - 4/11*w + 6/11*w**5 + 6/11*w**2 + 6/11*w**3 - 14/11*w**4.
2*w*(w - 1)**3*(3*w + 2)/11
Factor -11 - 44*t + 7*t**3 - 1 - 20*t**2 + 5*t**3.
4*(t - 3)*(t + 1)*(3*t + 1)
Let h(a) be the second derivative of -a**5/30 + 3*a**2/2 - a. Let p(f) be the first derivative of h(f). Factor p(l).
-2*l**2
Let h(i) = -39*i**2 - 94*i - 40. Let t(k) = 155*k**2 + 375*k + 160. Let x(s) = -15*h(s) - 4*t(s). Suppose x(n) = 0. Calculate n.
-2, -4/7
Let z = -4 - -7. Let -6*s**2 + 2*s**5 + 0*s + 6*s**4 + s**5 - z*s = 0. What is s?
-1, 0, 1
Factor -2/3*x - 1/3*x**2 + 1.
-(x - 1)*(x + 3)/3
Let a(d) = -d - 1. Let b be a(-5). Factor 5 - 2*g**2 + 0 + g**b - 4.
(g - 1)**2*(g + 1)**2
Suppose 0 = 7*k - 6*k. Let w(q) be the second derivative of 0*q**3 + 1/36*q**4 + 2*q + k*q**2 + 0. Factor w(d).
d**2/3
Let m(q) = 4*q**2 - q - 10. Suppose -v = n + 7, -n + 18 = -5*n - 2*v. Let j(i) = -i**2 + 3. Let c(o) = n*m(o) - 7*j(o). Find a, given that c(a) = 0.
1
Factor -19*t**2 + 3*t**3 - 6 + 11*t + 5*t**2 + 6*t.
(t - 3)*(t - 1)*(3*t - 2)
Determine p so that 3/8*p**3 + 0*p**2 + 3/4 - 9/8*p = 0.
-2, 1
Let h = 38/9 + -118/45. Factor -4/5 - p**2 - 1/5*p**3 - h*p.
-(p + 1)*(p + 2)**2/5
Let c(h) be the third derivative of -1/24*h**4 + 0 + 0*h + 1/60*h**5 + 0*h**3 + h**2. Factor c(q).
q*(q - 1)
Let f = -6 + -6. Let g = -9 - f. Factor -75*m**2 - 48*m - 57*m**3 - 13*m**4 - m**4 - 12 - 3*m**4 - g*m**5 - 4*m**4.
-3*(m + 1)**3*(m + 2)**2
Let q be (-27)/(-15) - (-2)/10. Let s = -29 - -31. Factor 8*y**3 - s*y + y**2 - y**2 - q*y**3 + 4*y**2.
2*y*(y + 1)*(3*y - 1)
Let v(d) be the second derivative of d**6/20 - d**5/2 + d**4/2 - 18*d. Suppose v(m) = 0. Calculate m.
0, 2/3, 6
Let j(h) be the second derivative of h**4/48 - h**3/24 + h. Factor j(d).
d*(d - 1)/4
Suppose -t + 5 + 0 = 0. Determine u so that -4*u**2 + 3*u**3 - 6 + t*u + 1 - 2*u**3 + 3 = 0.
1, 2
Suppose -f - 3 + 6 = 0. Let r = -15 + 18. Factor 2 + r*d**3 - 4*d**f + 3*d + 0.
-(d - 2)*(d + 1)**2
Let d be 15/(-9) + (-176)/(-48). Factor -3/5*r**5 + 0 + 3/5*r**3 + 0*r + 3/5*r**4 - 3/5*r**d.
-3*r**2*(r - 1)**2*(r + 1)/5
Suppose 9 + 52 = w. Let b = -541/9 + w. Factor b*r - 2/9*r**2 - 8/9.
-2*(r - 2)**2/9
Let g(p) be the first derivative of p**4/8 + p**3/6 + 3. Factor g(a).
a**2*(a + 1)/2
Let j(b) be the first derivative of 2*b**5/45 - 2*b**3/27 + 14. Let j(a) = 0. What is a?
-1, 0, 1
Find y, given that -21*y**4 + 23*y**2 - 33*y + 15*y**3 + 4*y**2 + 18*y - 6 = 0.
-1, -2/7, 1
Let h(m) be the second derivative of 1/2*m**4 - 2*m**3 + 4*m**2 + 3*m + 0 - 1/20*m**5. Solve h(u) = 0 for u.
2
Let l(s) be the second derivative of 3*s**6/2 + 21*s**5/4 + 65*s**4/12 - 5*s**3/6 - 5*s**2 + 42*s. Solve l(f) = 0 for f.
-1, -2/3, 1/3
Let n(c) = -5*c**2 + c + 2 + 6*c - 12*c**3 + 4 - c**4 + 0*c. Let t(a) = 3*a**4 + 42*a**3 + 18*a**2 - 24*a - 21. Let f(b) = -18*n(b) - 5*t(b). Solve f(g) = 0.
-1, 1
Let h(o) be the third derivative of -o**8/60480 + o**7/15120 - o**5/30 - 4*o**2. Let t(q) be the third derivative of h(q). Let t(v) = 0. What is v?
0, 1
Let p(y) be the second derivative of y**4/12 - 4*y**3/3 + 7*y**2/2 + 3*y. Find x such that p(x) = 0.
1, 7
Solve -111/2*q**4 + 20*q**2 + 503/8*q**3 + 4 - 63/8*q**5 - 47/2*q = 0 for q.
-8, -2/3, 2/7, 1/3, 1
Find x, given that -x**2 - 6*x**2 + 5*x + 2*x**2 = 0.
0, 1
Suppose 4*h = -0*h - 4. Let q = 3 + h. Factor -5*b - b**5 - 2 + 4*b**4 - 2*b**2 - q*b**5 + 4*b**5 + 4*b**3.
(b - 1)*(b + 1)**3*(b + 2)
Let j = -16 - -20. Let h(m) be the first derivative of -1/3*m**3 - j*m + 1 - 2*m**2. Factor h(l).
-(l + 2)**2
Let s = 15 - 14. Let r(t) = -24*t**4 - 20*t**3 - 4*t**2 - 8*t. Let x(q) = -q**4 - q**3 - q**2 - q. Let k(c) = s*r(c) - 8*x(c). Factor k(a).
-4*a**2*(a + 1)*(4*a - 1)
Solve 1/3*f**3 + 4/3*f**4 - 2*f**2 + 0 + 1/3*f**5 + 0*f = 0.
-3, -2, 0, 1
Let m(a) be the third derivative of 1/420*a**6 + 2*a**2 + 1/210*a**5 - 1/21*a**3 - 1/84*a**4 + 0 + 0*a. Determine q, given that m(q) = 0.
-1, 1
Let d(j) be the second derivative of 0 + 1/5*j**6 + 0*j**2 + j + 7/6*j**4 + 4/5*j**5 + 2/3*j**3. Factor d(a).
2*a*(a + 1)**2*(3*a + 2)
Let b(i) = -2*i**3 + 14*i**2 + 6*i - 42. Let z(p) = -p**3 - p**2 - p - 1. Let n(q) = -b(q) + 6*z(q). Factor n(a).
-4*(a - 1)*(a + 3)**2
Factor 0*q - 2/3*q**2 + 8/9 - 2/9*q**3.
-2*(q - 1)*(q + 2)**2/9
Let q(k) = k**3 - 23*k**2 + 43*k - 16. Let f be q(21). Find a such that 0 - 7/3*a**3 - a**f + 10/3*a**4 + 4/3*a - 4/3*a**2 = 0.
-2/3, 0, 1, 2
Let g(u) be the second derivative of -2*u + 0 + 1/15*u**6 + 0*u**2 - 1/3*u**4 + 2/3*u**3 + 1/42*u**7 - 3/20*u**5. Factor g(z).
z*(z - 1)**2*(z + 2)**2
Let f(r) be the second derivative of -r**5/5 - 2*r**4 - 6*r**3 + 41*r. Factor f(g).
-4*g*(g + 3)**2
Suppose 0 = 3*x + x - 16. Solve 6 - 12*h - x*h**4 + 12*h**3 - 20*h**4 - 7*h + 18*h**2 - 2*h + 9*h**5 = 0.
-1, 2/3, 1
Let k(h) be the third derivative of h**7/70 + 3*h**6/20 + 13*h**5/20 + 3*h**4/2 + 2*h**3 + 8*h**2 - 1. Determine d so that k(d) = 0.
-2, -1
Let p = 15 + -15. Let z(x) be the third derivative of -1/42*x**4 + p + 1/21*x**3 + 0*x + 1/210*x**5 - x**2. Factor z(f).
2*(f - 1)**2/7
Factor 0 + 1/2*y**2 + 1/2*y.
y*(y + 1)/2
Suppose 0 = -5*i - 3 + 18. Factor -o + 2*o**2 + 1 + 35*o**3 - i*o**2 - 34*o**3.
(o - 1)**2*(o + 1)
Let s = 32 - 32. Let p(k) be the second derivative of -1/25*k**6 - 1/30*k**4 + 0*k**2 - 3/50*k**5 - 1/105*k**7 + s + 0*k**3 - k. Let p(h) = 0. Calculate h.
-1, 0
Suppose -6*m + 6 = -4*m. Let o = -3 + m. Factor 0 + 2*f**4 + o*f + 6/5*f**3 - 4/5*f**2.
2*f**2*(f + 1)*(5*f - 2)/5
Factor 14*j**3 + 12*j**4 - 12*j + 53*j**2 - 5*j**3 - 65*j**2 + 3*j**5.
3*j*(j - 1)*(j + 1)*(j + 2)**2
Let y(r) be the third derivative of 0*r**4 + 0*r + 1/180*r**5 - r**2 - 1/504*r**8 + 7/720*r**6 + 0*r**3 + 0 + 1/315*r**7. Factor y(a).
-a**2*(a - 2)*(2*a + 1)**2/6
Let x(q) = 15*q**5 + 6*q**4 - 8. Let c(g) = -5*g**5 - 2*g**4 + 3. Let u(l) = 8*c(l) + 3*x(l). Suppose u(h) = 0. What is h?
-2/5, 0
Suppose -3*l = -9 + 3. Determine y so that -2*y**3 + 5*y**2 + 9 - 11 - 3*y**2 + 2*y + 0*y**l = 0.
-1, 1
Let v(q) be the third derivative of 1/12*q**3 - 1/60*q**6 - 1/12*q**4 + 0 + 1/20*q**5 + 0*q + 3*q**2 + 1/420*q**7. Determine s, given that v(s) = 0.
1
Let f be 3/12*152/247. Determine d so that 4/13 - f*d - 2/13*d**2 = 0.
-2, 1
Factor -5/2*r**2 - 3/2*r + 1.
-(r + 1)*(5*r - 2)/2
Let c be (-4)/1*10/(-8). Find g, given that g**2 + 3*g - 5*g + c*g = 0.
-3, 0
Let f(x) be the second derivative of x**5/30 - x**4/18 - 2*x**3/9 - 19*x. Factor f(b).
2*b*(b - 2)*(b + 1)/3
Factor -56*n**3 - 33*n**2 - 24*n**4 + 3*n**5 + 0 - 7*n**5 - 8 - 31*n**2 - 36*n.
-4*(n + 1)**4*(n + 2)
Let d(r) = -r**2 + r. Let o(b) = -b**2 + 2*b - 1. Let u(h) = 5*d(h) - 3*o(h). Le