) be the third derivative of 3*p**6/280 - p**5/210 - 3*p**4/56 + p**3/21 - 33*p**2. Factor k(t).
(t - 1)*(t + 1)*(9*t - 2)/7
Let p(y) be the first derivative of -y**3/12 - 5*y**2/4 - 25*y/4 - 11. Suppose p(i) = 0. What is i?
-5
Let i be 10/(-3)*(-12)/10. Factor -2*c - 14*c**2 - i - 19*c + 3*c.
-2*(c + 1)*(7*c + 2)
Suppose 5*y = 4*y + 4. Let 0 + 0*a + 2*a**3 - 4/5*a**2 - 6/5*a**y = 0. Calculate a.
0, 2/3, 1
Factor 1/4*i + 1/4*i**2 - 1/2.
(i - 1)*(i + 2)/4
Let a = 3 + 0. Let j(m) = m**2 - 3*m + 4. Let d be j(a). Determine u, given that 3*u + d*u**3 - 5*u**3 - u - u**3 = 0.
-1, 0, 1
Let o(t) be the first derivative of t**7/105 + t**6/25 + 3*t**5/50 + t**4/30 + 8*t - 5. Let b(l) be the first derivative of o(l). Let b(m) = 0. Calculate m.
-1, 0
Let n(x) = x**2 - x + 2. Suppose v - 4 + 1 = 0. Let r be n(v). Let i**2 + 5*i**5 - i**4 + r*i**4 + 5*i**3 - 2*i**5 = 0. What is i?
-1, -1/3, 0
Suppose 13 = 3*r + 1. Let u(x) be the second derivative of -2*x + 1/15*x**6 + 0*x**3 + 0 + 1/6*x**r + 0*x**2 + 1/5*x**5. Factor u(q).
2*q**2*(q + 1)**2
Let s(m) be the third derivative of -m**7/210 + m**6/60 - m**5/60 + 3*m**2. Determine z so that s(z) = 0.
0, 1
Let l(u) = -10*u**2 + 1 + 4*u**2 - 2*u**3 - 7*u + u**3 + 8*u**3. Let f(h) = -6*h**3 + 5*h**2 + 6*h - 1. Let c(q) = -5*f(q) - 4*l(q). Let c(z) = 0. What is z?
-1, 1/2, 1
Let z = 5/168 + 3/56. Let g(w) be the second derivative of -w + 2*w**2 + 2/3*w**3 + z*w**4 + 0. Let g(s) = 0. Calculate s.
-2
Let f(y) = y**4 - 3*y**3 - 5*y**2 + 3*y - 8. Let r(p) = p**2 + 1. Let l(t) = -f(t) - 6*r(t). Find g such that l(g) = 0.
-1, 1, 2
Let f(g) be the second derivative of g**5/35 - 2*g**4/21 + 2*g**3/21 - 7*g. Determine q, given that f(q) = 0.
0, 1
Let k(c) = -c**3 - 9*c**2 + 11*c + 13. Let p be k(-10). Factor -4*z**2 + 2*z**p + 0*z**2 + z**4 + 5*z**2.
z**2*(z + 1)**2
Suppose 0 = -b - 2*b + 3. Let z(w) = 1. Let q(k) be the third derivative of k**5/60 - k**4/24 - 2*k**3/3 - 3*k**2. Let p(f) = b*q(f) + 4*z(f). Factor p(t).
t*(t - 1)
Let z(u) be the second derivative of u**5/20 + u**4/9 + u**3/18 - 5*u. Find o such that z(o) = 0.
-1, -1/3, 0
Let m be -1*5 - (-4 - 21/15). Factor 2/5*j**3 - 16/5 - 8/5*j + 4*j**2 - 8/5*j**4 + m*j**5.
2*(j - 2)**3*(j + 1)**2/5
Let i(l) be the third derivative of l**6/420 + 2*l**5/105 + 5*l**4/84 + 2*l**3/21 - 45*l**2 - 2*l. Factor i(q).
2*(q + 1)**2*(q + 2)/7
Factor -2*r**5 - 16*r**2 + 16*r**4 + 5*r**3 - 9*r + 6*r**5 - 7*r + 7*r**3.
4*r*(r - 1)*(r + 1)*(r + 2)**2
Let h(p) = -p**2 + p. Let o(a) = 14*a**2 - 8*a. Let g(v) = 5*v**2 - 3*v. Let l(m) = -8*g(m) + 3*o(m). Let b(z) = -2*h(z) - 2*l(z). Factor b(d).
-2*d*(d + 1)
Let n(d) be the first derivative of 1/36*d**6 - 4/3*d + 25/24*d**4 + 11 - 19/9*d**3 - 4/15*d**5 + 7/3*d**2. Factor n(v).
(v - 2)**3*(v - 1)**2/6
Let t be ((-3)/(-36))/(6/(-32)). Let g = 7/9 + t. Factor -g*o**2 + 1/3*o**3 + 1/3 - 1/3*o.
(o - 1)**2*(o + 1)/3
Let o(z) be the first derivative of 3/2*z**2 + 2 + 2*z + 1/3*z**3. Factor o(r).
(r + 1)*(r + 2)
Determine b so that 8/11 + 8/11*b - 2/11*b**2 - 2/11*b**3 = 0.
-2, -1, 2
Let s(z) be the second derivative of 0 + 0*z**3 + 0*z**2 + 1/18*z**5 - 1/27*z**4 + 1/189*z**7 + 2*z - 4/135*z**6. Factor s(w).
2*w**2*(w - 2)*(w - 1)**2/9
Let t be (38/6)/(60/216). Let u = 23 - t. Let 0*f**3 + u*f**5 + 2/5*f**2 - 2/5*f**4 + 0 - 1/5*f = 0. Calculate f.
-1, 0, 1
Let t = -4 - -7. Suppose -3*n**3 - 2*n**3 + t*n**3 + 3*n**3 = 0. What is n?
0
Let k(t) be the second derivative of -t**4/12 + t**3/2 + 2*t**2 + 17*t + 2. Factor k(q).
-(q - 4)*(q + 1)
Let h(o) be the second derivative of o**4/28 + 2*o**3/7 + 6*o**2/7 + 43*o. Let h(r) = 0. Calculate r.
-2
Factor -20*d**3 + d**3 + 2*d**3 - 36*d + d**3 - 8 - 48*d**2.
-4*(d + 2)*(2*d + 1)**2
Suppose 4*f = -f - 25. Let n = f - -8. Let 0*a - 2/3*a**3 + 0*a**2 + n*a**4 + 0 - 7/3*a**5 = 0. What is a?
0, 2/7, 1
Let b(u) be the second derivative of 1/12*u**4 + 1/40*u**5 + 1/12*u**3 + 0*u**2 + 0 + 4*u. Let b(o) = 0. What is o?
-1, 0
Let q(w) be the third derivative of -5*w**8/336 + w**7/21 + w**6/24 - w**5/6 + 5*w**2. Determine d, given that q(d) = 0.
-1, 0, 1, 2
Let g(y) be the second derivative of -7*y**4/12 + 3*y**3 - 4*y**2 - 6*y + 5. Let g(t) = 0. Calculate t.
4/7, 2
Let k(n) be the first derivative of n**6/10 + 6*n**5/5 + 6*n**4 + 16*n**3 + 24*n**2 + 2*n + 8. Let x(a) be the first derivative of k(a). Factor x(s).
3*(s + 2)**4
Let b(z) be the first derivative of -z**6/9 - 2*z**5/3 - 4*z**4/3 - 8*z**3/9 - 12. What is p in b(p) = 0?
-2, -1, 0
Suppose -16 = -3*k - 7. Let l(z) be the second derivative of 2*z - 1/40*z**5 + 1/12*z**k + 0 + 0*z**4 + 0*z**2. Determine f so that l(f) = 0.
-1, 0, 1
Let 12/7*l**4 - 8/7*l - 4/7*l**2 + 16/7*l**3 + 0 = 0. Calculate l.
-1, 0, 2/3
Let v(l) be the second derivative of l**7/5040 - l**6/720 + l**5/240 + l**4/6 - l. Let p(f) be the third derivative of v(f). Suppose p(o) = 0. What is o?
1
Let q = 3 - -1. Factor 2 + q*d + 2 - d**2 - 7.
-(d - 3)*(d - 1)
Let n = -6 + 10. Suppose 0 = -3*v - n*r - 0*r + 2, -v - 3*r = 1. Factor -3*m**5 + 4 + 3*m**3 + 0*m**2 - 4 - 3*m**v + 3*m**4.
-3*m**2*(m - 1)**2*(m + 1)
Suppose 1 = 3*y - 2. Let t be (y - 2) + 5/3. Find z such that 2*z**5 - t*z - 2/3 + 4*z**2 - 10/3*z**4 - 4/3*z**3 = 0.
-1, -1/3, 1
Let b(a) be the second derivative of 3/50*a**5 - 1/25*a**6 + 0 - 1/30*a**4 + 0*a**3 + 0*a**2 - 4*a + 1/105*a**7. Factor b(r).
2*r**2*(r - 1)**3/5
Let x(d) be the first derivative of -d**4/16 - d**3/6 - d**2/8 - 11. Solve x(i) = 0.
-1, 0
Suppose 5*f - 3*g + 13 = 53, -g + 20 = 5*f. Let t be 2/2 - (-22)/11. Suppose 0*i**3 - 2*i**3 + f*i**t = 0. Calculate i.
0
Suppose 0 = -5*i + 16 - 6. Factor i*v - 2 + 1 + 1 - 2*v**3.
-2*v*(v - 1)*(v + 1)
Let w(o) be the first derivative of o**4/20 - o**3/3 + 4*o**2/5 - 4*o/5 - 1. Factor w(k).
(k - 2)**2*(k - 1)/5
Factor 0*d - 8/5 + 6/5*d**2 - 2/5*d**3.
-2*(d - 2)**2*(d + 1)/5
Suppose -4*y + 16 = -0. Let b(t) be the second derivative of 0*t**2 + 0 - 1/12*t**y - 1/3*t**3 + 2*t. Suppose b(u) = 0. Calculate u.
-2, 0
Let w be 2/(-12) + (-25)/(-140). Let h(k) be the second derivative of -w*k**7 + 0 - 1/40*k**5 + 0*k**3 + 1/30*k**6 + 0*k**4 + 0*k**2 - k. Solve h(q) = 0.
0, 1
Let f(l) be the second derivative of l**4/12 + l**3/6 - 2*l**2 - l. Let j(v) = v**2 + v - 5. Let i(r) = -5*f(r) + 4*j(r). Factor i(w).
-w*(w + 1)
Let c be 0/((0 - -2) + -3). Suppose -6 = -3*k - c. Factor -3*z**2 + 0*z**4 - z**k + 2 + 2*z**4.
2*(z - 1)**2*(z + 1)**2
Let c(x) be the first derivative of 0*x**2 + 2 + 3/4*x**4 + 0*x - x**3. Solve c(p) = 0.
0, 1
Let n(h) be the third derivative of 0*h - 1/56*h**7 + 0 - 1/4*h**3 - 17/160*h**6 - 21/80*h**5 - 4*h**2 - 11/32*h**4. Solve n(k) = 0.
-1, -2/5
Let r(g) be the third derivative of g**8/20160 - g**7/1260 + g**6/180 + g**5/60 + 2*g**2. Let k(c) be the third derivative of r(c). What is t in k(t) = 0?
2
Factor 0*k + 2/7*k**4 + 0*k**2 + 0 + 0*k**3.
2*k**4/7
Let n(x) = 2*x + 6. Let q be n(-3). Let w = q - -2. Factor -4/9*h + 0 + 2/9*h**w.
2*h*(h - 2)/9
Let x(f) be the first derivative of 0*f - 4*f**4 + 8/3*f**3 + 0*f**2 - 1/3*f**6 + 1 + 2*f**5. Determine g so that x(g) = 0.
0, 1, 2
Let k(v) be the third derivative of -v**6/24 + v**5/4 - 5*v**4/12 + 5*v**2 - 6. Factor k(d).
-5*d*(d - 2)*(d - 1)
Suppose 4*z + 0*z = 16. Suppose -3*y = -4*w + w - 9, z*w = 2*y - 12. Find p such that 12 + 483*p**2 + y - 696*p**3 - 3*p**4 + 243*p**4 - 132*p + 12*p**2 = 0.
1/4, 2/5, 2
Let c be (-3)/(-6)*(1 - 1). Let g(o) be the third derivative of 1/120*o**6 + c*o**3 + 0 + 0*o - o**2 + 1/30*o**5 + 1/24*o**4. Factor g(v).
v*(v + 1)**2
Let o(s) be the first derivative of -s**4/20 - s**3/15 + s**2/10 + s/5 + 4. Let o(z) = 0. Calculate z.
-1, 1
Let h(p) be the third derivative of 2*p**2 + 0 + 0*p**4 + 1/80*p**5 - 1/2*p**3 + 0*p. Factor h(v).
3*(v - 2)*(v + 2)/4
Let i(d) = -49*d + 53. Let q be i(1). Suppose 0 - 8/3*y**3 - 4*y**2 + q*y**4 + 8/3*y = 0. What is y?
-1, 0, 2/3, 1
Let c(i) be the second derivative of -i**5/110 + i**4/11 - 3*i**3/11 + 4*i**2/11 - 4*i. Suppose c(k) = 0. Calculate k.
1, 4
Suppose 2*p + 0*p = 8. Find j, given that 2/7*j**5 - 2/7*j**3 + 0 - 2/7*j**p + 0*j + 2/7*j**2 = 0.
-1, 0, 1
Factor 1/4*w**4 + 7/4*w + 5/4*w**3 + 1/2 + 9/4*w**2.
(w + 1)**3*(w + 2)/4
Let y = -63 - -191/3. Factor 0 - 2/3*u**3 + 0*u - y*u**2.
-2*u**2*(u + 1)/3
S