 2.
2*(p - 1)**2*(p + 1)
Let o(y) = -y**2 - 3*y - 1. Let b be o(-3). Let a be (b/(-3))/((-48)/(-36)). Suppose -1/4*h + 0*h**2 + a*h**3 + 0 = 0. What is h?
-1, 0, 1
Let k(a) be the third derivative of 0*a**3 + 0*a**6 + 0 + 0*a - 1/420*a**7 + 2*a**2 + 0*a**5 + 0*a**4. Factor k(f).
-f**4/2
Let t(d) = -d**3 + d**2 + 2. Let j be t(0). Let o(f) be the third derivative of -1/6*f**3 + 0*f - j*f**2 - 1/20*f**5 + 0 + 1/6*f**4. Find k such that o(k) = 0.
1/3, 1
Let c(h) = 3*h**2 - 17*h. Let l = 11 + -6. Suppose -2*w = -l*d + 39, 4*w + 54 = 2*d - 16. Let b(o) = -o**2 + 6*o. Let g(f) = w*b(f) - 6*c(f). Factor g(k).
-k**2
Let h(o) be the second derivative of -o**5/16 - 65*o**4/48 - 5*o**3/2 - 15*o. Factor h(g).
-5*g*(g + 1)*(g + 12)/4
Suppose 5*f + 2*r - 20 = 0, -2*f - 29*r + 31*r = 6. Factor 8/5*w**f - 8/5*w - 2/5*w**3 + 0.
-2*w*(w - 2)**2/5
Let g(j) = -j**3 + j**2 + 2*j. Let n be g(2). Let h(t) be the first derivative of 0*t**2 + 1 + 1/12*t**4 - 1/9*t**3 + n*t. Factor h(s).
s**2*(s - 1)/3
Determine d so that -4/7 + 4/7*d**2 - 4/7*d**3 + 4/7*d = 0.
-1, 1
Let q(g) be the third derivative of -g**7/1995 - g**6/285 - 2*g**5/285 + 10*g**2. Determine b so that q(b) = 0.
-2, 0
Let h(x) be the first derivative of x**6/24 - x**5/10 - x**4/16 + x**3/6 + 51. Factor h(m).
m**2*(m - 2)*(m - 1)*(m + 1)/4
Suppose 5*n - 5*y = 2*n + 33, -5*n - 2*y + 24 = 0. Let r = -4 + n. Factor -7/2*b**3 + 7/2*b + b**r - 1.
-(b - 1)*(b + 1)*(7*b - 2)/2
Let r(h) be the first derivative of -2*h**6/3 + 2*h**4 - 2*h**2 + 38. Let r(d) = 0. What is d?
-1, 0, 1
Let h be 8*(0 + 3/6). Let k = 6 - 4. Factor h*y + 0 - k + 8*y**3 + 4*y - 2*y**4 - 12*y**2.
-2*(y - 1)**4
Let i(m) = m - 2. Let s be i(10). Let h = s - 4. What is w in 2/5*w**h + 16/5*w**3 + 64/5*w + 32/5 + 48/5*w**2 = 0?
-2
Determine v, given that -10/7*v**2 + 6/7*v + 4/7 = 0.
-2/5, 1
Suppose a + 1 = -2*c, 2*c - 9 = 2*a + 5. Solve -2 - t**3 + 0*t + c*t**2 + 3*t**3 + t - 3*t = 0 for t.
-1, 1
Let u = 138/5 - 27. Factor u*g**2 + 3/5*g**3 - 3/5*g - 3/5.
3*(g - 1)*(g + 1)**2/5
Let b = 39/25 - 53/50. Factor -b*i**3 - i + 0 - 3/2*i**2.
-i*(i + 1)*(i + 2)/2
Let r(w) be the third derivative of -w**7/4620 + w**6/990 - w**3/2 - 2*w**2. Let s(j) be the first derivative of r(j). Factor s(c).
-2*c**2*(c - 2)/11
Let x(g) be the first derivative of 3/2*g**4 + 2 + 16/9*g + 4*g**3 + 4*g**2. Factor x(u).
2*(3*u + 2)**3/9
Suppose 3 = 3*c - 9. Let g = 9 - c. Solve 0*v**3 + 2*v**g + 7*v**3 + 2*v**2 - v**3 + 6*v**4 = 0 for v.
-1, 0
Let s = 20 + -10. Suppose 20 = s*v - 6*v. Find t such that -2/7*t**v + 0*t + 2/7*t**4 + 2/7*t**3 + 0 - 2/7*t**2 = 0.
-1, 0, 1
Let m(v) = -v**3 + 6*v**2 - 5*v + 5. Let t be m(5). Let z = -8 + 12. What is b in b**2 + t*b + 0*b - z*b = 0?
-1, 0
Let y be 9/(-12) + 1790/(-24). Let i = 76 + y. What is o in 2/3*o + 2/3 - i*o**3 - 2/3*o**2 = 0?
-1, 1
Let t(o) be the third derivative of o**7/1050 - o**5/100 + o**4/60 + o**2. Let t(a) = 0. What is a?
-2, 0, 1
Let p(c) be the second derivative of 1/60*c**5 - 1/3*c**2 + 5/18*c**3 - c + 0 - 1/9*c**4. Let p(x) = 0. What is x?
1, 2
Let g(r) be the first derivative of 1 - r**2 - 1/42*r**4 + 1/21*r**3 + 1/210*r**5 + 0*r. Let a(v) be the second derivative of g(v). Factor a(m).
2*(m - 1)**2/7
Let -16/7 - 4/7*h**2 - 48/7*h**3 + 20/7*h**4 + 48/7*h = 0. Calculate h.
-1, 2/5, 1, 2
Let n(j) be the second derivative of -j**4/8 - j**3/4 + 3*j**2/2 - 2*j. Solve n(m) = 0 for m.
-2, 1
Let n(c) be the second derivative of -c**6/90 + c**4/12 - c**3/9 + 6*c. Solve n(x) = 0.
-2, 0, 1
Let u(d) = -d**3 - d**2 + d. Let c(y) = -15*y**3 - 63*y**2 + 162*y + 192. Let o(a) = -c(a) + 18*u(a). Find w, given that o(w) = 0.
-1, 8
Let p = 151 - 331/2. Let t = p - -16. Suppose -t*l**5 + 0*l + 0*l**2 + 0*l**3 + 0 + 3/2*l**4 = 0. What is l?
0, 1
Let k(h) = -3*h + 2. Let d be k(-3). Let a be -3 - (1 + (0 - d)). Factor 0*t**2 + a*t**2 - 18*t - t**2 + 2*t**2 + 4.
2*(t - 2)*(4*t - 1)
Suppose -4*q = w + 17, -5*q = 3*w - 1 + 17. Factor 2/3*i**2 - 2/3*i**w + 0 + 0*i.
-2*i**2*(i - 1)/3
Factor 2 + 30 - 2*i + 10*i - 4*i**2.
-4*(i - 4)*(i + 2)
Factor -4/3 - 2/3*p**2 + 2*p.
-2*(p - 2)*(p - 1)/3
Find d, given that 0 + 9/2*d - 3/4*d**2 = 0.
0, 6
Let t(d) be the second derivative of d**4/36 + 5*d**3/18 - d**2 + 11*d. Factor t(a).
(a - 1)*(a + 6)/3
Let k be 3 + (3/3 - 1). Solve 2*s - 4*s + 5*s - 3*s**k = 0.
-1, 0, 1
Let n(s) = -8*s**3 + 15*s**2 - 9*s + 2. Let j(k) = -9*k**3 + 16*k**2 - 9*k + 2. Let p(a) = 5*j(a) - 6*n(a). Factor p(d).
(d - 2)*(d - 1)*(3*d - 1)
Factor -2/5*w**5 + 0*w**4 + 6/5*w**3 + 0 + 4/5*w**2 + 0*w.
-2*w**2*(w - 2)*(w + 1)**2/5
Let l be 3*2/6 - -1. Let k be 5/(-2) + 6/l. Factor n + k*n**3 - 5/4*n**2 - 1/4.
(n - 1)**2*(2*n - 1)/4
Suppose v = -1, 4*w + 3*v + 1 = -2. Suppose 2*x + 3*t = 6 + 3, 0 = x - t + 3. Factor x*p + p**3 + w*p**3 - p.
p*(p - 1)*(p + 1)
Suppose 2*q - 12 = -4*v - 8, -5*v = -2*q - 5. Find a, given that 2/3*a**4 + q*a + 0 + 0*a**3 - 2/3*a**2 = 0.
-1, 0, 1
Let n(m) = m**3 + 6*m**2 + 6*m - 4. Let o be n(-3). Suppose -16/13*i**3 - 30/13*i**4 - 8/13*i**o - 8/13 + 38/13*i**2 + 24/13*i = 0. What is i?
-2, -1, 1/4, 1
Let y = 63 + -61. Factor 2/11*u**y - 6/11 - 4/11*u.
2*(u - 3)*(u + 1)/11
Suppose -536 = 3*v - 161. Let d = v + 379/3. Solve d*m + 2/3*m**2 - 2*m**3 + 0 = 0.
-2/3, 0, 1
Find w such that -5 + 10 - 3 + 2*w - w**3 + w = 0.
-1, 2
Determine i, given that -8/7*i**2 - 2/7*i**3 - 4/7 - 10/7*i = 0.
-2, -1
Let b(s) = 2*s - 6. Let g be b(3). Let t(v) be the first derivative of -1 - 1/6*v**3 + g*v**2 + 0*v. Suppose t(n) = 0. What is n?
0
Let a(u) be the second derivative of u**7/14 - u**6/6 + u**5/20 + u**4/12 + 10*u. Determine h, given that a(h) = 0.
-1/3, 0, 1
Let f(h) be the second derivative of 2*h**4 + 0*h**2 + 1/10*h**6 + 7*h - 3/4*h**5 + 0 - 2*h**3. Determine w so that f(w) = 0.
0, 1, 2
Let k(n) = n**4 + n**3 - n + 1. Let r(m) = 2 + m**4 - m + 0*m + 4*m**3 - m. Let u(l) = -6*k(l) + 3*r(l). Factor u(t).
-3*t**3*(t - 2)
Let v be (4/(-6))/((-4)/66). Let h(g) = -13*g**2 + 6*g - 15. Let s(f) = 6 + 7 + 7*f**2 - 3*f - 5. Let n(y) = v*s(y) + 6*h(y). Determine w so that n(w) = 0.
1, 2
Let c be -2 - ((-9)/3 - -1). Suppose c = x - 1 - 2. What is r in 0 + 1/3*r**2 - 1/3*r**4 + 1/3*r - 1/3*r**x = 0?
-1, 0, 1
Let m(l) be the third derivative of l**8/1344 - l**7/420 + l**6/480 + 8*l**2. Factor m(p).
p**3*(p - 1)**2/4
Suppose -414*t - 27 = -423*t. Determine d, given that 1/4*d**2 + 3/4*d + 1/4 - 1/2*d**4 - 3/4*d**t = 0.
-1, -1/2, 1
Let b = 192 - 1342/7. Factor 0 - b*s**4 + 2/7*s**2 - 2/7*s**5 + 0*s + 2/7*s**3.
-2*s**2*(s - 1)*(s + 1)**2/7
Let m(j) be the second derivative of -1/24*j**3 + 1/80*j**5 + 0 + 0*j**2 + 0*j**4 + 2*j. Factor m(t).
t*(t - 1)*(t + 1)/4
Let b(f) = -5*f + 20. Let q be b(4). Factor 4/5*w + 1/5*w**3 - 4/5*w**2 + q.
w*(w - 2)**2/5
Let h(r) be the second derivative of -r**6/30 + r**5/6 - r**4/36 - r**3/3 + 2*r - 24. Factor h(m).
-m*(m - 3)*(m - 1)*(3*m + 2)/3
Find k such that -k**2 + 4/5*k + 2/5*k**3 - 1/5 = 0.
1/2, 1
Let v = -3/46 - -211/414. Factor -v*u**2 - 2/9*u + 2/9*u**5 + 0 + 4/9*u**4 + 0*u**3.
2*u*(u - 1)*(u + 1)**3/9
Let i = 1 + 2. Factor 7*w**3 - 9*w**4 - 3*w**3 + 2*w**i.
-3*w**3*(3*w - 2)
Let h(s) = 5*s**3 + 3*s**2 - 6*s - 4. Let w(f) = -5*f**3 - 3*f**2 + 5*f + 3. Let k(i) = -3*h(i) - 4*w(i). What is y in k(y) = 0?
-1, 0, 2/5
Let o(y) be the third derivative of 8/3*y**3 + y**2 + 1/5*y**5 - y**4 + 0*y + 0 - 1/60*y**6. Factor o(r).
-2*(r - 2)**3
Let x be ((-77)/28*4)/(12/(-4)). Suppose -1/3*v**2 + 4/3*v**5 + 3*v**3 + 0 - 1/3*v - x*v**4 = 0. Calculate v.
-1/4, 0, 1
Suppose 2*t = -6, -4*j + 4*t + 21 - 1 = 0. Find u, given that 0*u + 1/5*u**3 + 0*u**j - 1/5*u**5 + 0*u**4 + 0 = 0.
-1, 0, 1
Suppose -2*q = -h, 26 = -h + 6*h + 3*q. Let y(i) be the second derivative of -2/3*i**3 - 11/20*i**5 + i + 0 - h*i**2 + 1/15*i**6 + 3/2*i**4. Factor y(l).
(l - 2)**3*(2*l + 1)
Let q be (-2)/13 - (-6)/39. Let b(o) be the second derivative of 2/3*o**3 + q*o**2 + 1/6*o**4 + 0 - o. Factor b(i).
2*i*(i + 2)
Solve 12*u**3 - 1/3*u**4 - 162*u**2 - 2187 + 972*u = 0 for u.
9
Let q(t) = 7*t**3 - 4*t**2 + 4*t + 5. Let c(i) = -6*i**3 + 5*i**2 - 4*i - 4. Let b(s) = -5*c(s) - 4*q(s). Factor b(m).
m*(m - 4)*(2*m - 1)
Suppose 4*i = -8*i - 12*i. Let -1/5*w**3 + 1/5*w**4 + i + 1/5*w - 1/5*w**2 = 0. What is w?
-1, 0, 1
Let c(m) be the se