p**2 - x - 6*p + 7.
2*(p - 2)*(p - 1)
Let d = 10 + -7. Suppose -4*z - 5*z + z**2 + d*z + 9 = 0. What is z?
3
Let k(c) be the second derivative of -3*c**5/140 - c**4/28 + c**3/7 - 12*c. Determine q, given that k(q) = 0.
-2, 0, 1
Let q(n) = -12*n**3 - 105*n**2 + 90*n + 27. Let r(m) = -m**3 - 8*m**2 + 7*m + 2. Let l(f) = 2*q(f) - 27*r(f). Determine p, given that l(p) = 0.
-3, 0, 1
Let z(p) = -p**2 - 1. Let f(d) = -13*d**2 - 2*d - 6. Let s(c) = 105*c**2 + 15*c + 48. Let t(i) = -33*f(i) - 4*s(i). Let r(x) = -t(x) - 6*z(x). Factor r(a).
-3*a*(a + 2)
Suppose 12/7*r**4 - 16/7*r + 16/7*r**3 - 4/7 - 8/7*r**2 = 0. Calculate r.
-1, -1/3, 1
Let b(t) be the first derivative of t**5/25 + 3*t**4/20 - 2*t**2/5 + 10. Factor b(u).
u*(u - 1)*(u + 2)**2/5
Let s = -46 + 51. Let q(i) be the first derivative of 0*i**4 + 1/33*i**6 + 4/55*i**s + 0*i**2 + 0*i**3 + 0*i + 3. Factor q(h).
2*h**4*(h + 2)/11
Let x(l) = 15*l**4 + 57*l**3 - 3*l**2 - 33*l. Let n(r) = 6*r**4 + 23*r**3 - r**2 - 13*r. Let t(j) = -12*n(j) + 5*x(j). Factor t(c).
3*c*(c - 1)*(c + 1)*(c + 3)
Let b = -5 - -7. Suppose -3*p - r = -b*p - 26, 0 = -3*p - 2*r + 77. Suppose 19*n - 81 + 36*n - 27*n**2 + 3*n**3 + 51*n - p*n = 0. Calculate n.
3
Suppose 2*r = -5*s - 25, 6 = -3*s - r - 2*r. Let o = -3 - s. Suppose 3*n - 2 - o + 3*n**2 - 1 + 1 = 0. Calculate n.
-2, 1
Suppose -2*h + 0*h = 0. Suppose h = 3*b - 6. Factor -2/9*v**3 - 8/9*v + 0 - 8/9*v**b.
-2*v*(v + 2)**2/9
Let g(m) be the first derivative of 2 + 1/3*m**3 - 1/2*m**2 + 1/4*m**4 - 1/5*m**5 + 0*m. Solve g(s) = 0 for s.
-1, 0, 1
Let f = -7 + 11. Suppose 4*k + f = 5*k. Factor 2*p**4 - p**k + 0*p**4.
p**4
Let i(k) be the third derivative of k**6/180 - k**5/30 + 4*k**3/9 - 21*k**2. Let i(o) = 0. What is o?
-1, 2
Let n = 4/23 - -15/46. What is i in 1/2*i**5 + 1/2*i**2 + 0 + 0*i - 1/2*i**3 - n*i**4 = 0?
-1, 0, 1
Let -4/3*m**4 + 0*m**3 - 2/3*m**5 + 0 + 4/3*m**2 + 2/3*m = 0. What is m?
-1, 0, 1
Let j(v) be the first derivative of -2*v**5/5 - v**4 + 2*v**2 + 2*v - 5. Factor j(h).
-2*(h - 1)*(h + 1)**3
Let q(p) be the second derivative of -49*p**5/10 + 7*p**4/2 + 8*p**3 + 4*p**2 - 18*p. Let q(m) = 0. What is m?
-2/7, 1
Let f be (-18)/(-60) - 6/(-12). Suppose 2/5 + 16/5*y**3 - 8/5*y**4 - 6/5*y**2 - f*y = 0. What is y?
-1/2, 1/2, 1
Let o(g) = -g**3 - 13*g**2 - 12*g - 4. Let q be o(-12). Let n be (-18)/q + (8 - 11). Factor 0*p + 0*p**2 + 3/2*p**3 + 0 - n*p**4.
-3*p**3*(p - 1)/2
Let o(l) be the third derivative of l**5/25 - l**4/40 - 13*l**2. Factor o(i).
3*i*(4*i - 1)/5
Let o(u) be the third derivative of -u**8/112 + 3*u**7/70 - u**5/5 + 28*u**2. Solve o(r) = 0 for r.
-1, 0, 2
Let y(s) be the first derivative of -7*s**6 - 34*s**5 - 43*s**4 + 8*s**3/3 + 8*s**2 + 23. Solve y(c) = 0 for c.
-2, -1/3, 0, 2/7
Let l(w) be the third derivative of w**5/60 - 3*w**4/4 - 17*w**3/6 - w**2. Let i be l(19). Factor -1/4*t**i + 1/4 + 1/4*t - 1/4*t**3.
-(t - 1)*(t + 1)**2/4
Let t(d) be the second derivative of d**6/40 + 3*d**5/20 + 5*d**4/16 + d**3/4 - 3*d. Find b, given that t(b) = 0.
-2, -1, 0
Suppose -5*v + 165 = 4*q, 4*q - 270 = 5*v - 75. Let z be 50/q - (-2)/9. Suppose -2/3*t**2 + z + 2/3*t = 0. Calculate t.
-1, 2
Let m(j) be the second derivative of j**7/28 - j**6/6 + j**5/40 + j**4/4 + 8*j. Determine r so that m(r) = 0.
-2/3, 0, 1, 3
Let m be (-8 - 76/(-10))/((-3)/5). Factor 0 - 2/3*u**3 - m*u - 4/3*u**2.
-2*u*(u + 1)**2/3
Let l(y) = -330*y**4 - 440*y**3 - 155*y**2 - 45. Let r(o) = 15*o**4 + 20*o**3 + 7*o**2 + 2. Let c(n) = 2*l(n) + 45*r(n). Factor c(w).
5*w**2*(w + 1)*(3*w + 1)
Let o(k) be the third derivative of k**6/540 - k**4/27 + 17*k**2. Find d, given that o(d) = 0.
-2, 0, 2
Let i be (-125)/(-220) - 20/(-110). Determine c so that -3/4*c**2 + 0 - i*c = 0.
-1, 0
Suppose 2*f - 9 = -3*c, 4*f + 12 = 4*c - f. Let w be (-4)/c*(-8)/16. Suppose -7/3*k - 5/3*k**2 - w = 0. What is k?
-1, -2/5
Let q be 3 - (-1)/12 - 3. Let r(l) be the third derivative of 0*l - q*l**4 + l**2 + 0 + 0*l**3 + 1/30*l**5. Solve r(c) = 0.
0, 1
Let g(c) be the first derivative of -1 - 1/4*c**3 - 3/2*c + 9/8*c**2. Factor g(h).
-3*(h - 2)*(h - 1)/4
Let t(u) be the second derivative of u**6/30 - 3*u**5/20 + u**4/4 - u**3/6 + 4*u. Factor t(v).
v*(v - 1)**3
Let d(l) be the first derivative of -l**4/26 + l**2/13 - 7. Factor d(c).
-2*c*(c - 1)*(c + 1)/13
Let r(x) be the first derivative of x**5/20 - x**4/8 - x**3/12 + x**2/4 + 6. Factor r(u).
u*(u - 2)*(u - 1)*(u + 1)/4
Determine x so that 0 - 36/5*x**2 - 24/5*x - 6/5*x**3 + 3/5*x**5 + 9/5*x**4 = 0.
-2, -1, 0, 2
Solve 48*s**2 + 14*s + 4*s + 28*s**3 - 34*s = 0.
-2, 0, 2/7
Suppose 2*w = -3*l, l + 3*w + 4 + 3 = 0. Suppose -4*r + l*g + 21 = -5, -2*g = 2*r + 2. Factor -2 - 4*h**2 - 3 - 1 + r - h**3 - 5*h.
-(h + 1)**2*(h + 2)
Suppose -20*h + 12 = -17*h. Factor -39*c**h - 2*c**3 + 2*c**2 - c**2 + 40*c**4.
c**2*(c - 1)**2
Suppose 4 = 4*h - 8. Let u(l) be the second derivative of 4/11*l**2 + 2*l + 0 - 4/33*l**h + 1/66*l**4. Factor u(t).
2*(t - 2)**2/11
Let z be -1*12/8*1/(-3). Solve 0*b - z*b**2 - 1/2*b**4 + 0 + b**3 = 0.
0, 1
Factor -f + 1 + f**3 - 1/4*f**4 - 3/4*f**2.
-(f - 2)**2*(f - 1)*(f + 1)/4
Let t(y) be the first derivative of 1/10*y**2 + 0*y - 3 - 1/15*y**3. Determine p, given that t(p) = 0.
0, 1
Let l(y) = -2*y**3 + 6*y**2 - 6*y - 4. Let d(c) = 4*c**3 - 12*c**2 + 12*c + 9. Let s(j) = -6*d(j) - 13*l(j). Factor s(o).
2*(o - 1)**3
Let k(d) be the first derivative of -2*d**5/45 + 4*d**3/9 - 8*d**2/9 + 2*d/3 + 18. Factor k(n).
-2*(n - 1)**3*(n + 3)/9
Let s be (-6 + -1)/(1/(-5)). Suppose s = -3*p - 4*c + 93, -2*p = 5*c - 41. Solve p*b**3 + b**4 - 7*b**4 - 15*b**5 - 3*b**3 + 6*b**2 = 0.
-1, -2/5, 0, 1
Let q(w) be the first derivative of 3 + 0*w**2 - 1/2*w**6 + w**3 + 0*w + 3/4*w**4 - 3/5*w**5. Factor q(c).
-3*c**2*(c - 1)*(c + 1)**2
Let o(s) be the second derivative of s**5/30 + s**4/12 + 3*s**2/2 + s. Let m(z) be the first derivative of o(z). Factor m(i).
2*i*(i + 1)
Let g be 2 + 5/12 - (-1)/3. Find w such that 0 - 3*w**2 + 3*w**4 - g*w**3 + 7/4*w**5 + w = 0.
-2, -1, 0, 2/7, 1
Let w(o) = -9*o**5 + 37*o**4 + 71*o**3 + 40*o**2 - 5. Let k(c) = 4*c**5 - 18*c**4 - 36*c**3 - 20*c**2 + 2. Let m(v) = -5*k(v) - 2*w(v). Factor m(a).
-2*a**2*(a - 10)*(a + 1)**2
Let r(q) be the second derivative of q**5/130 - 2*q**4/39 - q**3/13 - 5*q**2/2 + q. Let a(z) be the first derivative of r(z). What is p in a(p) = 0?
-1/3, 3
Suppose 0 = -3*m + 5 + 4. Suppose 138 = 3*r - m*g, -3*r - 2*r + 4*g = -234. Factor -20*v + 32*v**4 - r*v**3 + 58*v**2 + 2 + 8*v**2 - 30*v**3.
2*(v - 1)**2*(4*v - 1)**2
Suppose 0 = 4*v - 12 - 0, -4*v + 21 = 3*u. Suppose -18 - 21 = -u*q. Factor 11*g**4 + 3 + 2*g**5 + 2*g - q*g**4 - 4*g**3 - 5 + 4*g**2.
2*(g - 1)**3*(g + 1)**2
Suppose 0 = -w + 4*w + 9, 4*p = -5*w - 3. Factor p*m - 3*m + m - 2 + m**2.
(m - 1)*(m + 2)
Let y = -11 + 15. Let a(l) = l**3 + 5*l**2 - l + 1. Suppose i + 6 = 2*i. Let h(m) = -m**3 - 4*m**2 + m. Let z(n) = i*h(n) + y*a(n). Factor z(p).
-2*(p - 1)*(p + 1)*(p + 2)
Let d = 23 + -49. Let k be (-4)/d - 236/(-156). Let k*y**4 + 1/3*y**5 + 0 + 7/3*y**2 + 3*y**3 + 2/3*y = 0. What is y?
-2, -1, 0
Factor -12*u**2 + 4047*u**3 - 3*u**4 + 0*u**4 + 6*u**4 + 12*u - 4050*u**3.
3*u*(u - 2)*(u - 1)*(u + 2)
Factor -1/2*p**2 + 0*p + 1/2.
-(p - 1)*(p + 1)/2
Let i(b) = b**2 + b + 1. Let o(y) = -y**2 - y - 1. Let v(q) = q**2 + q. Let f(d) = -6*o(d) - 2*v(d). Let s(p) = -f(p) + 6*i(p). Factor s(j).
2*j*(j + 1)
Factor 2*l + 8*l**3 + 10*l**2 + 4 - 6 + 2.
2*l*(l + 1)*(4*l + 1)
Solve 0 - 2/9*t - 2/9*t**3 + 4/9*t**2 = 0 for t.
0, 1
Let z = -957 - -957. Let 0*q - 1/8*q**4 + z + 0*q**3 + 1/8*q**2 = 0. Calculate q.
-1, 0, 1
Suppose -7*m + 5*m = 12. Let p = m - -9. Factor 1/4*w**4 + 3/2*w**2 - w + 1/4 - w**p.
(w - 1)**4/4
Let z(x) = 5*x - 40. Let v(p) = p - 8. Let s(k) = -22*v(k) + 4*z(k). Let t be s(8). Factor 2/11*i**3 + 0 - 2/11*i + t*i**2.
2*i*(i - 1)*(i + 1)/11
Suppose -203 - 13*o**2 + 10*o**2 + 66*o - 160 = 0. What is o?
11
Let g(p) be the second derivative of p**6/10 - 3*p**5/5 + 5*p**4/4 - p**3 - 7*p. Factor g(v).
3*v*(v - 2)*(v - 1)**2
Let f(g) be the third derivative of -g**7/210 - g**6/30 + g**5/12 + 11*g**2. Factor f(b).
-b**2*(b - 1)*(b + 5)
Let t(h) = -4*h**3 - 2*h**2 - 4*h + 2. Let w(d) = 13*d**3 + 5*d**2 + 13*d - 7. Let s(x) = -7*t(x) - 2*w(x). Factor s(z).
2*z*(z