h(n) = 3*n**5 + 3*n**4 - 2*n**3 + 2*n**2 - 5*n + 3. Let q(g) = 5*h(g) - 4*z(g). Solve q(u) = 0.
-1, 1
Let g(p) = -5*p - 73. Let v be g(-15). Factor 0 + l + 5/2*l**v + 3/2*l**3.
l*(l + 1)*(3*l + 2)/2
Let m(z) be the third derivative of z**8/168 - z**7/105 - 3*z**6/20 - 11*z**5/30 - z**4/3 + 18*z**2. Find j such that m(j) = 0.
-1, 0, 4
Let s(l) be the third derivative of -l**6/270 + l**5/135 + l**4/27 + 3*l**2. Suppose s(v) = 0. Calculate v.
-1, 0, 2
Let i = 85 - 83. Factor 2/5*c**i - 2/5*c + 0.
2*c*(c - 1)/5
Let p(w) = -16*w**2 - 13*w + 7. Let n(g) = 63*g**2 + 51*g - 27. Let t(c) = 4*n(c) + 15*p(c). Factor t(o).
3*(o + 1)*(4*o - 1)
Let c(r) be the third derivative of r**8/840 + 2*r**7/525 + r**6/300 + 24*r**2. Factor c(m).
2*m**3*(m + 1)**2/5
Let f be (-5)/15 + (-7)/(-3). Determine i, given that -f*i - 2*i**2 + 25 - 25 = 0.
-1, 0
Factor 1/3 - 1/3*h**2 + 0*h.
-(h - 1)*(h + 1)/3
Suppose 0 = j - 6*j + 20. Solve -22*t**2 - 3*t**j - 2*t**2 + 12*t + 6*t**3 + 9*t**3 = 0 for t.
0, 1, 2
Let p(i) = 2*i**4 - 20*i**3 - 4*i**2 - 22*i - 22. Let r(v) = v**3 + v + 1. Let l(x) = 2*p(x) + 44*r(x). Factor l(j).
4*j**2*(j - 1)*(j + 2)
Let a(i) = -i**3 + i**2 + i + 1. Let r(b) = -5*b**4 - 20*b**3 + 35*b**2 + 20*b + 30. Let q(u) = -30*a(u) + r(u). Factor q(l).
-5*l*(l - 2)*(l - 1)*(l + 1)
Let n(v) be the second derivative of 2*v**6/105 - v**4/21 - 4*v. Find k, given that n(k) = 0.
-1, 0, 1
Let m be (24/(-32))/(6/(-44)). Let k = -5 + m. Factor c + k + 1/2*c**2.
(c + 1)**2/2
Let a = -23 - -16. Let h be (-1 + a/(-6))*4. Factor 0 - 2/3*s - h*s**2.
-2*s*(s + 1)/3
Suppose 4*x - 28 = -0*x. Let b(d) = d**2 - d - 3. Let k be b(3). Let a**3 - 4*a**k - 9*a**2 + a**3 - x*a**3 - 3*a**4 - 3*a = 0. What is a?
-1, 0
Let y = 37/42 + -8/21. Let w(q) be the first derivative of 1/12*q**3 + y*q**2 + q + 1. Factor w(a).
(a + 2)**2/4
Suppose -1 + 3 - 48*g + 52*g + 2*g**2 = 0. What is g?
-1
Let u(y) be the second derivative of 9/5*y**2 + 1/30*y**4 - 2/5*y**3 + 6*y + 0. Solve u(v) = 0.
3
What is t in 18*t**2 + 135/2*t + 75 + 3/2*t**3 = 0?
-5, -2
Suppose 3*m + 2*m + a = 0, -4*m - 5*a = 0. Solve -3*y**2 + m*y**2 - 4 - 8*y - y**2 = 0.
-1
Let p(l) be the first derivative of -3*l**4/16 + l**3/4 + 3*l**2/4 + 3. What is x in p(x) = 0?
-1, 0, 2
Find w, given that -4*w**2 + 5*w**2 + w**2 + 8 + 8*w = 0.
-2
Let c(b) be the third derivative of b**6/420 + 2*b**5/105 + 5*b**4/84 + 2*b**3/21 - 4*b**2. Determine n so that c(n) = 0.
-2, -1
Let j(g) = -5*g**2 + 9*g + 8. Let c(r) = -12 - 19*r - 4 - 1 + 10*r**2 + 0. Let o = -27 + 14. Let i(b) = o*j(b) - 6*c(b). Suppose i(t) = 0. Calculate t.
-2/5, 1
Let d(i) be the third derivative of i**6/1140 - i**5/285 - i**4/57 + 8*i**3/57 + 17*i**2. Factor d(a).
2*(a - 2)**2*(a + 2)/19
Let -6/5*k**3 - 3/5*k**4 + 3/5*k**2 + 6/5*k + 0 = 0. What is k?
-2, -1, 0, 1
Let w be (6/(-12))/((-1)/(-24)). Let v be (-6)/4*16/w. Factor 0*m - 1/2 + 1/2*m**v.
(m - 1)*(m + 1)/2
Let b = 94/3 + -30. Factor -2/3*t**2 - 2/3*t**4 + 0 - b*t**3 + 0*t.
-2*t**2*(t + 1)**2/3
Factor -a**3 + 0*a**3 + 4*a + 6*a**2 + a**4 + 1 - 3*a**3 + 8*a**3.
(a + 1)**4
Let g = 28 - 111/4. Let s(j) be the first derivative of g*j + 3/8*j**2 - 1/3*j**3 + 1. Suppose s(w) = 0. What is w?
-1/4, 1
Let u(f) = -9*f + 6. Let m be u(-8). Let i = m + -542/7. Factor 2/7 + 0*g**2 + 4/7*g - i*g**3 - 2/7*g**4.
-2*(g - 1)*(g + 1)**3/7
Factor 4*j**3 + 2 - 4 - 7*j - j**2 - j**2 + j**5 + 2*j + 4*j**4.
(j - 1)*(j + 1)**3*(j + 2)
Let s be 144/(-30) - 1/5. Let t = s - -9. Determine n, given that -4/3*n**2 + 0*n**3 + 2/3*n**t + 0*n + 2/3 = 0.
-1, 1
Let k(g) = g**3 - 11*g**2 + 10*g + 3. Let f be k(10). Determine o, given that -o + 4*o + 4*o**2 + 2*o**f - o = 0.
-1, 0
Let c be (-21)/(-9) + 2/(-6). Suppose c = -5*k - 3*b + 12, 3*k - b = 6. Find n, given that n**k - 3/2*n + 3/2*n**3 - 1 = 0.
-1, -2/3, 1
Let z = 2 + 1. Suppose -2 = z*b - 17. Determine f, given that 6*f**2 - f - 4*f**2 + b*f = 0.
-2, 0
Let y(p) be the first derivative of p**6/12 - p**5/10 - p**4/8 + p**3/6 + 1. Find i, given that y(i) = 0.
-1, 0, 1
Let s(h) be the third derivative of 5/8*h**4 + 1/40*h**6 + 0 + 1/5*h**5 + h**3 - 3*h**2 + 0*h. Suppose s(f) = 0. Calculate f.
-2, -1
Let v = 7 + -5. Let u be 0/(7/(7/v)). Factor u - 2/3*b**2 + 2/3*b**4 + 0*b**3 - 1/3*b**5 + 1/3*b.
-b*(b - 1)**3*(b + 1)/3
Suppose -4*o + o = -2*o. Let k(u) be the second derivative of 0*u**5 + 0*u**6 - 1/189*u**7 + 0*u**2 + 3*u + 0*u**4 + o + 0*u**3. Find l, given that k(l) = 0.
0
Suppose -1/4*f**3 - 5*f + 4 + 2*f**2 = 0. Calculate f.
2, 4
Let g(y) be the second derivative of -y**5/25 + y**4/15 + 8*y**3/15 - 8*y**2/5 + 41*y. Solve g(o) = 0.
-2, 1, 2
Let y(z) = 4*z**3 + 2*z**2 - 7*z - 5. Let u(o) = -3*o**3 - o**2 + 6*o + 4. Let x(b) = -5*u(b) - 4*y(b). Factor x(i).
-i*(i + 1)*(i + 2)
Suppose -30 = -2*d - d. Let n = d + -10. Factor -1/2*x**4 + n + 1/2*x**2 - 1/2*x + 1/2*x**3.
-x*(x - 1)**2*(x + 1)/2
Let s(x) = -x**2 + x + 1. Let p(z) = -5*z**2 + 6*z + 5. Let b(n) = p(n) - 6*s(n). Find g such that b(g) = 0.
-1, 1
Solve t + 120*t**2 + 3*t**3 - 245*t**4 + t + 102*t**3 + 18*t = 0.
-2/7, 0, 1
Let g(a) be the second derivative of a**6/60 - a**5/15 + a**4/12 + 3*a**2/2 + a. Let z(h) be the first derivative of g(h). Suppose z(x) = 0. Calculate x.
0, 1
Let j(o) = -o**3 - 4*o**2 - 9*o - 6. Let t(y) be the first derivative of -y**2/2 - y + 3. Let h(f) = -j(f) + 4*t(f). Factor h(s).
(s + 1)**2*(s + 2)
Let w(s) be the third derivative of s**6/6 - 5*s**5/12 + 5*s**4/24 + 4*s**2. Factor w(x).
5*x*(x - 1)*(4*x - 1)
Factor -4 + x + 4*x**3 - 2*x**2 - 4*x - 7*x.
2*(x - 2)*(x + 1)*(2*x + 1)
Let o(z) = 2*z - 4. Suppose 4*c - f - 11 = 0, -3*c + 2*f + 3*f + 4 = 0. Let h be o(c). Factor -6*u - 3*u**2 + h + 3*u**2 + 3*u**2 + 3*u**2 - 2*u**3.
-2*(u - 1)**3
Let p(g) = -2*g - 2 + 2*g + 3 - 3*g. Let a be p(-1). Factor -4*n + 6*n + 5*n**3 - 3*n - a*n**3.
n*(n - 1)*(n + 1)
Suppose -4*n - 3*a = -17, -4*a + 4 + 6 = -n. Find d, given that d**2 + 0 - n - 2*d + 2 = 0.
0, 2
Factor 0 - 1/4*m**5 + 0*m**2 + 1/2*m**3 + 0*m + 1/4*m**4.
-m**3*(m - 2)*(m + 1)/4
Let f(b) be the third derivative of b**5/330 + b**4/33 - 5*b**3/33 + b**2. Factor f(j).
2*(j - 1)*(j + 5)/11
Let s(j) be the first derivative of 4*j**3/3 - j**2 - 14*j - 2. Let l(a) = -3*a**2 + 3*a + 13. Let v(r) = 6*l(r) + 5*s(r). Determine q so that v(q) = 0.
-2
Let i = 293761/360 - 816. Let v(b) be the third derivative of 0*b**3 - 1/72*b**4 + 0*b**5 + i*b**6 + 0 + b**2 + 0*b. Factor v(y).
y*(y - 1)*(y + 1)/3
Let c be -5 + 5 - 1628/14. Let n = -116 - c. Find p, given that -8/7 - 8/7*p**3 + 6/7*p**2 + 8/7*p + n*p**4 = 0.
-1, 1, 2
Let l(i) = 14*i**3 + 4*i**2 - 6*i - 4. Let z(x) = -5*x**3 - x**2 + 2*x + 1. Let m(j) = 3*l(j) + 8*z(j). Factor m(y).
2*(y - 1)*(y + 1)*(y + 2)
What is y in -3/7*y**4 + 0*y + 0*y**3 + 0 - 3/7*y**5 + 0*y**2 = 0?
-1, 0
Suppose -2 = 4*q + 3*n - 15, 2*q + n = 7. Let c(v) be the second derivative of -1/90*v**6 + 1/36*v**q + v + 0*v**2 - 1/60*v**5 + 0 + 1/18*v**3. Factor c(p).
-p*(p - 1)*(p + 1)**2/3
Let v(d) be the first derivative of -2*d**3/21 - 6*d**2/7 - 18*d/7 + 16. Determine g so that v(g) = 0.
-3
Let k be 11/14 - (-2)/(-7). What is x in k + 3/2*x - 2*x**2 = 0?
-1/4, 1
Let i = -1/68 - -9/34. Let u(k) be the first derivative of -1/4*k**2 - 1/20*k**5 + i*k + 0*k**3 + 1/8*k**4 - 1. Factor u(q).
-(q - 1)**3*(q + 1)/4
Solve r**3 + 0 + 1/3*r - 1/3*r**4 - r**2 = 0 for r.
0, 1
Let r = -5/14 - -67/70. Suppose r*n**2 - 3/5*n - 6/5 = 0. Calculate n.
-1, 2
Let a(n) = -2*n**2 + 2*n - 14. Let s(q) = 4*q**2 - 5*q + 27. Let w(z) = -z**3 - z**2 + 11. Let m be w(0). Let c(g) = m*a(g) + 6*s(g). Factor c(b).
2*(b - 2)**2
Let s(j) = 2*j**3 + 3. Let g(w) = -4*w**3 - w**2 - w - 7. Let m(r) = 2*g(r) + 5*s(r). Let z(i) be the first derivative of m(i). Factor z(u).
2*(u - 1)*(3*u + 1)
Suppose 3*x + 15 = 0, 4*x = 3*t + 2*x + 17. Let o be (0 - (-6)/t)*-6. Factor j**3 - j**4 - 3*j**o + j**5 - 4*j**2 + 6*j**2 - 4*j**5.
-j**2*(j + 1)**2*(3*j - 2)
Let i(n) = 11*n**3 - 48*n**2 + 25*n + 19. Let w(l) = 5*l**3 - 24*l**2 + 13*l + 10. Let x(y) = -4*i(y) + 7*w(y). Let x(a) = 0. Calculate a.
-1/3, 1, 2
Let i(o) be the third derivative of o**7/350 - 3*o**5/100 - o**4/20 - 8*o**2. Factor i(z).
3*z*(z - 2)*(z + 1)**2/5
Let a(p) be the third derivative of p**5/210 + 5*p**4/84 + 2*p**3/7 + 36*p**2. Factor