g(z) = 8*z**4 + z**3 - 3*z**2 - z. Let t(a) = -13*a**4 - 2*a**3 + 5*a**2 + 2*a. Let y(p) = -8*g(p) - 5*t(p). Factor y(w).
w*(w - 1)*(w + 1)*(w + 2)
Let u = 53 - 48. Let h(m) = -m**3 + 6*m**2 - 6*m + 8. Let r be h(u). Solve -q + q**r - 1/2*q**2 + 1/2*q**4 + 0 = 0 for q.
-2, -1, 0, 1
Let g(x) = 3*x**3 + 5. Let j(w) = 8*w**3 + 14. Let f(k) = 11*g(k) - 4*j(k). Let u(q) = 3*q + 1. Let h(s) = -2*f(s) + 2*u(s). Solve h(i) = 0 for i.
-1, 2
Suppose -5*i - 2*i = -42. Let w be -3*(2/i)/((-4)/16). What is u in -3/5*u - 2/5*u**2 + 3/5*u**w + 2/5*u**3 - 1/5 + 1/5*u**5 = 0?
-1, 1
Let u be 2/(-4)*20/(-25). Suppose -2*g + 12 = 2*b, 5*b + 4 = 4*g - 2. Solve 6/5*r**b + 2/5 + u*r**3 + 6/5*r = 0 for r.
-1
Let c(u) be the first derivative of -27*u**4/4 + 31*u**3/3 - 2*u**2 - 553. Factor c(k).
-k*(k - 1)*(27*k - 4)
Suppose 0*b**3 + 11*b**5 - 18*b**5 + 5*b**3 + 2*b**5 = 0. What is b?
-1, 0, 1
Factor 72*c + 3*c**4 + 90501 - 12*c**2 - 90501 - 18*c**3.
3*c*(c - 6)*(c - 2)*(c + 2)
Let q(t) = 5*t + 7*t**4 + 5*t**2 + 10*t**3 - t**4 - t**4 + 5. Let m(g) = -5*g**4 - 11*g**3 - 6*g**2 - 6*g - 6. Let c(b) = 5*m(b) + 6*q(b). Solve c(i) = 0.
-1, 0
Suppose 5*d - 18 = 2*p, 2*d + d = 3*p + 18. Suppose 3 = 4*j - 13. Factor d*c**2 - 2*c**4 + 5*c**3 + 0*c**5 + 6*c**j + c**5.
c**2*(c + 1)**2*(c + 2)
Solve -6157*s + 6157*s + 2*s**3 + 2*s**2 = 0 for s.
-1, 0
Let x = 60 - 51. Suppose -x*o**2 - 9 - 8*o - 4*o + 6 = 0. What is o?
-1, -1/3
Let m(b) be the second derivative of 6*b**3 + 0 + 27/4*b**4 + 2*b**2 - 23*b. Let m(a) = 0. Calculate a.
-2/9
Let x(h) = -2*h**2 - 37*h - 167. Let w be x(-10). Determine n so that 144/5 - 2*n**w - 312/5*n - 116/5*n**2 = 0.
-6, 2/5
Find a such that 11/6*a**2 + 1/2*a + 0 - 7/3*a**3 = 0.
-3/14, 0, 1
Let q(a) be the first derivative of a**4/14 + 4*a**3/21 - 661. Determine k so that q(k) = 0.
-2, 0
Let l(s) be the second derivative of s**7/2 - s**6/5 - 28*s. Factor l(n).
3*n**4*(7*n - 2)
Factor -68/3 + 2/3*j**2 + 10*j.
2*(j - 2)*(j + 17)/3
Let v(j) be the second derivative of -j**4/30 - 2*j**3/5 - j**2 + 40*j + 2. Factor v(t).
-2*(t + 1)*(t + 5)/5
Let b(l) = l**3 + 12*l**2 - l - 12. Let q be b(-12). Let w(y) be the first derivative of -1/3*y**3 + 1/2*y**2 + 3 + q*y. Find h such that w(h) = 0.
0, 1
Let s(l) be the third derivative of -l**7/105 + 11*l**6/240 - 3*l**5/40 - 7*l**4/24 + 11*l**2. Let x(q) be the second derivative of s(q). Factor x(h).
-3*(h - 1)*(8*h - 3)
Let y(v) be the first derivative of -1/19*v**2 + 1/38*v**4 + 2/57*v**3 + 0*v - 8 - 2/95*v**5. Determine r, given that y(r) = 0.
-1, 0, 1
Let w(d) be the second derivative of -d**5/90 - d**4/9 - 4*d**3/9 + 9*d**2/2 + 9*d. Let s(p) be the first derivative of w(p). Let s(y) = 0. Calculate y.
-2
Let j(d) = -11*d**4 - 4*d**3 - 4*d**2 + 4*d - 25. Let k(t) = -13*t**4 - 5*t**3 - 5*t**2 + 5*t - 30. Let a(m) = 6*j(m) - 5*k(m). Factor a(x).
-x*(x - 1)**2*(x + 1)
Factor 34*r + 109*r + 13*r - 4*r**2.
-4*r*(r - 39)
Suppose -21/2*v + 3/2*v**2 - 27 = 0. Calculate v.
-2, 9
Factor 1/4*p**4 + 3/4*p**3 - 255/4*p - 50 - 53/4*p**2.
(p - 8)*(p + 1)*(p + 5)**2/4
Let x(v) = -v**2 - 12*v + 66. Let f be x(-16). Solve -9/7*k + 6/7*k**f + 6/7*k**3 + 3/7*k**5 + 3/7 - 9/7*k**4 = 0 for k.
-1, 1
Let k(y) be the first derivative of -y**6/2 - 522*y**5/5 - 22707*y**4/4 - 217. Factor k(r).
-3*r**3*(r + 87)**2
Let w(x) be the second derivative of -5*x**4/12 - 5*x**3/2 + 68*x. Factor w(p).
-5*p*(p + 3)
Suppose -g - 21 = -a - 34, -2*g - 37 = 5*a. Find f such that 1/2*f - 1/2*f**3 - 1/2*f**2 + 0 + 1/2*f**g = 0.
-1, 0, 1
Factor -18*i + 42/5*i**2 - 2/5*i**4 + 0 + 2/5*i**3.
-2*i*(i - 3)**2*(i + 5)/5
Let a = 57 + -55. Suppose 2 + 11*i**2 - 17*i**2 + 8*i**a - 4*i = 0. What is i?
1
Let a = 14983 + -104877/7. Factor 16/7*n - 12/7 - a*n**2.
-4*(n - 3)*(n - 1)/7
Let q be 480/256 + (-1)/(-8). Solve 45/2*l**q + 5*l + 25*l**3 + 15/2*l**4 + 0 = 0 for l.
-2, -1, -1/3, 0
Let p(n) be the first derivative of -11 + 0*n + 0*n**2 + 4*n**3 - 3/4*n**4. Solve p(y) = 0 for y.
0, 4
Determine t so that 12/7*t - 4/7*t**4 - 4/7 + 8/7*t**2 - 24/7*t**3 + 12/7*t**5 = 0.
-1, 1/3, 1
Let t(i) = -2 + 13*i**3 + 12*i**2 + 2*i - 21*i + 4 - i**4 - 1. Let n(x) = x**3 + x**2 - x + 1. Let b(w) = -18*n(w) + 2*t(w). Determine h so that b(h) = 0.
-1, 2, 4
Let r(b) be the first derivative of -2*b**5/45 + 2*b**4/9 - 8*b**3/27 + 241. Factor r(p).
-2*p**2*(p - 2)**2/9
Let z = -201/95 - -44/19. Solve -1/5*n**2 + z + 0*n = 0 for n.
-1, 1
Suppose o = 5*o - 20. Suppose 3*b - 1 = o. Solve 2*u - u - 3*u - u**b = 0.
-2, 0
Let n(r) = -11*r**2 + 22*r - 5. Let u(v) be the first derivative of -v**3/3 + v**2 - 5. Let l(y) = -n(y) + 6*u(y). Determine p, given that l(p) = 0.
1
What is a in 0*a - 3/8 + 9/4*a**2 + 3*a**3 + 9/8*a**4 = 0?
-1, 1/3
What is v in 54 + 3/2*v**2 + 30*v = 0?
-18, -2
Let d(i) be the first derivative of -7*i**6/30 + 29*i**5/25 + 3*i**4/20 - 29*i**3/15 + 2*i**2/5 - 12. Find r, given that d(r) = 0.
-1, 0, 1/7, 1, 4
Let h be (0 + 0 + 0)*1. Suppose u = 38*p - 33*p - 9, -2*p - 2*u = -6. What is l in 1/5*l**p - 1/5 + h*l = 0?
-1, 1
Let a(t) = -t - 6. Let i be a(-3). Let o be ((-3 + 3)/(-5))/i. Suppose 4/3 + o*k - 1/3*k**2 = 0. Calculate k.
-2, 2
Let i(x) = 2*x**3 + 186*x**2 + 363*x - 89. Let k be i(-91). Factor 8/3 + 10/3*z**k - 2/3*z**3 - 16/3*z.
-2*(z - 2)**2*(z - 1)/3
Suppose 0 = -k + 6*k. Let j be 6/(-12) - (-3)/3. Factor 0 + k*m + j*m**2.
m**2/2
Let m(a) = a**3 + 10*a**2 - 5*a - 2. Let l be m(-10). Factor 27*s**4 + 2*s + 2*s - l*s**3 + 15*s**2 + 2*s.
3*s*(s - 1)**2*(9*s + 2)
Let j = -10817 - -10820. Factor 96/5 + 48/5*r**2 + 6/5*r**j + 24*r.
6*(r + 2)**2*(r + 4)/5
Let p(m) = -2*m**2 - 6*m - 4. Let v(a) = a. Let t(c) = p(c) - 3*v(c). Factor t(d).
-(d + 4)*(2*d + 1)
Let r(n) be the first derivative of 0*n**2 - 1/3*n**3 + 1/4*n**4 - 10 + 1/40*n**5 + 0*n - 1/120*n**6. Let v(u) be the third derivative of r(u). Factor v(j).
-3*(j - 2)*(j + 1)
Let s be -1 + 25/35*21/6. Factor -s*l + 0*l**2 + 1/2*l**3 - 1.
(l - 2)*(l + 1)**2/2
Let i = 9929 - 9929. Factor -1/6*v + 0 + 1/6*v**3 + i*v**2.
v*(v - 1)*(v + 1)/6
Let q(x) = 30*x + x**2 - 2*x**2 - 31*x. Let t(h) = -3*h**3 + 28*h**2 - 77*h. Let r(y) = -2*q(y) + t(y). Suppose r(g) = 0. What is g?
0, 5
Let c(h) be the first derivative of 4*h**4 + 80*h**3 - 126*h**2 + 64*h + 577. Factor c(j).
4*(j + 16)*(2*j - 1)**2
Factor -36/7*i**2 + 4/7 + 10/7*i.
-2*(2*i - 1)*(9*i + 2)/7
Let x = 20 - 12. Let y = -6 + x. Factor -3*r**3 + 0*r**3 + 3*r - 2*r**2 + y*r**2.
-3*r*(r - 1)*(r + 1)
Let l = -5212/9 + 580. Let d(w) be the first derivative of l*w - 4 + 2/9*w**3 + 8/9*w**2. Factor d(r).
2*(r + 2)*(3*r + 2)/9
Let 141*s**2 + 79*s**2 - s**3 - 197*s**2 = 0. What is s?
0, 23
Suppose 235*j = 3*u + 230*j - 16, -5*u + 16 = -3*j. Solve 3/4*s**3 - 45/4*s**u + 225/4*s - 375/4 = 0 for s.
5
Let n be -3 + -1 + ((-16)/24 - (-545)/30). Suppose -21/2*k**5 + 15/2*k**3 + n*k**2 + 0 + 3*k - 27/2*k**4 = 0. Calculate k.
-1, -2/7, 0, 1
Let y(i) be the third derivative of 0*i + 1/18*i**4 + 14*i**2 + 1/90*i**5 + 0 + 1/9*i**3. Factor y(m).
2*(m + 1)**2/3
Let a(p) be the third derivative of 0*p**4 + 0*p + 1/270*p**5 - 1/27*p**3 + 0 - 18*p**2. Factor a(m).
2*(m - 1)*(m + 1)/9
Factor 2*w - 28/9 - 2/9*w**2.
-2*(w - 7)*(w - 2)/9
Factor 4/3*n**5 + 8*n**3 - 20/3*n**4 + 0*n + 0 + 0*n**2.
4*n**3*(n - 3)*(n - 2)/3
Let l(z) be the third derivative of 11*z**6/120 - 10*z**5/3 + 3*z**4/2 - 2*z**2 - 133*z. Suppose l(y) = 0. What is y?
0, 2/11, 18
Let a(i) = 7*i**2 - 2*i. Let g be a(1). Suppose o - 7 = -g. Let -4*p**5 + 3*p**4 - 3*p**4 - o*p**4 - 2*p**5 + 4*p**3 = 0. Calculate p.
-1, 0, 2/3
Let i(s) be the third derivative of -s**6/60 + s**5/30 + 17*s**4/6 + 56*s**3/3 + 303*s**2. Find r such that i(r) = 0.
-4, -2, 7
Suppose 20 = 2*k - 4*j, -3*j = -4*k - 9 + 34. Let -2*y**3 + 13*y**2 - 34*y**2 + 2 + 2 - 8*y + 7*y**k = 0. Calculate y.
-1, 2/7, 2
Let h be (-6)/(-66) - 65/(-495). Factor 0 + 2/9*s**2 + h*s.
2*s*(s + 1)/9
Let a(m) be the third derivative of 0*m + 0 - 1/3*m**4 + 1/15*m**5 + 2/3*m**3 - 24*m**2. What is n in a(n) = 0?
1
Determine b, given that 46/11*b**3 - 4/11 - 14/11*b**4 - 54/11*b**2 + 26/11*b = 0.
2/7, 1
Let j(y) = -73*y**3 + 77*y**2 + 12*y - 12. Let s(k) = 72*k**3 - 78*k**2 - 12*k + 12. Let g(f) = 3*j(f) + 2*s(f). Factor g(m).
-3*(m - 1)*(5*m - 2)*(5*m + 2)
Let x(b) be the second derivativ