Suppose -2*l = 5*c - k*c - 2, -5*c - 4 = -4*l. Factor -2/5*g**4 - 6/5*g**2 - 2/5*g - 6/5*g**3 + c.
-2*g*(g + 1)**3/5
Factor 0 - 2/9*l - 2/9*l**2 + 4/9*l**3.
2*l*(l - 1)*(2*l + 1)/9
Let g(y) be the third derivative of y**9/52920 - y**8/8820 + y**7/3528 - y**6/2520 - y**5/12 - 3*y**2. Let x(v) be the third derivative of g(v). Factor x(s).
2*(s - 1)*(2*s - 1)**2/7
Suppose -44/3*z**2 - 12 + 76/3*z + 4/3*z**3 = 0. What is z?
1, 9
Let w(z) be the third derivative of -7/80*z**6 + 0 - z**2 + 11/48*z**4 + 1/6*z**3 + 0*z + 1/15*z**5. Factor w(x).
-(x - 1)*(3*x + 1)*(7*x + 2)/2
Factor -3*a**4 - 4*a + 5*a**4 + 12*a**2 - 3 - 6*a**4 - 5 + 4*a**3.
-4*(a - 2)*(a - 1)*(a + 1)**2
Suppose -2*z + 4*z = z. Let u(r) be the first derivative of 1/3*r**3 - 1/5*r**5 + 1/4*r**2 - 2 + z*r + 0*r**4 - 1/12*r**6. Suppose u(t) = 0. Calculate t.
-1, 0, 1
Let p(s) be the third derivative of -s**6/15 + 31*s**5/15 - 56*s**4/3 - 128*s**3/3 + 6*s**2 - 3. Determine n so that p(n) = 0.
-1/2, 8
Suppose -16*l = -l - 30. Suppose -5 = 5*q, -2*o - 2*q = 2*o - 38. Factor -6*b**4 + o*b**l - b + 4*b - 3*b**5 - 4*b**2.
-3*b*(b - 1)*(b + 1)**3
Let 10*d**5 - 142/5*d**3 - 16/5 + 8*d**4 - 44*d**2 - 104/5*d = 0. Calculate d.
-1, -2/5, 2
Factor 10*d**2 - 12*d**2 + 2*d**3 - d**4 + d**2.
-d**2*(d - 1)**2
Let w = 9 + -5. Factor r**3 + w*r**5 + r**5 - 2*r**5 - 4*r**5.
-r**3*(r - 1)*(r + 1)
Suppose 5*v + 20 = 4*g, -2 = -3*g + 4*v + 14. Suppose g = -4*f + 20, -f + 11 = -2*q + 2*f. Find h, given that -1/5*h - 1/5*h**q + 2/5 = 0.
-2, 1
Let f(z) = z**3 + z. Let m be (-3)/4*-4 + 0. Let q(o) = -3*o**2 + 2*o - 1. Let t(u) = m*f(u) + 3*q(u). Suppose t(g) = 0. What is g?
1
Suppose -2*o = -3*d + 1, -o - 2 = -0*o - 2*d. Let n(w) = w**3 + 4*w**2 + w - 2. Let p be n(-3). Factor -2*t**p + 2*t**o + 2*t**3 + 2*t**5 + 4*t**4.
2*t**3*(t + 1)**2
Let o be (1/2)/((-1)/(-2)). Solve -1 - 2*k**2 - 12*k - o + 8*k = 0 for k.
-1
Suppose -5 - 5 = -2*w. Let q be w/((-5)/2) - -18. Factor q*b**2 + 4*b - 7*b**4 + 4*b**3 - 3*b**3 + 4*b**3.
-b*(b - 2)*(b + 1)*(7*b + 2)
Suppose 0 = o + 4*r + 15, 40 = 4*o + o - 3*r. Factor -5*s - 7 - 4 + 3*s**3 - 4*s + o.
3*(s - 2)*(s + 1)**2
Let x(n) be the first derivative of -2/5*n**2 + 1 - 2/5*n - 2/15*n**3. Let x(w) = 0. What is w?
-1
Let n = 8 - 5. Suppose 5 = d - 0*d. Factor -n*y + 2*y - d*y**4 + 15*y**2 - 19*y**3 + 12*y**4 - 2.
(y - 1)**3*(7*y + 2)
Suppose 4*l + 2*u = -8, -3*u = 14 - 2. Let g(h) be the third derivative of -1/30*h**4 + l*h**3 - 1/150*h**5 + 0 + h**2 + 0*h. Factor g(y).
-2*y*(y + 2)/5
Let s(q) be the first derivative of q**5/420 + q**4/168 + q**2/2 - 2. Let n(o) be the second derivative of s(o). Factor n(w).
w*(w + 1)/7
Factor -1/3*p**3 - p**4 + 4/3*p**5 + 0 + 0*p + 0*p**2.
p**3*(p - 1)*(4*p + 1)/3
Factor 2/5 - 2/5*k**2 + 0*k.
-2*(k - 1)*(k + 1)/5
Suppose 0 = -299*t + 298*t + 3. Find q, given that -6/7*q**2 + 3/7*q + 0 - 3/7*q**5 + 0*q**t + 6/7*q**4 = 0.
-1, 0, 1
Let c(d) = 2*d**2 + 4*d - 2. Let u be c(2). Let y be (-4 - -3) + u/6. Factor 2/3*x**2 + 0 + y*x.
2*x*(x + 2)/3
Let m = 5891494214/1715 + -3435273. Let x = m + 2/343. Let 0 - x*v + 0*v**3 + 3/5*v**5 + 6/5*v**4 - 6/5*v**2 = 0. What is v?
-1, 0, 1
Factor 2*p + 0 - 1/2*p**2.
-p*(p - 4)/2
Let m(d) = -d**3 + 5*d**2 - 4*d. Let t(z) = -z**2 + z. Let a(i) = -m(i) - 4*t(i). Factor a(g).
g**2*(g - 1)
Let b(m) be the third derivative of 0 + 0*m + 0*m**6 + 0*m**4 + 0*m**3 - 1/30*m**5 + 1/105*m**7 + m**2. Factor b(f).
2*f**2*(f - 1)*(f + 1)
Let x be 4 + 7/((-14)/(-30)). Suppose 3*n + 4 = 3*l + x, -2*n + 3*l + 13 = 0. Factor -8/7*f + 8/7 + 2/7*f**n.
2*(f - 2)**2/7
Suppose -4*z - 5*r = 13, -3*z = -2*z + 3*r + 12. Let k = 9 + -7. Factor -3*i**3 + i**4 + 5*i**z + 4*i**k - 3*i**2.
i**2*(i + 1)**2
Let d be 18/8 + (-2)/8. Suppose 0*g + d*g = 8. Factor 0*u**2 + 0*u + 0 - 1/2*u**5 + 0*u**g + 1/2*u**3.
-u**3*(u - 1)*(u + 1)/2
Suppose 4 = -2*g + 4*g. Factor -8 - 3*q**g + 3*q + 8.
-3*q*(q - 1)
Let v(s) be the third derivative of s**8/20160 + s**7/840 + s**6/80 + 7*s**5/60 + 5*s**2. Let x(c) be the third derivative of v(c). Factor x(q).
(q + 3)**2
Let o be 3/4*(-2 - 22). Let x be ((-1)/2)/(3/o). Determine h, given that 0 + 16/7*h**4 + 30/7*h**x - 16/7*h**2 + 2/7*h - 32/7*h**5 = 0.
-1, 0, 1/4, 1
Let s(q) be the second derivative of -4/3*q**3 + 2*q + 1/4*q**4 + 0 + 2*q**2. Determine d so that s(d) = 0.
2/3, 2
Let h = 468 - 1402/3. Factor h + 2/3*f**3 + 2*f**2 + 2*f.
2*(f + 1)**3/3
Let x be -5 - ((-9)/(-3) - 2). Let b be 0/(1 - x/(-3)). Factor -8/5*l**5 - 14/5*l**2 - 6*l**3 - 26/5*l**4 - 2/5*l + b.
-2*l*(l + 1)**3*(4*l + 1)/5
Let v(s) be the first derivative of 3*s**5/5 - 3*s**4/4 - 3*s**3 + 3*s**2/2 + 6*s + 4. Suppose v(n) = 0. What is n?
-1, 1, 2
Let p(s) = 5*s + 47. Let b be p(-9). Factor 0*x + 0*x**b - 2/9*x**3 + 0.
-2*x**3/9
Suppose -2 = -i + 3. Suppose -i*w = -4*w. Suppose 2/3*j**2 + 2/3*j + w = 0. What is j?
-1, 0
Let p be 10/3*12/10. Let i(h) be the first derivative of 0*h**2 + 1 + 2/21*h**3 + 0*h + 1/14*h**p. Let i(y) = 0. What is y?
-1, 0
Factor -12*v**3 + 0*v - v + 28*v**3 - 15*v**3.
v*(v - 1)*(v + 1)
Let w = -4 - -6. Let r(u) = -u**5 + u**4 + 5*u**3 + u**2 - u + 1. Let q(l) = -l**5 + l**4 + 4*l**3 - l + 1. Let f(s) = w*r(s) - 3*q(s). Factor f(x).
(x - 1)**3*(x + 1)**2
Factor -1/3*d**2 + 0 + 2/3*d.
-d*(d - 2)/3
Let v(q) = q**3 + 2*q**2 - 3*q + 3. Let f(d) = -d**2 - 7*d - 3. Let k be f(-7). Let i be v(k). Solve 2*u - 2*u**i + 0 + 0 + 2 - 2*u**2 = 0.
-1, 1
Let k(x) be the second derivative of -x**5/10 + x**4/2 + x**3/3 - 3*x**2 + 13*x. Factor k(c).
-2*(c - 3)*(c - 1)*(c + 1)
Let v be (2/6)/((-10)/(-12)). Suppose 3*p - 12 = 2*m, 2*p - 16 = -m - 2*p. Let 0*w**2 + m*w**4 + 4/5*w**3 - v*w - 2/5*w**5 + 0 = 0. Calculate w.
-1, 0, 1
Let i(y) = 3*y**2 + 5*y + 4. Let q(h) = 4*h**2 + 6*h + 5. Let r(z) = -3*i(z) + 2*q(z). Factor r(c).
-(c + 1)*(c + 2)
Let d(r) be the second derivative of 0*r**2 + 1/50*r**5 + 0 + 1/15*r**3 + 3*r + 1/15*r**4. Find i such that d(i) = 0.
-1, 0
Let u(i) be the third derivative of -i**6/780 - i**5/130 + 4*i**3/39 + 9*i**2. Solve u(c) = 0 for c.
-2, 1
Suppose -h**3 - h**3 + 6*h**2 - 6*h**4 + 2*h**3 - 3*h**5 + 3*h = 0. What is h?
-1, 0, 1
Let i be 3/(6/(-10)) + 391/69. Find b such that i*b**4 - 2/3*b - 2*b**3 + 2*b**2 + 0 = 0.
0, 1
Let 1/3*v**2 - v**3 + 2/3*v + 0 = 0. Calculate v.
-2/3, 0, 1
Suppose 0*u + 4*u + z = 15, 5*u = -3*z + 24. Let p be u*3/(-108)*-3. Let 1/4 + p*f**2 - 1/2*f = 0. Calculate f.
1
Let i = -15 + 18. Let y(t) be the third derivative of 0*t**i + 0*t**4 + 0 - 1/120*t**5 + t**2 + 0*t. Factor y(d).
-d**2/2
Let q be 1 + 9/(36/8). Let k(a) be the first derivative of 4/3*a - 2*a**q - 2 + 7/3*a**2. Solve k(d) = 0.
-2/9, 1
Find t, given that 4/3*t**2 - 4/3 - 2/3*t + 2/3*t**3 = 0.
-2, -1, 1
Let z(o) be the third derivative of o**8/224 - 3*o**6/80 - o**5/20 + 4*o**2. Factor z(b).
3*b**2*(b - 2)*(b + 1)**2/2
Let c(s) be the second derivative of s**4/3 - 8*s**3/3 + 8*s**2 - s. Factor c(x).
4*(x - 2)**2
Let v(y) be the second derivative of y**6/165 - y**4/22 - 2*y**3/33 + 12*y. Suppose v(o) = 0. What is o?
-1, 0, 2
Let i(y) be the first derivative of -1/2*y**2 + 3 - 1/2*y - 1/6*y**3. Suppose i(h) = 0. Calculate h.
-1
Suppose 0 = 4*d + 4*a - 10 - 10, 5*d = a + 13. Determine o, given that 2/7*o**5 + 0*o + 0*o**d + 0 + 0*o**2 + 2/7*o**4 = 0.
-1, 0
Let c be 17/5 + 14/(-35). Let a(m) be the first derivative of 1/2*m**2 + 1/3*m**c + 0*m + 1. Factor a(j).
j*(j + 1)
Let y(r) be the second derivative of -r**5/60 + 3*r**2/2 + 3*r. Let o(h) be the first derivative of y(h). Factor o(x).
-x**2
Let l(q) be the first derivative of -q**8/504 - q**7/315 + q**6/180 + q**5/90 - q**2 - 2. Let h(o) be the second derivative of l(o). Factor h(c).
-2*c**2*(c - 1)*(c + 1)**2/3
Suppose 0 = 5*c - 8*c. Suppose w = g + 3, c = w + g + 4*g + 3. Let -1/2*u**w + 0 + 0*u = 0. Calculate u.
0
Let d(m) be the second derivative of 3*m**6/70 + 57*m**5/140 - 41*m**4/84 + m**3/6 - 23*m. Factor d(c).
c*(c + 7)*(3*c - 1)**2/7
Solve 0*k**3 + 3/2*k**2 - 1/2*k**4 + k + 0 = 0.
-1, 0, 2
Suppose 2*q - 4 = 2. Find r such that 0*r**2 - 1/4*r**4 + 0*r + 0 + 1/4*r**q = 0.
0, 1
Factor -h**3 + 3*h**2 + 10 - 8 - 6.
-(h - 2)**2*(h + 1)
Let d = -85 - -89. Let l(o) be the first derivative of 1/3*o**3 + 0*o + 1/2*o**2 - 1/5*o**5 - 1 - 1/4*o**d. Factor l(g).
-g*(g - 1)*(g + 1)