5*a + 7 = 6*a. Let z(r) be the third derivative of -1/12*r**5 + 0*r**3 + 3*r**2 + 0*r + 1/42*r**a - 1/40*r**6 - 1/24*r**4 + 1/84*r**8 + 0. Factor z(b).
b*(b - 1)*(b + 1)**2*(4*b + 1)
Factor 2/5*i**2 + 8/15 + 16/15*i.
2*(i + 2)*(3*i + 2)/15
Suppose 4*j + 18 = -o - 7, 4*j + 27 = -3*o. Let x be -2*(-3)/j - -7. Factor 2*b + b**2 - 8 - 3*b**2 + x*b.
-2*(b - 2)**2
What is l in 4*l**2 - l**2 + 3*l**3 - 5*l**2 + 0*l**2 = 0?
0, 2/3
Let p(b) be the third derivative of b**8/112 - b**7/35 + b**5/10 - b**4/8 + 5*b**2. Suppose p(q) = 0. Calculate q.
-1, 0, 1
Let v(q) be the second derivative of -1/3*q**3 + 0 + 0*q**5 - 1/3*q**4 + 2/15*q**6 + 3*q + 1/21*q**7 + 0*q**2. Solve v(i) = 0.
-1, 0, 1
Solve 3/2*m + 1/4*m**3 + 0 - 7/4*m**2 = 0 for m.
0, 1, 6
Find z such that -z**3 + z + 2*z**4 + 2*z**2 - z - 3*z**4 = 0.
-2, 0, 1
Let d(g) = 2*g**2 - 3*g. Let i be d(2). Factor -15*y**i + 33*y**2 - 21*y**2.
-3*y**2
Let s(o) be the first derivative of 3*o**5/5 - 3*o**4/2 + o**3 - 3. Factor s(d).
3*d**2*(d - 1)**2
Let z(k) = -k**3 - 8*k**2 - 7*k + 5. Let w be z(-7). Suppose 8 = w*c - 2. Factor 20*l**c - 6*l**3 - 20*l**2 + 3*l**4.
3*l**3*(l - 2)
Factor 821*o - 5*o**3 - 821*o.
-5*o**3
Let m(g) be the third derivative of g**5/80 + g**4/32 - 13*g**2. Let m(d) = 0. Calculate d.
-1, 0
Let v be (-4 - -3)/(1/(-6)). Let i be ((-4)/(-7))/(v/35). Factor 0*z + 4/3*z**2 + 6*z**3 + i*z**5 + 0 + 8*z**4.
2*z**2*(z + 1)**2*(5*z + 2)/3
Suppose 285*j - 25*j**3 + 85*j**3 - 5*j**4 - 240*j**2 + 115*j - 240 = 0. Calculate j.
2, 6
Let r(n) = -3*n**4 + 7*n**3 + 20*n**2 - 22*n - 2. Let d(y) = 5*y**4 - 15*y**3 - 40*y**2 + 45*y + 5. Let g(j) = -2*d(j) - 5*r(j). Factor g(s).
5*s*(s - 2)*(s - 1)*(s + 2)
Let f(a) = -a**2 - 9*a - 9. Let b be f(-7). Let r(k) = -k + 7. Let x be r(b). Suppose -7*j**x + 2 - 3*j - j - j = 0. Calculate j.
-1, 2/7
Find f such that 2*f + 1/4*f**3 + 5/4*f**2 + 1 = 0.
-2, -1
Let i = 2399/858060 + -3/3178. Let w(c) be the third derivative of 2*c**2 + i*c**6 + 0*c - 1/270*c**5 + 0 + 0*c**3 + 0*c**4. Factor w(g).
2*g**2*(g - 1)/9
Let b = 12 - 12. Suppose -6 = 5*g - 3*v, 3*g - 2 = -v - b. Suppose 0*p**3 - 1/2*p**4 + g*p + 0*p**2 + 0 = 0. Calculate p.
0
Solve -19 + m + 19 + m**2 = 0.
-1, 0
Suppose -5*a - 1 - 4 = -5*i, -2 = -3*a - 2*i. Suppose 2*b - 8 = -2*b. Find k such that 4*k**3 + a*k**3 - b*k**3 + 4*k**2 + 2*k = 0.
-1, 0
Let s(u) be the second derivative of -3*u**7/70 - 2*u**6/15 - 13*u**5/100 - u**4/30 + 18*u. Find q, given that s(q) = 0.
-1, -2/9, 0
Let l(y) be the first derivative of y**7/168 - y**6/40 + 3*y**5/80 - y**4/48 + 2*y - 2. Let d(z) be the first derivative of l(z). Factor d(b).
b**2*(b - 1)**3/4
Suppose -4 = 5*t - 9. Suppose -2*x + 13 = 2*x - 5*a, 0 = -x + 2*a + 4. Determine c, given that t + 4*c - 2 - 2*c**x - 1 = 0.
1
Suppose -26*y = -16*y - 20. Factor -1/3*p - 1/3*p**y + 0.
-p*(p + 1)/3
Let k be -6*(1270/(-315) + 4). Let y(t) be the second derivative of 0 - 1/105*t**6 - k*t**3 - 2/35*t**5 - 1/7*t**2 - 1/7*t**4 + t. Factor y(n).
-2*(n + 1)**4/7
Let h be (-364)/(-784) + 4/14. Suppose 0*s + 3/4*s**2 - h = 0. Calculate s.
-1, 1
Suppose 4*j + 70 = 90. Let k(x) be the third derivative of -1/24*x**4 + 1/120*x**6 + 0*x + 0 + 2*x**2 + 7/120*x**j - 1/60*x**7 + 0*x**3. Factor k(m).
-m*(m - 1)*(m + 1)*(7*m - 2)/2
Let v(d) = d**2 - 5*d + 2. Suppose 15 - 5 = 4*s + 5*m, 4*m = -8. Let h be v(s). Factor -2/11*q**h - 2/11*q + 0.
-2*q*(q + 1)/11
Let l(r) be the second derivative of r**6/50 + 12*r**5/25 + 24*r**4/5 + 128*r**3/5 + 384*r**2/5 - 16*r. Factor l(v).
3*(v + 4)**4/5
Let q(m) be the second derivative of 0 - 1/4*m**3 - 9/20*m**5 + 0*m**2 - 1/5*m**6 - 1/28*m**7 + m - 1/2*m**4. Factor q(r).
-3*r*(r + 1)**4/2
Let y(i) be the second derivative of -5*i**7/21 + 17*i**6/15 - 8*i**5/5 + 2*i**4/3 - 17*i. Solve y(f) = 0.
0, 2/5, 1, 2
Let s(l) be the third derivative of 0 + 0*l + 1/40*l**4 - 1/100*l**5 + 0*l**3 + 4*l**2. Factor s(b).
-3*b*(b - 1)/5
Let z(a) be the second derivative of a**4/12 + 4*a**3/3 + 7*a**2/2 + 10*a. Let p be z(-7). Solve -1/3*s**2 + 0*s - 1/3*s**3 + p + 1/3*s**5 + 1/3*s**4 = 0.
-1, 0, 1
Let v = 0 - -4. Let d be v/(-5) - (-66)/45. Factor -d*u + 0 + 1/3*u**2.
u*(u - 2)/3
Suppose p - 5*p = -3*l - 10, -16 = 3*l - p. Let r be 2 - 3/((-9)/l). What is u in -2*u**3 + r*u**2 + u**2 + 5*u**3 - 5*u**3 + u**4 = 0?
0, 1
Factor -1/2*y**2 + 1/4*y**4 + 1/2*y**3 - 1/4*y**5 + 1/4 - 1/4*y.
-(y - 1)**3*(y + 1)**2/4
Let t = 249 - 246. Factor 3/2*j**2 - j**4 - 3/2*j**t + 0 + j.
-j*(j - 1)*(j + 2)*(2*j + 1)/2
Let c(h) be the second derivative of -5*h**4/12 - 5*h**3/6 + 2*h. Factor c(a).
-5*a*(a + 1)
Factor -21/5*t + 24/5*t**2 + 3/5*t**5 - 6/5*t**4 - 6/5*t**3 + 6/5.
3*(t - 1)**4*(t + 2)/5
Let c(f) be the first derivative of f**6/120 + f**5/20 + f**4/8 + 4*f**3/3 - 1. Let u(p) be the third derivative of c(p). Suppose u(r) = 0. What is r?
-1
Let q(f) be the second derivative of -1/16*f**4 + 0 + 1/8*f**3 + f + 3/4*f**2. Factor q(o).
-3*(o - 2)*(o + 1)/4
Suppose -8 = -3*p + 1. Suppose -5 + 5*y**5 + 1 + 4 - 2*y**p + 3*y**4 = 0. Calculate y.
-1, 0, 2/5
Suppose 0*h = 3*h. Factor -3*x**2 + 3*x**3 + 3*x**4 - x + h*x + x - 3*x.
3*x*(x - 1)*(x + 1)**2
Factor -2/9*a**2 + 0 + 4/9*a - 2/9*a**3.
-2*a*(a - 1)*(a + 2)/9
Let h(k) be the third derivative of 5*k**8/1344 + k**7/112 + k**6/160 - k**3/6 - k**2. Let n(i) be the first derivative of h(i). Find q, given that n(q) = 0.
-3/5, 0
Let t(o) be the first derivative of -o**3/7 - 6*o**2/7 - 9*o/7 + 1. Find r such that t(r) = 0.
-3, -1
Factor 4/7*b**2 - 2/7*b + 0*b**3 + 0 - 4/7*b**4 + 2/7*b**5.
2*b*(b - 1)**3*(b + 1)/7
Let d(c) be the first derivative of c**3/3 + 2*c**2 + 18. Suppose d(u) = 0. What is u?
-4, 0
Let x(k) = -k - 2. Let y be x(-5). Let l be 0 + 1 + (-3)/y. Factor i**3 + 0*i - i**2 + l*i.
i**2*(i - 1)
Let x be 0/(3/3 + -2). Let g = x + 0. Factor -2 + w**2 - 5*w + 6*w + g*w.
(w - 1)*(w + 2)
Suppose 2*w - 2*a - 8 = 0, -5*w - 5*a = -1 + 21. Let c = -7/4 + 9/4. Let 1/2*x**3 - c*x + w + 0*x**2 = 0. What is x?
-1, 0, 1
Determine c, given that 0 - c**2 + 1/3*c = 0.
0, 1/3
Let d(y) = -y**3 - y - 1. Let w(v) = -40*v - 35. Let s(q) = -5*d(q) + w(q). Factor s(r).
5*(r - 3)*(r + 1)*(r + 2)
Let v = -178/3 - -60. Suppose 3*c - 9 = -3*r, -3*c - 3*r - 2*r + 15 = 0. Solve -v*i**3 + 1/3*i**4 + 1/3*i**2 + c + 0*i = 0 for i.
0, 1
Let a(x) = x**4 + x**3 + x - 1. Let q(r) = 7*r**4 + 2*r**3 + r**2 + 14*r - 8. Let c(n) = 24*a(n) - 3*q(n). Factor c(o).
3*o*(o - 1)*(o + 1)*(o + 6)
Determine b so that 1/3*b**3 + 0 + 2*b**2 + 5/3*b = 0.
-5, -1, 0
Let u = 13/36 - 1/4. Let g(v) be the first derivative of u*v**3 - 3 + 0*v + 1/3*v**2. Factor g(h).
h*(h + 2)/3
Let n(x) be the second derivative of -3*x + 0 - 1/40*x**6 + 3/80*x**5 - 1/8*x**3 + 1/16*x**4 + 0*x**2. Factor n(v).
-3*v*(v - 1)**2*(v + 1)/4
Factor 16 + 4*d - 8 - 2*d**2 - 8.
-2*d*(d - 2)
Let z = 37 + -30. Suppose -3*c + 18 = 2*v, 0*v + z = c + v. Factor -1/2*o + 0 + 1/2*o**3 + 1/4*o**c - 1/4*o**2.
o*(o - 1)*(o + 1)*(o + 2)/4
Let i(f) = -f**2 - 5*f - 2. Let r be i(-3). Let o be (84/(-735))/(r/(-14)). Factor 2/5*q**2 + o*q**4 + 0*q + 0 - 4/5*q**3.
2*q**2*(q - 1)**2/5
Let k(d) be the first derivative of d**7/126 + d**6/90 - d**5/60 - d**4/36 + 3*d + 3. Let l(s) be the first derivative of k(s). Factor l(f).
f**2*(f - 1)*(f + 1)**2/3
Find q, given that -1/3*q**3 - q - 5/3*q**2 + 1/3*q**4 + 0 = 0.
-1, 0, 3
Suppose -t + 7 = 5. Factor -t*i**2 + i**2 + i**3 + i**2.
i**3
Let p(w) be the first derivative of w**3 + 3*w**2 + 3*w - 10. Solve p(a) = 0 for a.
-1
Suppose f - 4*f = o - 11, -o + 3 = -f. Suppose d + 3 = f*d. Factor 8/7*j**d + 2/7*j**2 - 2/7 - 8/7*j.
2*(j - 1)*(j + 1)*(4*j + 1)/7
Let a(z) be the first derivative of -z**5/14 + z**4/21 + 2*z - 2. Let w(u) be the first derivative of a(u). Determine d so that w(d) = 0.
0, 2/5
Suppose 0 = 4*b - r - 2, -4*b - 3*r + 6*r + 6 = 0. Solve b*a + 0 - 2/5*a**2 = 0.
0
Let i(f) be the second derivative of -f**8/336 + f**7/70 - f**6/40 + f**5/60 - f**3/3 - 3*f. Let s(a) be the second derivative of i(a). Factor s(n).
-n*(n - 1)**2*(5*n - 2)
Let a(w) be the third derivative of w**5/15 + w**4/2 - 7*w**2. Factor a(u).
4*u*(u + 3)
Factor k**2 + 2*k**2 - 3*k**2 + 3*k**2 - 3.
3*(k - 1)*(k + 1)
Solve 9/2*q + 0 - 3/4*q**2 - 3/4*q**3 = 0.
-3, 0, 2
Let g(i) = -12*i**4 + 21*i**3 + 15*i**2 - 3. Let 