**4 + 2*x**3 + 3*x**2. Let c(m) = -m**2 + 3*m**3 - 2*m**3 - 4*m**2 - 4*m**3 - 3*m**4. Let a(z) = -6*c(z) - 10*v(z). Factor a(j).
-2*j**3*(j + 1)
Let m = 135 + -133. Factor 4/7*o**3 - 4/7 + 10/7*o**m + 2/7*o.
2*(o + 1)*(o + 2)*(2*o - 1)/7
Factor -3/2*j**3 - 1/2*j - 7/4*j**2 + 0.
-j*(2*j + 1)*(3*j + 2)/4
Suppose 5*z = 2*t + 18, 7*t = 5*z + 4*t - 22. Let x = -7 + 7. Factor -1/3*f**z - 1/3*f + x.
-f*(f + 1)/3
Let b(p) = -7*p**3 + 242*p**2 - 3840*p + 20484. Let c(w) = 50*w**3 - 1695*w**2 + 26880*w - 143390. Let y(q) = -15*b(q) - 2*c(q). Factor y(s).
5*(s - 16)**3
Suppose 0 = -4*l - 2 + 14. Factor 3*s**4 + 53*s + 6*s**l - 53*s.
3*s**3*(s + 2)
Determine i, given that 1/2*i**5 + 0 - i**3 + 1/2*i + 0*i**2 + 0*i**4 = 0.
-1, 0, 1
Factor a**3 - 37*a**2 - 13*a**2 - 4913 + 16*a**2 + 867*a - 17*a**2.
(a - 17)**3
Let h(s) be the second derivative of -s**6/15 - 2*s**5/5 - 2*s**4/3 + 4*s. Factor h(q).
-2*q**2*(q + 2)**2
Let v(l) = l**2 - l - 2. Let c(s) = 4*s - 5 - 3*s + 3*s**2 - 2*s - s. Let q(y) = 4*c(y) - 10*v(y). Factor q(g).
2*g*(g + 1)
Suppose s - 7 = -f, 0 = 4*f - 2*s - 6 - 4. Factor -1/4 - 3/4*j - 1/2*j**2 + 1/4*j**5 + 1/2*j**3 + 3/4*j**f.
(j - 1)*(j + 1)**4/4
Let y(n) be the first derivative of -2*n**3/9 + 13*n**2/3 + 53. Determine x so that y(x) = 0.
0, 13
Let s(t) be the third derivative of t**6/60 + t**5/15 + t**4/12 - 5*t**2. Factor s(g).
2*g*(g + 1)**2
Let z(o) be the first derivative of -2/25*o**5 + 2 + 3*o - 4/15*o**3 + 1/75*o**6 + 1/5*o**4 + 1/5*o**2. Let a(i) be the first derivative of z(i). Factor a(x).
2*(x - 1)**4/5
Let r be (4 - 4)/2*(-2 - -3). Find x such that -1/5*x**5 + 1/5*x**3 + 0 + 0*x**2 + r*x + 0*x**4 = 0.
-1, 0, 1
Let k be (1/(-10))/(50/(-375)). Factor 3/2*g - 15/4*g**2 + 0 - k*g**4 + 3*g**3.
-3*g*(g - 2)*(g - 1)**2/4
Let a(w) be the second derivative of w**8/1680 - w**7/210 + w**6/90 - 2*w**3/3 - 5*w. Let k(i) be the second derivative of a(i). Let k(r) = 0. Calculate r.
0, 2
Let d = 7 + -4. Factor 2*t + 2*t**d - t**3 - 4*t**2 + 2*t.
t*(t - 2)**2
Suppose -8*s + 4*s = 0. Factor 2/3*a**5 + s*a + 0 - 2/3*a**4 + 2/3*a**2 - 2/3*a**3.
2*a**2*(a - 1)**2*(a + 1)/3
Let f(b) be the second derivative of -b**5/20 - b**4/6 + 2*b. Determine m, given that f(m) = 0.
-2, 0
Solve 62 - 26*s**2 - 102 - 180*s - 49*s**2 - 68 = 0.
-6/5
Let v(f) be the first derivative of -9*f**3 + 30*f**2 - 12*f - 11. Factor v(k).
-3*(k - 2)*(9*k - 2)
Let n(b) be the second derivative of -1/12*b**4 + 0*b**2 + 6*b + 1/3*b**3 + 0 - 1/20*b**5. Factor n(s).
-s*(s - 1)*(s + 2)
Let v be (-10)/16 + (-2)/(-3). Let q(j) be the third derivative of -2*j**2 - v*j**3 + 0*j + 0 + 0*j**4 + 1/240*j**5. Factor q(c).
(c - 1)*(c + 1)/4
Let k(x) = 8*x + 1. Let u be k(1). Factor -2 + 1 - 3*t**2 - u*t - 5.
-3*(t + 1)*(t + 2)
Let w = 10 + -5. Suppose 0 = 7*x - 4*x + 3*y - 15, -w*x + 20 = 4*y. Solve -2/7*o + x + 2/7*o**2 = 0 for o.
0, 1
Let n be 3*((2 - -1) + -2). Let p be ((-24)/(-90))/(6/5). What is h in -2/9*h**n + p*h + 2/9*h**4 + 0 - 2/9*h**2 = 0?
-1, 0, 1
Let q(g) be the second derivative of -g**5/15 + g**4/24 - 3*g**2/2 - 2*g. Let r(f) be the first derivative of q(f). Determine o, given that r(o) = 0.
0, 1/4
Let x = 9 - 9. Let k(c) be the third derivative of x*c**3 + 1/24*c**4 + 0*c - 1/60*c**5 - c**2 + 0. Solve k(h) = 0.
0, 1
Let i = -371/2 + 3355/18. Let q(m) be the second derivative of -1/12*m**5 - 17/36*m**4 + 3*m + 0 - 2/3*m**2 - i*m**3. Suppose q(s) = 0. What is s?
-2, -1, -2/5
Let i(g) be the first derivative of -g**6/6 + 2*g**5/5 - g**4/4 + 17. Determine v so that i(v) = 0.
0, 1
Suppose 6*t - 2*t - 16 = 0, 0 = 2*m - 2*t + 4. Let p = 233 + -1627/7. Factor 10/7*n**4 + 6*n**m + 34/7*n**3 + 22/7*n + p.
2*(n + 1)**3*(5*n + 2)/7
Let r(i) be the first derivative of 1/21*i**6 - 1/7*i**2 + 0*i + 4/21*i**3 + 0*i**4 - 3 - 4/35*i**5. Factor r(b).
2*b*(b - 1)**3*(b + 1)/7
Let b = 9 + -6. Factor i - i + 3*i**b - i**2 - 4*i**3.
-i**2*(i + 1)
Suppose 0 = -i + 4*i - 6. Suppose -6 = -o - 2*o. Let -o*d + 2 + 1/2*d**i = 0. Calculate d.
2
Let o(s) be the third derivative of -s**8/168 - s**7/105 + s**6/20 + s**5/6 + s**4/6 + 30*s**2. What is j in o(j) = 0?
-1, 0, 2
Let m be 1*(-6)/2 - -6. Suppose m*h = 5*h. Factor h + 0*s + 4/7*s**2 + 2/7*s**3.
2*s**2*(s + 2)/7
Let z(l) be the first derivative of -3*l**5/25 + 2*l**3/5 - 3*l/5 + 19. Let z(t) = 0. What is t?
-1, 1
Let c(m) be the third derivative of -1/10*m**5 + 1/20*m**6 - 1/105*m**7 + 0*m + 1/12*m**4 + 0*m**3 + 0 - 2*m**2. Find j, given that c(j) = 0.
0, 1
Factor 0*d + 0*d**3 + 3/7*d**4 - 3/7*d**2 + 0.
3*d**2*(d - 1)*(d + 1)/7
Let s(n) = -n**3 + 4*n**2 + 2*n - 6. Let d be s(4). Suppose 0 = -u - 4 + 1, -d*l = 3*u - 1. Factor -x + l - 5 + x**3.
x*(x - 1)*(x + 1)
Let t(c) = -2*c**2 - 20*c + 2. Let b be t(-10). Factor 0*m**b + 2/13*m**3 + 4/13 - 6/13*m.
2*(m - 1)**2*(m + 2)/13
Suppose -2*q = -47 + 19. Let n = q + -3. What is l in -n*l**2 + 4*l + 8*l**2 - 11*l**2 = 0?
0, 2/7
Let d(p) be the first derivative of -p**6/33 + 16*p**5/55 - 21*p**4/22 + 12*p**3/11 - 21. Find y such that d(y) = 0.
0, 2, 3
Let a = 2/279 + 271/1116. Suppose -1/4*l**4 + 1/4*l + 0 - a*l**3 + 1/4*l**2 = 0. What is l?
-1, 0, 1
Solve -2 - 4*c**5 + 2 - 4*c**4 + 8*c**4 = 0 for c.
0, 1
Let k(j) be the second derivative of 2*j + 5/3*j**3 + 0 + 7/40*j**5 - 3/4*j**4 - 2*j**2 - 1/60*j**6. Solve k(w) = 0.
1, 2
Let t(x) be the first derivative of -x**6/12 + 3*x**5/10 - 3*x**4/8 + x**3/6 - 5. Factor t(s).
-s**2*(s - 1)**3/2
Let y be 6/4 - (-69)/(-46). Let q be (1/(-3))/((-2)/4). What is d in y + q*d + 2/3*d**2 = 0?
-1, 0
Suppose 6*f = f + 10. Factor -f*k**4 - k + k - k + k**5 + 2*k**2.
k*(k - 1)**3*(k + 1)
Let x(d) be the second derivative of d**7/15120 + d**6/1440 + d**5/360 - d**4/12 - 3*d. Let i(z) be the third derivative of x(z). Find b, given that i(b) = 0.
-2, -1
Factor -11/3*g - 2/3 - 4/3*g**2 + 5/3*g**3.
(g - 2)*(g + 1)*(5*g + 1)/3
Suppose 0 = -5*f + 16 - 11. Let r = -14 - -16. Factor 2/3*k + f - 1/3*k**r.
-(k - 3)*(k + 1)/3
Let w(u) be the second derivative of u**4/72 - u**3/12 + u**2/6 + 6*u. Find o such that w(o) = 0.
1, 2
Let o be 22/11*(-3)/(-2). Factor 0*h**o + 0*h**4 - h**4 - 4*h + 3*h**3.
-h*(h - 2)**2*(h + 1)
Let q(b) = 14*b**2 - 20*b + 8. Let f = 8 - 0. Let o(i) = 5*i**2 - 7*i + 3. Let u(a) = f*o(a) - 3*q(a). Factor u(p).
-2*p*(p - 2)
Let o(f) be the second derivative of -f**6/360 + f**5/30 - f**4/6 + f**3/2 - 2*f. Let y(v) be the second derivative of o(v). Determine m, given that y(m) = 0.
2
Determine a so that -29*a**2 + a + 15*a**2 + 0*a + 13*a**2 = 0.
0, 1
Let z be 18/(-27)*(-6)/32. Factor 1/4 - z*l**2 - 1/8*l.
-(l - 1)*(l + 2)/8
Let q(z) = 2*z - 18. Let l be q(11). Let f(o) be the third derivative of 1/15*o**3 + 0*o + 2*o**2 + 0 + 1/150*o**5 + 1/30*o**l. Factor f(h).
2*(h + 1)**2/5
Let a(n) be the third derivative of n**9/60480 + n**8/10080 + n**7/5040 - n**5/20 - 3*n**2. Let b(u) be the third derivative of a(u). Factor b(z).
z*(z + 1)**2
Let s = -188/3 + 190/3. Solve -2/9*u**3 - s*u**2 - 2/3*u - 2/9 = 0.
-1
Factor 0*b + 4*b**3 + 0 - 8/7*b**2.
4*b**2*(7*b - 2)/7
Suppose p + 4*t = -13, 2*p = -2*t - 4 + 2. Find u such that 0*u**2 + 0 + 2/5*u**p + 0*u = 0.
0
Let z(c) be the first derivative of 1 + 0*c**3 + c**3 - 1 + 4 - 3*c**2. Factor z(q).
3*q*(q - 2)
Let n(r) = 6*r + 4. Let f be (1 - 3)*16/(-8). Let u(s) = s**2 + 6*s + 4. Let y(m) = f*u(m) - 5*n(m). Factor y(i).
2*(i - 2)*(2*i + 1)
Find q such that 0*q**2 - 4/7*q**3 + 4/7*q + 0 = 0.
-1, 0, 1
Let n(y) be the first derivative of -2*y**4 + y**5 + 0*y + 0*y**2 + 5 - 1/6*y**6 + 4/3*y**3. Solve n(k) = 0 for k.
0, 1, 2
Let b be (-15)/6*(-633)/(-2190). Let x = 2/73 - b. Determine u, given that x*u + 1/2*u**2 + 1/4 = 0.
-1, -1/2
Let t(u) = 4*u**2 + 3*u - 4. Let y(a) = 5*a**2 + 4*a - 5. Let n(r) = 4*t(r) - 3*y(r). Find q, given that n(q) = 0.
-1, 1
Factor 0 + 2/9*g**2 + 4/9*g.
2*g*(g + 2)/9
Determine t, given that 2 + 1/4*t**3 + 3*t + 3/2*t**2 = 0.
-2
Let z(r) be the third derivative of 0*r**4 - 1/6*r**3 + 0*r**5 + 0 + 0*r + 1/180*r**6 - r**2. Let i(a) be the first derivative of z(a). Factor i(w).
2*w**2
Suppose -3*t + 7 = 3*y + 19, -3*t = -6. Let a = y - -10. Factor o**5 + 0 + 15/4*o**3 + 1/4*o - 13/4*o**a - 7/4*o**2.
o*(o - 1)**3*(4*o - 1)/4
Let x(a) = -4*a**2 - 4 + 0 + 0*a**3 + a**3 - 5*a**2 + 9*a. Let h be x(8). Factor 0 + 2