**3 + k**2 + k. Let p = -16 + 15. Let l(i) = p*h(i) - 6*r(i). Factor l(u).
u**2*(u + 2)
Let o = -31/9 - -91/9. Let n(i) be the second derivative of 343/15*i**6 + 0 - 4*i - o*i**3 - 21*i**4 + 49/2*i**5 + 8*i**2. Let n(l) = 0. What is l?
-1, -2/7, 2/7
Let p(u) = u**3 + u**2 + 1. Let g(f) = 18*f**3 - 7*f + 17*f + 12 + 22*f**2 + 4*f**2. Let h(m) = g(m) - 10*p(m). Factor h(y).
2*(y + 1)*(2*y + 1)**2
Determine v, given that -3/4*v**2 + 15/4*v + 0 = 0.
0, 5
Suppose 2*u + 25 = -5*o, -2*o - 10 = 4*u - u. Factor 1/3*y**2 + 0*y + 1/3*y**3 + u.
y**2*(y + 1)/3
Let j(i) = 4*i**2 + 2*i. Let u(s) be the first derivative of 5/3*s**3 + 3/2*s**2 + 2 + 0*s. Let t(z) = 3*j(z) - 2*u(z). Let t(m) = 0. What is m?
0
Let c(n) = -n**3 + n - 1. Let w(o) = 2*o**4 + o**3 - 4*o**2 + 3*o + 4. Let v(t) = -3*c(t) + w(t). Let s(y) be the first derivative of v(y). Factor s(j).
4*j*(j + 2)*(2*j - 1)
Let t = -3 - -3. Suppose 3*f = -t*f. Factor 4*y + f*y**2 - 3*y**2 + y**2 - 2.
-2*(y - 1)**2
Let a = 71 - 68. Suppose 6/5*m - 4/5 + 2/5*m**2 + 2/5*m**4 - 6/5*m**a = 0. Calculate m.
-1, 1, 2
Let l(c) be the second derivative of 5*c**4/6 - 5*c**3/6 + 12*c. Factor l(z).
5*z*(2*z - 1)
Let y be 2/360*2/1. Let i(u) be the second derivative of 0 + 1/36*u**4 - u + 1/18*u**3 + 0*u**2 - 1/60*u**5 - y*u**6. Factor i(q).
-q*(q - 1)*(q + 1)**2/3
Let b = 61 - 57. Let v(g) be the second derivative of 0 + 0*g**2 + 2*g + 1/3*g**3 + 1/20*g**5 + 1/4*g**b. Let v(y) = 0. What is y?
-2, -1, 0
Let p(u) be the first derivative of 3/4*u**4 - 2 + 1/2*u**2 - u + 5/3*u**3. Factor p(s).
(s + 1)**2*(3*s - 1)
Let c(i) be the second derivative of 0 + 0*i**2 - 1/20*i**5 - 1/6*i**3 - 3*i + 1/6*i**4. Factor c(a).
-a*(a - 1)**2
Let z be (-30)/(-80)*(-2)/(-1). Suppose 3/2*p - z - 3/4*p**2 = 0. What is p?
1
Factor -1/5*c**2 + 0 + 0*c**3 + 0*c + 1/5*c**4.
c**2*(c - 1)*(c + 1)/5
Let a be ((-8)/(-6))/((-11)/(-3) + -3). Solve -8/7 - 4/7*v**3 + 4/7*v + 8/7*v**a = 0 for v.
-1, 1, 2
Let b = 274874/135 + -2036. Let h = b - -8/27. Factor 0 + 2/5*w**2 + 2/5*w**3 - 2/5*w - h*w**4.
-2*w*(w - 1)**2*(w + 1)/5
Let g(s) be the first derivative of s**8/560 + s**7/280 - s**6/120 - s**5/40 + 2*s**3/3 - 4. Let m(q) be the third derivative of g(q). Factor m(d).
3*d*(d - 1)*(d + 1)**2
Let 0*r**2 + 6/5*r**5 - 4/5 - 2*r + 4*r**4 + 4*r**3 = 0. What is r?
-1, 2/3
Suppose -9*u + 40 = -u. Let c(z) be the third derivative of 1/84*z**4 + 0 - 1/210*z**6 + 0*z**3 + 1/210*z**u - 2*z**2 + 0*z. Factor c(k).
-2*k*(k - 1)*(2*k + 1)/7
Let z(j) be the first derivative of j**5/10 + 3*j**4/8 + 5. Suppose z(i) = 0. What is i?
-3, 0
Let b(a) = 3*a**2 - 6*a. Let q(d) be the third derivative of -d**4/24 - 2*d**2. Let f(w) = b(w) - 9*q(w). Factor f(o).
3*o*(o + 1)
Factor 0 + 3/2*l**4 + 0*l**2 + 0*l + 15*l**3.
3*l**3*(l + 10)/2
Let k(l) be the second derivative of l**5/4 + 5*l**4/6 - 20*l**3/3 + 14*l. Factor k(c).
5*c*(c - 2)*(c + 4)
Let p(v) = -8*v**2 - 8*v - 5. Let i(k) = -12*k**2 - 12*k - 8. Let f(h) = -5*i(h) + 8*p(h). Determine j so that f(j) = 0.
-1, 0
Let b(c) = 3*c**3 - 4*c**2. Let j(m) = 6*m**3 - 7*m**2. Let z(a) = -5*b(a) + 2*j(a). Factor z(i).
-3*i**2*(i - 2)
Let h(j) be the third derivative of -j**9/2268 + j**8/840 - j**7/1260 - j**3/3 + 6*j**2. Let p(n) be the first derivative of h(n). Factor p(f).
-2*f**3*(f - 1)*(2*f - 1)/3
Let w(g) = g**4 + 2*g**3 + 2*g**2 - 4*g - 1. Let t(q) = q**4 + q**2 - q - 1. Let b(a) = -4*t(a) + 2*w(a). Factor b(h).
-2*(h - 1)**3*(h + 1)
Let c be (-2 - -2*1) + 14. Let g = -8 + c. Factor g*w + 2 + 2 + 2*w**2 + 0.
2*(w + 1)*(w + 2)
Let w(j) = j**2 - 4*j + 5. Let s be w(4). Let p(u) = -7*u**3 - 7*u**2 - 5*u - 5. Let x(f) = 6*f**3 + 6*f**2 + 4*f + 4. Let b(i) = s*p(i) + 6*x(i). Factor b(v).
(v - 1)*(v + 1)**2
Suppose -4*l = -2*y + 26, 0*y + 37 = 4*y - 3*l. Let q be (-3 - y)*4/(-10). Suppose -2/7*b**q - 26/7*b**2 - 24/7*b - 12/7*b**3 - 8/7 = 0. What is b?
-2, -1
Let u = 31 + -45. Let b be -1 + ((-58)/u - 2). Factor 10/7*k**2 - 4/7*k + 0 + 2/7*k**4 - b*k**3.
2*k*(k - 2)*(k - 1)**2/7
Let j(s) = 4*s**2 + 4. Let p(w) = 4*w**2 + 3. Let z(t) = 3*j(t) - 4*p(t). Find o, given that z(o) = 0.
0
Let z(v) = -v**2 + v + 2. Let y(w) be the second derivative of w**4/12 - w**2/2 - w. Let s(g) = -6*y(g) - 4*z(g). Determine l, given that s(l) = 0.
-1
Suppose -5*s - w = -24, 3*s - 2*w = 3*w + 20. Let 2/9*j**s - 2/9*j**3 + 0 + 0*j + 2/9*j**2 - 2/9*j**4 = 0. Calculate j.
-1, 0, 1
Let o be 14*20/70 - 16/6. Suppose 5*j - 9 = 2*j. Find h, given that 0 + 1/3*h**2 + h**4 + 0*h - o*h**j = 0.
0, 1/3, 1
Factor 1/3*a**4 + 48 - 88*a + 22/3*a**3 + 97/3*a**2.
(a - 1)**2*(a + 12)**2/3
Let z(v) be the second derivative of v**6/270 - v**5/180 - v**4/108 + v**3/54 - 7*v + 2. Suppose z(o) = 0. What is o?
-1, 0, 1
Let t(w) = w**2 + 3*w. Suppose 0 = -v - 3 - 0. Let n be t(v). Factor -2/3*k**5 + 2/3*k**4 + n*k + 2/3*k**3 + 0 - 2/3*k**2.
-2*k**2*(k - 1)**2*(k + 1)/3
Let c(p) be the first derivative of 3*p**5/10 + 3*p**4 + 12*p**3 + 24*p**2 + 24*p - 6. Factor c(b).
3*(b + 2)**4/2
Factor -26 - 8 + 31*b**2 - 135 - 26*b - 32*b**2.
-(b + 13)**2
Let r(h) = -h**2 - 5*h. Let l be r(-5). Suppose l = -2*z + z. Factor 0*n**2 - 1/2*n**4 + z - 1/4*n**5 + 0*n - 1/4*n**3.
-n**3*(n + 1)**2/4
Let p be 43/55 + (3 - (-54)/(-15)). Factor -2/11*o**3 + 0*o - p*o**2 + 0.
-2*o**2*(o + 1)/11
Let c(r) be the second derivative of -r**4/126 + r**3/21 + 9*r. Solve c(i) = 0 for i.
0, 3
Let z(d) = -2*d - 5. Suppose 5 - 15 = 2*u. Let w be z(u). Solve -14*h**3 + 16*h + 0*h**5 + 3*h**5 - 10*h**4 + 0*h - 5*h**w + 2*h**2 + 8 = 0 for h.
-2, -1, 1
Let s = 11 - 9. Suppose -s*b = 2*b. Let 1/2*u + 1/2*u**3 + b - u**2 = 0. What is u?
0, 1
Suppose 4*v**4 + 4*v**5 + 8*v - 24*v**2 + 20*v**2 - 15*v**3 + 3*v**3 = 0. What is v?
-2, -1, 0, 1
Let s = -431/8 - -54. Let k(y) be the first derivative of 2/3*y**6 + 2*y**5 + 1 + 5/6*y**3 + 0*y + 33/16*y**4 + s*y**2. Factor k(z).
z*(z + 1)**2*(4*z + 1)**2/4
Let r(g) be the second derivative of -11*g**5/20 + 11*g**4/6 - 17*g**3/3 + 4*g**2 - g. Let j(d) = d**3 + d. Let t(c) = 6*j(c) + r(c). Factor t(f).
-(f - 2)**2*(5*f - 2)
Let f(j) be the second derivative of -j**4/12 + j**3/2 - 9*j. Factor f(m).
-m*(m - 3)
Let u be 3 + 42/(-9) + 93/45. Solve -2/5*r**2 + u*r + 0 = 0.
0, 1
Let v(k) be the first derivative of k**3 - 15*k**2/2 + 12*k + 35. Find u, given that v(u) = 0.
1, 4
Let z be (0 + 0)*18/(-72). Let r(x) be the first derivative of 2/15*x**5 + 0*x**2 - 2/9*x**3 + z*x + 1/4*x**4 + 2. Solve r(t) = 0 for t.
-2, 0, 1/2
Let k(m) be the first derivative of -2*m - 2/5*m**5 + 1/3*m**6 - m**4 + 4/3*m**3 + m**2 - 1. Find z such that k(z) = 0.
-1, 1
Let q = -13 - -10. Let c = 2 - q. Factor 0*x**2 - 2 + c*x**2 + 4*x - 7*x**2.
-2*(x - 1)**2
Let b(g) be the first derivative of 3*g**5/25 - 3*g**4/10 + 3*g**2/5 - 3*g/5 + 6. Factor b(a).
3*(a - 1)**3*(a + 1)/5
Let o(u) = u - 8. Let j be o(11). Factor -2 + l + 5 - 2*l - j*l**4 + 6*l**3 - 5*l.
-3*(l - 1)**3*(l + 1)
Let x(g) be the second derivative of 9/20*g**5 + 3*g**2 + 3/2*g**3 + 3*g + 0 - 2*g**4. Factor x(d).
3*(d - 2)*(d - 1)*(3*d + 1)
Suppose 6 = z + 2*z. Let y be -8*45/(-216) - 10/(-6). Factor -5/3*t - 2/3 + 0*t**z + y*t**3 + 10/3*t**4 + t**5.
(t + 1)**4*(3*t - 2)/3
Let n(d) = -8*d**4 - 4 + d + d**2 - d**3 + d**2 + 5*d**4. Let m(x) = x**4 + x**3 - x**2 - x + 2. Let b(i) = -5*m(i) - 2*n(i). Let b(f) = 0. What is f?
-1, 1, 2
Factor 4 - b**4 - 4*b**3 + 2 - 3*b**2 + 0 - 2 + 4*b.
-(b - 1)*(b + 1)*(b + 2)**2
Let r = -362/7 - -52. Let -r*d**4 - 2/7 + 0*d**3 + 0*d + 4/7*d**2 = 0. What is d?
-1, 1
Let a be -1 + (9 - 1) - 2. Let w(d) be the third derivative of 0*d**6 + 1/6*d**3 + 0 + 0*d + 1/210*d**7 + 0*d**4 - 1/30*d**a + d**2. Solve w(f) = 0 for f.
-1, 1
Let v(x) = 4*x**2 - 3*x. Let s be v(2). Suppose f = -f + 2*p + 4, -5*f + s = 5*p. Factor 2*w**4 + 3*w**3 - f + 2*w**3 - 4*w - w**3.
2*(w - 1)*(w + 1)**3
Let c(d) be the second derivative of -3/10*d**5 + 1/10*d**6 + 0 - 1/4*d**4 + 0*d**2 - 3*d + d**3. Factor c(o).
3*o*(o - 2)*(o - 1)*(o + 1)
Let b(h) be the third derivative of -3*h**5/20 - h**4/6 - h**3/2 - 4*h**2. Let z(c) = -19*c**2 - 8*c - 7. Let x(q) = -7*b(q) + 3*z(q). Factor x(a).
2*a*(3*a + 2)
Let s(k) be the second derivative of k**9/4536 + k**8/1260 + k**7/1260 - k**3/6 + k. Let m(a) be the second derivative of s(a). Factor m(l).
2*l**3*(