**7 + 0. Factor h(g).
-g*(g - 1)**3*(5*g - 2)
Let d(h) be the first derivative of -h**4/2 + 2*h**3 - 2*h**2 + 10. Determine x, given that d(x) = 0.
0, 1, 2
Let v(k) be the first derivative of -2/13*k + 6 + 1/26*k**4 + 3/13*k**2 - 2/13*k**3. Let v(m) = 0. Calculate m.
1
Suppose 0 = -0*b - 7*b. Factor -1/4 + b*x + 1/4*x**2.
(x - 1)*(x + 1)/4
Let p(d) be the second derivative of 1/2*d**2 - 2*d + 0 - 1/12*d**4 + 1/6*d**3. Let r(s) = 6*s**2 + 4*s + 4. Let n(i) = -4*p(i) - r(i). Factor n(v).
-2*(v + 2)**2
Let j be (-1)/((-2)/(4/9)). Suppose 0 = -5*c + 3*m - 12, 4*m - 7 = -5*c + 9. Solve 0*k - 2/9*k**2 + 2/9*k**4 - j*k**5 + 2/9*k**3 + c = 0.
-1, 0, 1
Let v = -11 + 13. Factor -5*t - 8*t**v + 2*t**2 + 3*t.
-2*t*(3*t + 1)
Let -2 - 150*d + 159*d + 0 - 7*d**2 = 0. Calculate d.
2/7, 1
Let f(p) = p**2 - 2*p - 4. Let c be f(4). Suppose 3*a - a - c = 0. What is h in -1/4 + 1/2*h - 1/4*h**a = 0?
1
Let w(x) = 2*x + 4. Let z be w(-2). Suppose -b + 3*b - 4 = z. Factor 1/2 - 1/2*a**4 + 1/4*a**5 + 2*a**b - 1/2*a**3 - 7/4*a.
(a - 1)**4*(a + 2)/4
Let i = 0 - 0. Let n = 5 + i. Factor k**3 + 10*k**4 + 6*k**n + k**3 + 2*k**3.
2*k**3*(k + 1)*(3*k + 2)
Let y(o) be the second derivative of -o**6/120 + 3*o**5/20 - 9*o**4/8 + 9*o**3/2 - 3*o**2 + 5*o. Let t(p) be the first derivative of y(p). Factor t(r).
-(r - 3)**3
Let o(v) = 2*v**4 + 23*v**3 + 25*v**2 - 8*v - 3. Let t(f) = -f**4 - 11*f**3 - 12*f**2 + 4*f + 2. Let g(z) = 6*o(z) + 13*t(z). Factor g(h).
-(h - 1)*(h + 2)**3
Suppose 4*l = -0*l + 4. Let u(y) = -y**2 + y. Let x be u(l). Find h such that x*h - 4*h**2 + 6*h**3 + 0*h = 0.
0, 2/3
Let d(n) be the first derivative of 3*n**5/5 - 3*n**4/2 + 3*n**2 - 3*n - 4. Suppose d(l) = 0. Calculate l.
-1, 1
Let p(r) be the third derivative of -r**6/40 + 3*r**5/20 - 3*r**4/8 + r**3/2 - 7*r**2. Factor p(a).
-3*(a - 1)**3
Let h(u) = -u**2 + 6*u - 5. Let l(y) be the first derivative of -2*y**3/3 + 13*y**2/2 - 11*y + 2. Let x(z) = -9*h(z) + 4*l(z). Let x(b) = 0. Calculate b.
1
Let i = -51 - -154/3. Let -z - i*z**2 - 2/3 = 0. What is z?
-2, -1
Solve 3/2 - 3/4*t**2 - 3/4*t = 0 for t.
-2, 1
Let g(a) be the third derivative of 1/10*a**5 + 0 - 1/2*a**3 + 0*a**4 + 0*a - 1/70*a**7 + 0*a**6 - 3*a**2. Find j, given that g(j) = 0.
-1, 1
Let y be -2 + (-9 + 3)*2. Let l be -7 + 5 - y/5. Let 2/5*a**2 + l*a - 4/5*a**3 - 2/5 = 0. Calculate a.
-1, 1/2, 1
Let j(w) be the second derivative of 0 - 2/3*w**3 + w + 2/3*w**4 + 2/5*w**5 - 2/15*w**6 - 2/21*w**7 - 2*w**2. Factor j(u).
-4*(u - 1)**2*(u + 1)**3
Suppose 0 = -36*s + 13*s. Let p(f) be the third derivative of 1/45*f**5 + s*f + f**2 - 1/24*f**4 - 1/18*f**3 + 0. Determine b so that p(b) = 0.
-1/4, 1
Let r = -1/96 + 389/480. Factor -r*i + 0 + 2/5*i**2.
2*i*(i - 2)/5
Factor 0*t**2 + 0 + 0*t**3 + t**4 - 1/3*t**5 + 0*t.
-t**4*(t - 3)/3
Suppose -g + 5*t - 25 = -4*g, -4*t + 20 = g. Factor -4/9*s**3 + 2/3*s**4 + 0 - 2/9*s**2 + g*s.
2*s**2*(s - 1)*(3*s + 1)/9
Let m be (20/(-30))/((-2)/6). Suppose 5*n**2 - 4 - 2*n**3 + 0*n + m*n - 3*n**2 + 2*n**2 = 0. What is n?
-1, 1, 2
Let u(b) = b**3 - 7*b**2 - 9*b + 8. Let a be u(8). Suppose 4*h + h - 10 = a. Determine y, given that 9*y**h - 81/4*y**3 - y + 0 = 0.
0, 2/9
Suppose 9*k - 4*k = -70. Let m = 14 + k. Suppose m*o + 0 + 1/3*o**2 - 1/3*o**4 + 1/3*o**5 - 1/3*o**3 = 0. What is o?
-1, 0, 1
Factor 8/5*k + 2/5*k**3 - 8/5*k**2 + 0.
2*k*(k - 2)**2/5
Let m(u) = -105*u**5 - 235*u**4 + 260*u**2 + 40*u + 40. Let c(w) = 8*w**5 + 18*w**4 - 20*w**2 - 3*w - 3. Let j(f) = -40*c(f) - 3*m(f). Factor j(y).
-5*y**2*(y - 1)*(y + 2)**2
Let p(j) = -10*j**4 + 10*j**3 - 20*j**2 + 2*j. Let s(h) = 9*h**4 - 11*h**3 + 20*h**2 - 3*h. Let c(q) = 5*p(q) + 6*s(q). Let c(l) = 0. What is l?
0, 1, 2
Let l(o) = -23*o**2 - 52*o. Let s(y) = 8*y**2 + 17*y. Let h(n) = 3*l(n) + 8*s(n). What is f in h(f) = 0?
-4, 0
Let i(y) be the third derivative of y**8/1680 + y**7/525 + y**6/600 - 4*y**2. Factor i(h).
h**3*(h + 1)**2/5
Let f(d) be the third derivative of -d**8/2800 + d**6/600 + d**3/6 - d**2. Let k(a) be the first derivative of f(a). Solve k(l) = 0.
-1, 0, 1
Let o = 191/3 - 59. Let w = o - 13/3. Factor 1/6*h**5 + 0 + 0*h**2 + 1/6*h**3 + 0*h - w*h**4.
h**3*(h - 1)**2/6
Suppose 2*f - 3*f = 0. Factor r**4 + f*r**4 + 2*r**4 - 3*r**5.
-3*r**4*(r - 1)
Let q = -1207/15 - -374/5. Let l = -79/15 - q. Find j, given that 0*j + l*j**3 - 2/5*j**5 + 2/5*j**2 - 2/5*j**4 + 0 = 0.
-1, 0, 1
Let i(l) be the third derivative of -1/8*l**4 + 0 - 3/40*l**6 + 0*l - 5*l**2 - 1/70*l**7 - 3/20*l**5 + 0*l**3. Determine y so that i(y) = 0.
-1, 0
Let m = 7 + -1. Let k be (-2 - m/(-4))*0. Factor -1 + 2*h + h + k*h + 4*h**2.
(h + 1)*(4*h - 1)
Let q be -2 - 3 - (-85)/15. Let q*r**2 - 4/3*r + 2/3 = 0. What is r?
1
Let p(r) be the second derivative of -8/3*r**2 + 5*r - 1/9*r**4 + 8/9*r**3 + 0. Factor p(a).
-4*(a - 2)**2/3
Suppose 0 = 4*j - 6*j - j. Let c(n) be the third derivative of 1/24*n**4 - n**2 + 1/120*n**6 + j*n**3 - 1/30*n**5 + 0*n + 0. Solve c(y) = 0 for y.
0, 1
Let s(y) = 9*y**2 - 6*y. Let k(m) = m**3 + 9*m**2 - 5*m - 1. Let f be (-2 + 0)*(3 + -1). Let a(i) = f*s(i) + 3*k(i). Suppose a(t) = 0. Calculate t.
1
Let f(r) be the third derivative of r**7/210 + r**6/120 - r**5/60 - r**4/24 + 34*r**2. What is b in f(b) = 0?
-1, 0, 1
Suppose -3 = 5*u + 2. Let n(g) = g**2 - g. Let k(m) = 0*m**2 + 356*m - 350*m - 3*m**2. Let v(i) = u*k(i) - 4*n(i). Suppose v(h) = 0. Calculate h.
-2, 0
Let v be (-2 - 1 - 3)/(6 + -16). Factor 1/5 - 1/5*f**3 - 3/5*f + v*f**2.
-(f - 1)**3/5
Suppose 3 = x + k, 4 = 5*x - 2*k + 17. Let t be (13/(-156))/(x/4). Suppose -t + 1/3*q + 1/3*q**2 - 1/3*q**3 = 0. What is q?
-1, 1
Let x = -8 - -11. Let r(m) be the first derivative of -1/5*m - 16/15*m**x - 1 + 4/5*m**2. Let r(s) = 0. What is s?
1/4
Factor 2/3*u**4 + 0 - 2*u - 2/3*u**3 - 10/3*u**2.
2*u*(u - 3)*(u + 1)**2/3
Let d(j) be the third derivative of -j**6/2 + 35*j**5/12 - 5*j**4 + 10*j**3/3 + 5*j**2. Factor d(u).
-5*(u - 2)*(3*u - 2)*(4*u - 1)
Let u(b) be the second derivative of -b**4/12 + b**3/6 + 7*b. Let u(h) = 0. What is h?
0, 1
Let t(y) be the third derivative of -y**9/181440 - y**8/30240 - y**7/15120 - y**5/30 - 7*y**2. Let p(r) be the third derivative of t(r). Factor p(o).
-o*(o + 1)**2/3
Let n(y) be the second derivative of y**6/900 - y**5/300 + y**3/3 - 2*y. Let h(k) be the second derivative of n(k). Factor h(p).
2*p*(p - 1)/5
Let f = -47 - -49. Let n(m) be the third derivative of 1/1680*m**8 + 0*m**4 + 0*m - 1/600*m**6 + 0 + 0*m**3 + f*m**2 + 1/150*m**5 - 1/525*m**7. Factor n(c).
c**2*(c - 2)*(c - 1)*(c + 1)/5
Let k = -27 - -406/15. Let r(m) be the second derivative of 0 + 1/60*m**4 + 3*m + k*m**3 + 1/10*m**2. Factor r(p).
(p + 1)**2/5
Suppose 0 = 8*j - 3*j - 25. Suppose -b + 45 = 4*b. Factor 3*y**3 + 6*y + b*y**2 + j - 5.
3*y*(y + 1)*(y + 2)
Let v(w) = -6*w**2 - 7*w - 6. Let k be 8/(-32) + (-19)/4. Let q(n) = -3*n**2 - 4*n - 3. Let b(o) = k*q(o) + 2*v(o). Factor b(z).
3*(z + 1)**2
Suppose 3*k = 2*s - 10, k - 13 - 2 = -3*s. Suppose 13 = s*w - 7. Factor 3*v**3 - 3*v**2 + 6*v**2 + 0*v + v**w + v.
v*(v + 1)**3
Let i(c) be the second derivative of -c**5/20 - c**4/4 - c**3/2 - c**2/2 + 23*c. Let i(p) = 0. Calculate p.
-1
Let m(v) be the third derivative of v**5/15 + v**4/3 - 9*v**2. Let m(q) = 0. What is q?
-2, 0
Suppose j = 4*j - 12. Let -6*p + 5 + 2*p**2 + 3 - j = 0. Calculate p.
1, 2
Let p(r) be the first derivative of -10*r**6/3 - 112*r**5/45 - 4*r**4/9 + 21. Factor p(k).
-4*k**3*(5*k + 2)*(9*k + 2)/9
Factor 0*m + 0 + 0*m**2 - 1/6*m**5 - 1/3*m**4 - 1/6*m**3.
-m**3*(m + 1)**2/6
Let q(i) = -6*i**3 + 2*i**2 - 11*i - 5. Let u(v) = 7*v**3 - v**2 + 12*v + 6. Let x(m) = -6*q(m) - 5*u(m). Factor x(s).
s*(s - 6)*(s - 1)
Let m(v) = 81*v**4 - 129*v**3 + 72*v**2 - 6*v - 6. Let k(g) = 80*g**4 - 130*g**3 + 72*g**2 - 7*g - 5. Let o(j) = -6*k(j) + 5*m(j). What is f in o(f) = 0?
0, 2/5, 1
Solve -3/2*h**4 + 0*h + 0 - 4*h**3 - 2*h**2 = 0 for h.
-2, -2/3, 0
Factor 1/3*y**2 + 0 - 1/3*y**3 + 0*y.
-y**2*(y - 1)/3
Let c(a) be the second derivative of 0*a**3 + 1/15*a**6 - 1/6*a**4 - 2/5*a**5 + a + 4/21*a**7 + 0*a**2 + 0. Let c(f) = 0. What is f?
-1, -1/4, 0, 1
Let w = 227 - 222. Factor -1/3*d**3 + 1/6*d**w + 1/3*d**2 - 1/6 - 1/6*d**4 + 1/6*d.
(d - 1)**3*(d + 1)**2/6
Suppose 14*o**3 - 4*o**4 - 9*o**3 - o**3 - 8*o**3 = 0. Calculate