h be x(7). Suppose j**3 + 2*j**3 + 2*j**2 + 2*j - 5*j**3 - 2*j**h = 0. What is j?
-1, 0, 1
Let f(s) = -20*s**5 + 24*s**4 - 12*s**3 - 4*s. Let u(c) = -c**5 - c**4 - c**3 + c**2 - c. Let h(r) = f(r) - 4*u(r). Factor h(g).
-4*g**2*(g - 1)**2*(4*g + 1)
Let u(x) be the first derivative of 1/15*x**5 + 1/8*x**4 - 1/18*x**3 - 1/6*x - 1/4*x**2 - 2. Factor u(t).
(t - 1)*(t + 1)**2*(2*t + 1)/6
Let i = -11 - -14. Factor i*h**2 + 0*h**2 + h**4 + 4*h**3 + h**2.
h**2*(h + 2)**2
Let j(k) be the second derivative of k**9/37800 - k**8/16800 - 2*k**4/3 + 7*k. Let v(r) be the third derivative of j(r). Factor v(q).
2*q**3*(q - 1)/5
Let y = -45 - -30. Let m be ((-1)/y)/(4/24). Suppose -m*q + 2/5*q**2 + 2/5*q**3 + 0 - 2/5*q**4 = 0. What is q?
-1, 0, 1
Let i(p) be the third derivative of -p**8/1512 + 2*p**6/135 - 4*p**4/27 - 2*p**2 + 4. Determine s, given that i(s) = 0.
-2, 0, 2
Let c(y) = 6*y**4 + 86*y**3 + 46*y**2 - 180*y + 14. Let s(r) = r**4 + 17*r**3 + 9*r**2 - 36*r + 3. Let n(k) = 3*c(k) - 14*s(k). Factor n(w).
4*w*(w - 1)*(w + 3)**2
Factor -6/5*x**4 + 0*x**2 + 0 + 0*x**3 - 3/5*x**5 + 0*x.
-3*x**4*(x + 2)/5
Factor 0*l**2 + 0*l + 1/2*l**3 + 0 + 1/2*l**4.
l**3*(l + 1)/2
Let r = 504/1385 - -10/277. Let s be (2/3)/(5/3). Determine m, given that 4/5*m**2 + 0 + s*m**3 + r*m = 0.
-1, 0
Suppose -2*p + 3*w + 87 = p, 0 = 4*w + 8. Let c be (-1 + p/15)/2. Factor 2/5*b**3 + c - 2/5*b - 2/5*b**2.
2*(b - 1)**2*(b + 1)/5
Let y(c) = -8*c**3 + 4*c**2 + 12*c. Let t be -1*(3 - 1 - 6). Let a(z) = -9*z**3 + 4*z**2 + 13*z. Let k(l) = t*a(l) - 5*y(l). Factor k(r).
4*r*(r - 2)*(r + 1)
Let o be (0 + -1)*(-1)/7. Let g(v) be the second derivative of 1/14*v**4 - v + o*v**2 - 1/70*v**5 + 0 - 1/7*v**3. Factor g(y).
-2*(y - 1)**3/7
Let t(j) be the first derivative of -7*j**7/3 - 42*j**6/5 - 109*j**5/10 - 6*j**4 - 4*j**3/3 - j - 1. Let b(c) be the first derivative of t(c). Factor b(d).
-2*d*(d + 1)**2*(7*d + 2)**2
Let p(m) be the third derivative of 2*m**7/105 - m**6/10 - m**5/15 + m**4/2 - 2*m**2. Solve p(t) = 0 for t.
-1, 0, 1, 3
Let k(c) be the second derivative of -c**7/2520 - c**6/540 - c**5/360 + c**3/6 - c. Let x(j) be the second derivative of k(j). Factor x(y).
-y*(y + 1)**2/3
Factor -6/5*f**4 - 4/5*f - 12/5*f**2 + 0 - 1/5*f**5 - 13/5*f**3.
-f*(f + 1)**2*(f + 2)**2/5
Let l(p) be the second derivative of p**4/21 - 20*p**3/21 - 3*p + 1. Factor l(n).
4*n*(n - 10)/7
Let v(f) be the first derivative of -f**3/24 - f**2/8 - f/8 - 12. Factor v(o).
-(o + 1)**2/8
Let a(y) be the second derivative of y**9/75600 + y**8/8400 + y**7/2520 + y**6/1800 + 3*y**4/4 - 2*y. Let p(r) be the third derivative of a(r). Factor p(n).
n*(n + 1)**2*(n + 2)/5
Let i be (-2)/(-13) - 96/(-390). Let 2/5*o**2 + 2/5*o - 2/5 - i*o**3 = 0. What is o?
-1, 1
Suppose -26 = -5*r + 7*r. Let h = r - -17. Factor -2/7*u**h + 0*u**2 + 0 + 0*u**3 + 2/7*u**5 + 0*u.
2*u**4*(u - 1)/7
Let y(z) be the first derivative of z**8/1344 - z**6/240 + z**4/96 - z**2 - 2. Let w(i) be the second derivative of y(i). Factor w(b).
b*(b - 1)**2*(b + 1)**2/4
Let -34*f + 4*f**2 + 62*f + 4*f**3 - 4 - 32*f = 0. Calculate f.
-1, 1
Let s(i) be the second derivative of i**5/40 - 3*i**4/4 + 9*i**3 - 54*i**2 + 9*i. Factor s(a).
(a - 6)**3/2
Let n(r) be the first derivative of 4*r**5/35 + 2*r**4/7 + r**3/7 + 2. Solve n(l) = 0 for l.
-3/2, -1/2, 0
Let -10/7*m**2 + 20/7 + 46/7*m = 0. What is m?
-2/5, 5
Let b(d) = 8*d**3 + 49*d**2 - 7*d - 161. Let y(f) = f**3 + 6*f**2 - f - 20. Let v(j) = -6*b(j) + 51*y(j). Factor v(h).
3*(h - 2)*(h + 3)**2
Let i(b) be the first derivative of 0*b**3 - 3 + 0*b - 3/20*b**5 + 1/8*b**4 + 1/24*b**6 + 0*b**2. Factor i(k).
k**3*(k - 2)*(k - 1)/4
Let q = 2 - 9. Let z(j) = 23*j**4 - 38*j**3 + 9*j**2 + 8*j - 2. Let f(s) = -70*s**4 + 115*s**3 - 27*s**2 - 25*s + 7. Let k(w) = q*z(w) - 2*f(w). Factor k(p).
-3*p*(p - 1)**2*(7*p + 2)
Solve -2/3*w - 4/3*w**5 + 0 + 2/3*w**2 - 2/3*w**4 + 2*w**3 = 0 for w.
-1, 0, 1/2, 1
Let i(v) be the second derivative of 3/20*v**5 + 0 - 3/4*v**4 - 3/2*v**2 + 3/2*v**3 + 2*v. Factor i(x).
3*(x - 1)**3
Suppose 0*a - 3/8*a**2 + 3/8*a**4 - 9/8*a**3 + 0 + 9/8*a**5 = 0. What is a?
-1, -1/3, 0, 1
Let i(c) be the second derivative of -c**5/20 - c**4/8 - 2*c**2 + 4*c. Let m(w) be the first derivative of i(w). Suppose m(f) = 0. Calculate f.
-1, 0
Let g(t) = 2*t**4 + 5*t**3 - 11*t**2 - 9*t + 5. Let r(j) = -j**4 - 3*j**3 + 6*j**2 + 5*j - 3. Let v(d) = 3*g(d) + 5*r(d). Factor v(u).
u*(u - 2)*(u + 1)**2
Let k(u) be the first derivative of 3*u**4/4 + 3*u**3 + 3*u**2 - 3. Factor k(n).
3*n*(n + 1)*(n + 2)
Let k(d) = -d**2 + 10*d + 2. Let f be k(10). Let m be 2/(-11)*(-231)/84. Factor -m*u**3 + 0 + 1/2*u**4 - 1/2*u**f + 1/2*u.
u*(u - 1)**2*(u + 1)/2
Let u(m) be the third derivative of -m**7/105 - m**6/14 - 4*m**5/105 - 5*m**2. Factor u(z).
-2*z**2*(z + 4)*(7*z + 2)/7
Let j be (0 - (-5 + 0)) + -1. Suppose -4*g - 3*o + 0 + 1 = 0, 15 = 5*g + o. Let 0*w**5 + w**5 - 2*w**j + 3*w**g = 0. What is w?
-1, 0
Let w(p) be the second derivative of 1/20*p**5 + 1/8*p**4 + 1/120*p**6 + p**2 + 1/6*p**3 + 0 + p. Let i(d) be the first derivative of w(d). Factor i(u).
(u + 1)**3
Let a(d) be the third derivative of 0*d**3 + 0*d**6 + 1/105*d**7 + 0*d + 0 + 0*d**5 + 3*d**2 + 0*d**4. Determine b, given that a(b) = 0.
0
Suppose 2*t - 10 = -2*u, -4*u + 0*u = -3*t - 20. Let o(c) be the third derivative of c**2 + 7/30*c**u - 5/12*c**4 + 0 + 0*c - 1/20*c**6 + 1/3*c**3. Factor o(g).
-2*(g - 1)**2*(3*g - 1)
Let i be 4 + 1/(2 + -3). Factor 1/2*f**4 + 3/2*f**2 + 0 - 3/2*f**i - 1/2*f.
f*(f - 1)**3/2
Suppose g = -v - 15, 63 = -4*v - v + g. Let w(r) = -15*r**2 - 7*r - 4. Let i(n) = 7*n**2 + 3*n + 2. Let z(c) = v*i(c) - 6*w(c). Determine x so that z(x) = 0.
1, 2
Let y be 0/(-3) - (-2 - 1). Find q, given that 12 - 21*q**3 - 3*q**5 + 24*q + 3*q + y*q**2 - 3*q - 15*q**4 = 0.
-2, -1, 1
Let w(f) be the first derivative of 2*f**3/21 + 4*f**2/7 - 17. Determine v so that w(v) = 0.
-4, 0
Let m(s) = -s - 5. Let n be m(-5). Suppose 0 = -d + 1 + 1. Factor 0 - 2/7*o**3 - 2/7*o**d + n*o.
-2*o**2*(o + 1)/7
Let k(l) be the first derivative of -2*l**3/5 - 2*l**2/5 - 4. Factor k(f).
-2*f*(3*f + 2)/5
Suppose 0*s + 25/3*s**2 + 0 + 1/3*s**4 - 10/3*s**3 = 0. Calculate s.
0, 5
Let n = -19 + 139/7. Suppose -n*j**2 + 9/7*j - 3/7 = 0. What is j?
1/2, 1
Let r(h) = -h**2 - 4*h + 3. Let m be r(-4). Let k be m/4 - 11/(-44). Factor -1/2*q**2 - k - 3/2*q.
-(q + 1)*(q + 2)/2
Let h(a) be the third derivative of -a**8/2184 + a**7/1365 + a**6/260 - a**5/78 + a**4/78 + 4*a**2. Factor h(y).
-2*y*(y - 1)**3*(y + 2)/13
Let s be 34/18 + 6/(-6). Suppose -25 = 5*x - 0*x + 5*n, 0 = 3*x + 5*n + 25. Solve x - 14/9*y**4 + 2/9*y**2 + 0*y - 4/9*y**3 - s*y**5 = 0.
-1, 0, 1/4
Let d(a) = -a**3 + 10*a**2 - 6*a + 6. Let b(g) = -15*g**3 + 140*g**2 - 85*g + 85. Let v(n) = 6*b(n) - 85*d(n). Factor v(s).
-5*s**2*(s + 2)
Solve -15*b**3 + 3*b**4 - b**4 + 2*b**4 - b**4 + 9*b**2 + 3*b**5 = 0.
-3, 0, 1
Let b be (-2 - 0)/((-4)/6). Factor 2*w**4 - 2*w**5 + 2*w**3 - 3*w**b - w**5 + 2*w**5.
-w**3*(w - 1)**2
Suppose 42 = -4*y + 50. Let h(z) be the first derivative of z**y + z + 1/3*z**3 + 3. Factor h(o).
(o + 1)**2
Suppose 5 = 5*a, k + 5*a - 7 = 1. Let 0*g**3 - g + 0*g**3 + g**4 + 2*g**k - g - 1 = 0. Calculate g.
-1, 1
Let g(q) be the second derivative of -q**6/120 + 3*q**5/80 - q**4/48 - q**3/8 + q**2/4 - q. Determine r, given that g(r) = 0.
-1, 1, 2
Let v be -53 + 4 - (0 + 1). Let x be 4/10 + (-5)/v. Factor -1/4*h**2 - 1/4 - x*h.
-(h + 1)**2/4
Let x(d) be the first derivative of -6 + 0*d - 2/15*d**3 - 1/5*d**2. Factor x(c).
-2*c*(c + 1)/5
Let q be 20/5 + 1 + -3. Suppose -q = -3*v + 4. What is m in -4/9*m - 14/9*m**5 + v*m**3 - 10/9*m**2 + 0 + 10/9*m**4 = 0?
-1, -2/7, 0, 1
Let j = 1 - -4. Find r, given that r**4 + 14*r**j + 22*r**4 - 4*r**2 + 6*r**3 + r**4 = 0.
-1, 0, 2/7
Let y(g) be the first derivative of 3*g**5/10 + 3*g**4/2 + 5*g**3/2 + 3*g**2/2 - 11. Factor y(h).
3*h*(h + 1)**2*(h + 2)/2
Let o = 473 - 4249/9. Solve 8/9 + 2/9*k**2 + o*k = 0.
-2
Let c = 23 - 19. Factor -c*l**2 + 3*l**3 + 0*l**3 + l**3.
4*l**2*(l - 1)
Let g(b) be the first derivative of 4*b + 3 + 0*b**2 - 1/4*b**4 - b**3. Let g(l) = 0. What is l?
-2, 1
Let v(f) be the third derivative of -1/1470*f**7 + 1/168*f**4 - 2*f**2 + 0 - 1/420*f**6 - 1/42*f**3 + 1/2352*f