**2 + 0*s**3 = 0.
-2, 0, 1
Let i(x) be the second derivative of 9*x**4/2 - 9*x**3/2 + x. Let s(g) = 54*g**2 - 27*g + 1. Let w(v) = -2*i(v) + 3*s(v). Suppose w(c) = 0. What is c?
1/6, 1/3
Let d = 20 - 14. Let j(f) be the second derivative of -1/20*f**5 - 1/60*f**d - 1/24*f**4 - 3*f + 0*f**2 + 0*f**3 + 0. Factor j(o).
-o**2*(o + 1)**2/2
Solve -127*h + 40*h**2 + 115*h**3 - 115*h**2 + 50 + 25*h**4 + 12*h = 0 for h.
-5, -1, 2/5, 1
Let d(z) be the third derivative of z**10/10080 - 5*z**4/24 + 5*z**2. Let q(k) be the second derivative of d(k). Let q(f) = 0. What is f?
0
Suppose 0 = -2*k - 2, -4*k - 24 = 3*q - 8*q. Determine u so that 4 + 80*u**3 - 12*u**2 + 14*u**5 - 14*u + 4*u**5 - 88*u**q + 12*u**5 = 0.
-2/5, 1/3, 1
Let y(q) = 9*q**2. Let z(k) = 5*k**2. Let o(f) = 6*y(f) - 11*z(f). Factor o(v).
-v**2
Let w(i) be the third derivative of 1/10*i**5 + 1/6*i**4 + i**2 + 1/60*i**6 + 0*i + 0*i**3 + 0. Suppose w(t) = 0. What is t?
-2, -1, 0
Suppose -v - 6 = -3*v. Factor 5*o**2 - 4*o**v - o - 2*o**2 + 5*o**3 + 1 - 4*o**2.
(o - 1)**2*(o + 1)
Let w = -60 + 63. Let j(h) be the first derivative of 1/8*h**4 + 0*h**3 - 3/4*h**2 - w - h. Suppose j(k) = 0. What is k?
-1, 2
Suppose 8*v**2 + 2*v**3 + 24*v - 1 + 17 + 4*v**2 = 0. What is v?
-2
Let z(f) = f**2 - 3*f. Let i(m) = m**2 - 6*m + 4. Let q be i(4). Let w(t) = 2*t**2 - 4*t. Let u(y) = q*z(y) + 3*w(y). Let u(l) = 0. Calculate l.
0
Let l(g) be the first derivative of g**5/15 + 8*g**4/3 + 128*g**3/3 + 1024*g**2/3 + 4096*g/3 - 6. Factor l(y).
(y + 8)**4/3
Factor 2/5*a**2 + 0 + 6/5*a.
2*a*(a + 3)/5
Let n = -1802/5 - -362. Let c = n + -14/15. Find v, given that 0*v + c*v**2 + 0 = 0.
0
Factor 14 - 4*w + 2/7*w**2.
2*(w - 7)**2/7
Let -q + 2*q - 2*q**2 - 5*q = 0. Calculate q.
-2, 0
Let m(f) be the first derivative of 1/60*f**4 + 1/300*f**6 - 1 - f**2 + 0*f**3 + 1/75*f**5 + 0*f. Let c(o) be the second derivative of m(o). Factor c(y).
2*y*(y + 1)**2/5
Suppose 444 = -2*q + 448. Factor 0*n**3 + 0*n - 1/3 + 2/3*n**q - 1/3*n**4.
-(n - 1)**2*(n + 1)**2/3
Suppose -6 + 2 = -2*b. Let h(i) be the third derivative of 1/360*i**6 - 1/72*i**4 + 1/18*i**3 + 0 + 2*i**b - 1/180*i**5 + 0*i. Determine s, given that h(s) = 0.
-1, 1
Let k(r) = -9*r**5 - r**4 + 8*r**3 + 4*r + 4. Let q(d) = 8*d**5 - 9*d**3 - d**2 - 3*d - 3. Let w(j) = 3*k(j) + 4*q(j). Let w(i) = 0. Calculate i.
-1, -2/5, 0, 2
Let t(m) be the third derivative of -m**6/15 - m**5/15 - m**4/48 + m**2 - 33. Let t(l) = 0. What is l?
-1/4, 0
Let u(r) be the second derivative of -r**6/20 + 3*r**4/4 + 2*r**3 + 9*r**2/4 + 9*r. Factor u(t).
-3*(t - 3)*(t + 1)**3/2
What is i in -2*i + 4 - 2*i**2 - 2 + i**2 + 1 = 0?
-3, 1
Let f(l) be the first derivative of l**5/330 + l**4/66 + l**3/33 - 5*l**2/2 + 2. Let z(a) be the second derivative of f(a). Solve z(t) = 0.
-1
Suppose -17*w - 8*w**4 - 22*w**3 - 6 + 0 + 2 - 28*w**2 - w**5 + 0*w**2 = 0. What is w?
-4, -1
Let l(k) = -81*k - 3. Let a be l(1). Let y be -3*(a/20 - -3). Let y*q**3 + 32/5*q + 42/5*q**2 + 8/5 = 0. What is q?
-1, -2/3
Suppose t - 10 = -4*v, 3 = -3*t - 3. Suppose 0 + 0*a + 1/2*a**2 + 1/2*a**v = 0. What is a?
-1, 0
Let i be ((-10)/30)/((-1)/12). Factor -8*u**3 - 3*u**2 + 4*u**2 - 4*u + 6*u**2 + 2*u**i + 3*u**2.
2*u*(u - 2)*(u - 1)**2
Determine q so that -3/5*q + 3/5*q**3 + 3/5*q**2 - 3/5 = 0.
-1, 1
Suppose -s - 4*u + 20 = 0, 0 = 2*s - 3*u - 1 + 5. Factor -7*m**2 - 5*m**2 - s*m + 14*m**2 + 2.
2*(m - 1)**2
Let 8*u**3 + 0 + 14/5*u**5 + 8/5*u**2 + 46/5*u**4 + 0*u = 0. What is u?
-2, -1, -2/7, 0
Let -56*f**3 + 19 + 8*f**4 - 16*f**2 + 28*f**5 - 33 + 22 + 28*f = 0. Calculate f.
-1, -2/7, 1
Let g(c) be the first derivative of -5*c**6/6 + 2*c**5 - 10*c**3/3 + 5*c**2/2 + 13. Factor g(b).
-5*b*(b - 1)**3*(b + 1)
Let g = -25 + 25. Let k be 8/2 + -2 + -2. Factor k*o**3 - 2/3*o**4 + g + 0*o + 2/3*o**2.
-2*o**2*(o - 1)*(o + 1)/3
Let q(x) be the second derivative of -x**5/30 - x**4/12 + 2*x**3/3 + 3*x**2 - 4*x. Let t(y) be the first derivative of q(y). Factor t(f).
-2*(f - 1)*(f + 2)
Let k(s) = s**2 + 4*s - 5. Let r be k(-5). Suppose 0*b = 3*m + b - 1, 5*m - b - 15 = r. What is x in 0 - 2/5*x + 2/5*x**m = 0?
0, 1
Let c(s) = -9*s**2 + 30*s + 15. Let v(t) = -2*t**2 + 6*t + 3. Let p(f) = 5*c(f) - 24*v(f). Solve p(y) = 0 for y.
-1
Let h(x) = 5*x**4 + 25*x**3 - 5*x**2 + 5*x + 5. Let v(t) = -7*t**4 - 38*t**3 + 8*t**2 - 8*t - 8. Let f(a) = 8*h(a) + 5*v(a). Find p, given that f(p) = 0.
-2, 0
Suppose -2*q = 2*f - 8, -2*q + 15 = 2*f - 7*q. Let j = f - 3. Factor p**3 - p**2 + 2*p**j + 0*p**3.
p**2*(p + 1)
Let r(w) be the second derivative of w**6/60 + 3*w**5/10 + 9*w**4/4 + 9*w**3 + 2*w**2 + 4*w. Let g(y) be the first derivative of r(y). Factor g(a).
2*(a + 3)**3
Let s = -5 + 7. Suppose -10*l - 2*l**3 - 9*l**2 - 6 - l**s + 2*l**2 + 2 = 0. Calculate l.
-2, -1
Let q = 8 + 94. Let f = q + -506/5. Find h such that 2/5*h**2 - f*h + 2/5 = 0.
1
Let w = 1187/231 - 56/11. Let s(q) be the first derivative of -w*q**6 + 6/35*q**5 - 3/14*q**4 + 0*q**2 + 2/21*q**3 + 2 + 0*q. Factor s(l).
-2*l**2*(l - 1)**3/7
Let c(d) be the second derivative of 0*d**5 + 0*d**2 + 1/70*d**7 + 0 + 1/10*d**4 - 1/10*d**3 - 1/25*d**6 + 4*d. Find s such that c(s) = 0.
-1, 0, 1
Suppose 4*m = -t + 10 + 7, 0 = 2*m - 6. Suppose -v + 5 = -f, t*v - v - f - 23 = 0. Determine w, given that v*w + 1 + w**2 - 3*w - w = 0.
-1
Let d(p) be the first derivative of -p**6/60 - p**5/15 - p**4/12 - p**2/2 - 1. Let a(o) be the second derivative of d(o). Factor a(b).
-2*b*(b + 1)**2
Let o be (3 - (8 + -4))/(-40). Let j(x) be the third derivative of 0*x + 1/240*x**6 - 2*x**2 - o*x**5 + 0 + 1/16*x**4 - 1/12*x**3. Factor j(h).
(h - 1)**3/2
Let x be 7/(-3) - ((-1 - -5) + -7). Find t, given that 2/3*t + 0 - 2/3*t**4 - x*t**3 + 2/3*t**2 = 0.
-1, 0, 1
Let g be 4/(-14) + (-107)/(-7). Suppose -2*c - g = -7*c. Factor -3 + c - d**4 - d**3.
-d**3*(d + 1)
Suppose -19*z**4 + 15*z**4 - 3*z**5 + z**5 - 2*z**3 = 0. What is z?
-1, 0
Let o(p) = 2*p - 8. Let x be o(5). Let a = 2 - x. Suppose -2/5*i + 0*i**2 + 2/5*i**3 + a = 0. Calculate i.
-1, 0, 1
Factor 7/3*g**2 + g + 0 + 1/3*g**4 + 5/3*g**3.
g*(g + 1)**2*(g + 3)/3
Let d(c) = -c - 1. Let f be d(5). Let s be f/2*(-2)/2. What is y in -3*y**2 - s*y**3 - 7*y + 7*y = 0?
-1, 0
Factor -g**2 + 12*g + 100 - 52*g + 5*g**2.
4*(g - 5)**2
Let i(b) = b**2 + 6*b + 6. Let c be i(-5). Let -v**2 + 0*v**2 - v - c + 2*v + 3*v**2 = 0. What is v?
-1, 1/2
Suppose -14 = -3*g + g. Let q(m) = -m + 9. Let z be q(g). Solve 2*o**5 + 6*o**3 + 0*o**3 - 9*o**4 + 3*o**4 - 2*o**z = 0 for o.
0, 1
Let i be 3 + 1 + 1 + -3. Let h(p) = 3*p - 3. Let t(w) = -10 + 15 + 11 - w**2 - 15*w. Let n(m) = i*t(m) + 11*h(m). Factor n(d).
-(d - 1)*(2*d - 1)
Let f(m) = -m**3 + m**2 + m. Let b(a) = a**4 + 9*a**3 - 11*a**2 - 15*a. Let r(d) = -2*b(d) - 14*f(d). Solve r(t) = 0 for t.
-2, 0, 2
Factor -c + 1/2 + 1/2*c**2.
(c - 1)**2/2
Let u be 1/((-4)/(-8)*1). Suppose -c = -0*c - u. Factor 0 + 4/9*k - 2/9*k**c.
-2*k*(k - 2)/9
Let n(l) be the third derivative of -l**8/2688 - l**7/420 - l**6/160 - l**5/120 - l**4/192 - l**2. Factor n(s).
-s*(s + 1)**4/8
Let w(a) be the third derivative of 0*a**3 - 5*a**2 - 1/36*a**5 - 1/36*a**4 + 1/126*a**7 + 0 + 0*a + 1/180*a**6. Factor w(v).
v*(v - 1)*(v + 1)*(5*v + 2)/3
Suppose d - 16 = -2*g, 2 + 0 = d. Factor g - u**2 + 2*u - u**2 - 3.
-2*(u - 2)*(u + 1)
Let d(h) be the third derivative of h**5/60 - h**4/2 + 11*h**3/6 + h**2. Let i be d(11). Factor 1/4*v**3 + 0 + 1/4*v**2 + i*v.
v**2*(v + 1)/4
What is l in -3/4*l**3 + 3 - 3/4*l**2 + 3*l = 0?
-2, -1, 2
Let n(u) be the first derivative of -2*u**5/35 + 2*u**4/7 - 4*u**3/7 + 4*u**2/7 - 2*u/7 + 2. Factor n(f).
-2*(f - 1)**4/7
Let q(s) = 9*s**2 - 62*s - 16. Let w(o) = 6*o**2 - 41*o - 10. Let v(u) = 5*q(u) - 8*w(u). Find m, given that v(m) = 0.
0, 6
Let g(k) = 2*k**2 - 4*k + 2. Let o be g(2). Let u be 6*-1*o/(-9). Factor -u*t**2 + 2/3*t**3 + 2/3*t + 0.
2*t*(t - 1)**2/3
Let s be 4/40*(2 + (-21)/18). Let u(v) be the second derivative of 1/20*v**5 + 0*v**2 - s*v**4 + 1/30*v**6 - 1/6*v**3 + 0 + 3*v. Factor u(g).
g*(g - 1)*(g + 1)**2
Suppose 3*c - 2*l - 8 = 2*c, -3*c - 3*l = -6. Let f be 6/4 - (-2)/c. Solve 0 + 4/7*b - 2/7*b**f - 6/7*b**3 = 0 for b.
-1, 0, 2/3
Let a(g) be the second derivative of -g**4/42 - 4*g**3/21 - 4*g**2/7 + 6*g. Factor a(m).
-2*(m + 2)**2/7
Le