 be the second derivative of -x**4/2 - 2*x**3/3 - x. Determine t, given that y(t) = 0.
-2/3, 0
Suppose -19*c + 8*c = -33. Solve 2*h**2 + 2*h**4 + 0 + 1/2*h + 1/2*h**5 + 3*h**c = 0 for h.
-1, 0
Let v(y) be the second derivative of 1/84*y**7 + 2*y - 1/40*y**5 + 0*y**2 + 0 + 0*y**6 + 0*y**3 + 0*y**4. Let v(l) = 0. What is l?
-1, 0, 1
Let n(j) be the third derivative of -2*j**7/735 + 11*j**6/840 - 3*j**5/140 + j**4/168 + j**3/42 - 8*j**2. Factor n(a).
-(a - 1)**3*(4*a + 1)/7
Let f(a) be the first derivative of 2*a**5/55 + 3*a**4/22 + 4. Find o, given that f(o) = 0.
-3, 0
Let n be -11 + 11 - 2878/22. Let k = n - -131. Factor -k*w**2 - 8/11*w - 8/11.
-2*(w + 2)**2/11
Let g(z) be the third derivative of -z**6/360 + z**5/20 - 3*z**4/8 - 7*z**3/6 + 9*z**2. Let h(f) be the first derivative of g(f). Factor h(a).
-(a - 3)**2
Let 3/7*o**3 + 9/7*o**2 + 6/7 - 3/7*o**4 - 15/7*o = 0. What is o?
-2, 1
Find v, given that 128/7*v**2 + 0 + 0*v + 2/7*v**4 + 32/7*v**3 = 0.
-8, 0
Let y(p) be the third derivative of -1/210*p**5 + 0 - 1/84*p**4 + 1/420*p**6 + 0*p + 1/21*p**3 - 4*p**2. Determine j, given that y(j) = 0.
-1, 1
Let d(m) be the second derivative of m**6/540 - m**4/108 + m**2 - 5*m. Let c(n) be the first derivative of d(n). Suppose c(k) = 0. Calculate k.
-1, 0, 1
Let t(b) be the second derivative of -b**4/12 + 3*b**3/2 + b**2 + 2*b. Let k be t(9). Find u, given that 2*u**3 + u**k + 0 + 2 - 2*u - 3*u**2 = 0.
-1, 1
Solve 2/9*q**2 + 0 - 2/9*q = 0 for q.
0, 1
Let h(z) be the first derivative of -3*z**5/25 - 7*z**4/20 - z**3/3 - z**2/10 - 14. Suppose h(x) = 0. Calculate x.
-1, -1/3, 0
Let y(d) be the third derivative of d**8/112 + d**7/315 + 3*d**4/8 - d**2. Let a(k) be the second derivative of y(k). Factor a(p).
4*p**2*(15*p + 2)
Let w be -1 + -3 + (184/44 - 0). Determine p, given that 0*p + 0*p**2 - w*p**4 + 0 - 2/11*p**3 = 0.
-1, 0
Solve 1/3*k**2 + 64/3 - 16/3*k = 0 for k.
8
Let b(k) be the third derivative of -k**8/20160 - k**7/840 - k**6/80 + k**5/15 - 3*k**2. Let z(i) be the third derivative of b(i). Factor z(j).
-(j + 3)**2
Let q(i) be the third derivative of -i**9/3024 - i**8/420 - i**7/168 - i**6/180 + 2*i**3/3 - 5*i**2. Let y(l) be the first derivative of q(l). Factor y(o).
-o**2*(o + 1)**2*(o + 2)
Let y be (-2 + (3 - 2))*0. Let p(d) be the third derivative of -1/240*d**5 + 0*d**4 + 1/480*d**6 + 0*d**3 + y + 0*d - 2*d**2. Factor p(g).
g**2*(g - 1)/4
Suppose 5*g + 4*x = 37, -g + 0*g - 4*x + 17 = 0. Let -g*b**2 + 5*b**3 + 1/2*b**5 - 5/2*b**4 - 1/2 + 5/2*b = 0. What is b?
1
Let h(u) = u**2 + 4*u + 4. Let f be h(-3). Suppose -6 = 2*m - 0*m, 0 = 2*g + 3*m + f. Factor 2*v**2 + 5 + 3 - g*v - 6.
2*(v - 1)**2
Let k(x) = x - 4. Let u be k(3). Let a be u/(-3)*(2 - -10). Factor -2*f**2 + 2*f**4 + 0*f**a - 4*f**5 + 3*f**5 + f.
-f*(f - 1)**3*(f + 1)
Solve 0*f + 2*f**3 + 10*f - 26*f**2 + 14*f**2 = 0 for f.
0, 1, 5
Suppose -13 = 3*h - 5*z, -5*h - z = -h - 21. What is g in -1/4*g + 0 - 1/2*g**h + 1/4*g**5 + 0*g**3 + 1/2*g**2 = 0?
-1, 0, 1
Let s(g) = -3*g**2 - 2*g - 3. Let x(f) be the second derivative of -7*f**4/12 - 2*f**3/3 - 3*f**2 - 4*f. Let i(z) = 9*s(z) - 4*x(z). Find l such that i(l) = 0.
-1, 3
Suppose -t - 3*t = q - 20, 4*t + 5*q - 36 = 0. Let d(i) = i**3 - 3*i**2 - 3*i - 1. Let u be d(t). Factor -2*v**3 - v**5 + 0*v**2 + 3*v**4 - v**u + v**2.
-v**2*(v - 1)**3
Suppose -3 = 5*y - 13. Factor -1 + 4*m**3 - 5*m**4 - y*m**2 + 3*m**4 + 1.
-2*m**2*(m - 1)**2
Let l(x) be the second derivative of -1/12*x**3 + 0 + 3*x + 0*x**4 - 1/120*x**6 + 1/8*x**2 + 1/40*x**5. Factor l(n).
-(n - 1)**3*(n + 1)/4
Let w be 1412/22 + (-4)/22. Let v be w/12 + (-4)/3. Factor 17/2*q**v + 1/2 + 2*q**5 + 4*q + 14*q**3 + 11*q**2.
(q + 1)**4*(4*q + 1)/2
Let a be (-11 + 7 + -4)/(-10). Factor a + 6/5*i + 2/5*i**2.
2*(i + 1)*(i + 2)/5
Let a(d) = -4*d**2 + 2 - 3*d**2 + 5*d**2. Let m(r) = -6*r**2 + 6. Let w = 19 - 16. Let b(x) = w*m(x) - 10*a(x). Factor b(t).
2*(t - 1)*(t + 1)
Solve 2/7*k**3 - 24/7*k**4 + 0 + 24/7*k**2 + 8/7*k - 10/7*k**5 = 0 for k.
-2, -1, -2/5, 0, 1
Let r(z) be the first derivative of z**4/16 + 7*z**3/2 + 147*z**2/2 + 686*z - 32. Factor r(v).
(v + 14)**3/4
Let m be (-2)/(2 - 4 - -1). Let v(k) be the third derivative of -1/330*k**5 - 1/132*k**4 + 0*k**3 + 0 + 2*k**m + 0*k. Factor v(a).
-2*a*(a + 1)/11
Let x(o) be the first derivative of 1/6*o**3 + 0*o + 0*o**4 - 1/10*o**5 + 0*o**2 + 6. Find q such that x(q) = 0.
-1, 0, 1
Let t(f) be the second derivative of -f**7/210 - 2*f**6/75 - 3*f**5/50 - f**4/15 - f**3/30 + 3*f. Let t(n) = 0. Calculate n.
-1, 0
Suppose 0*x + x + 2 = 0, -4*x = -3*w + 14. Let s(h) be the third derivative of 0 + 0*h**4 + 1/210*h**5 + 0*h**3 + 0*h + 2*h**w. Determine g so that s(g) = 0.
0
Let n(y) be the first derivative of -2*y**5/5 - 5*y**4/2 - 2*y**3 + 9*y**2 - 2. Factor n(t).
-2*t*(t - 1)*(t + 3)**2
Let n(t) be the second derivative of 0*t**2 - 5*t + 15/16*t**4 - 2/5*t**6 + 0 + 9/10*t**5 + 1/4*t**3. Suppose n(d) = 0. What is d?
-1/4, 0, 2
Factor 3/2*f**4 + 9/2*f - 9/2*f**3 + 3/2*f**2 - 3.
3*(f - 2)*(f - 1)**2*(f + 1)/2
Let i(g) be the first derivative of 2/3*g**3 + 0*g - 2/5*g**5 + 3 - g**2 + 1/2*g**4. Determine s so that i(s) = 0.
-1, 0, 1
Let h be -1 + 2 - 2/(-2). Factor 2/5 - 2/5*s + 2/5*s**3 - 2/5*s**h.
2*(s - 1)**2*(s + 1)/5
Suppose z = 3*z. Suppose 13 = -z*j - j + 4*c, 8 = 2*c. Factor 2*l + 2*l**j + 3*l**2 + 4*l**2 - 3*l**2.
2*l*(l + 1)**2
Let d(g) be the third derivative of 0*g - 1/70*g**6 + 1/392*g**8 + 0 + 2/735*g**7 + 1/28*g**4 + 2/21*g**3 + g**2 - 2/105*g**5. Suppose d(t) = 0. Calculate t.
-1, -2/3, 1
Suppose 2*w - 8*w + 18 = 0. Let x(j) be the second derivative of 1/5*j**5 + 0*j**4 - 1/15*j**6 + 3*j - 1/21*j**7 + 0*j**w + 0*j**2 + 0. Factor x(k).
-2*k**3*(k - 1)*(k + 2)
Let m(j) be the third derivative of -j**6/60 - 2*j**5/15 - 24*j**2. What is f in m(f) = 0?
-4, 0
Find h, given that 420*h**5 - 195*h**3 + 496*h**2 + 64*h + 567*h**4 + 758*h**3 + 717*h**3 + 701*h**4 = 0.
-4/3, -1, -2/5, -2/7, 0
Let v(q) = q**3 - 5*q**2 - q + 5. Let g be v(5). Suppose -6 = -r - g*r. Solve r*o - 2*o**2 - 6*o - 2*o**3 = 0.
-1, 0
Suppose 5*q - 4*s = 51, -3*s = 2*q + s + 2. Let d = -4 + q. Factor y**2 + y**2 + 4*y - 4*y**3 + 2*y**d.
-2*y*(y - 2)*(y + 1)
Let f(r) be the second derivative of r**7/6 + r**6/6 - r**5/10 - 2*r. Factor f(g).
g**3*(g + 1)*(7*g - 2)
Determine b, given that -4*b + 6*b - 5 + 8*b + 5*b**2 + 10 = 0.
-1
Let s(p) be the first derivative of -2*p**3/9 - p**2 - 4*p/3 + 7. Find y such that s(y) = 0.
-2, -1
Let m = 91 - 91. Determine f so that 2/5*f**3 + 0 - 2/5*f + m*f**2 = 0.
-1, 0, 1
Let t(u) be the first derivative of -u**3/3 + u**2/6 - 34. Factor t(g).
-g*(3*g - 1)/3
Let c(q) = 2*q**5 - 20*q**4 + 6*q**3 + 4*q**2 + 8*q. Let s(d) = d**5 - 13*d**4 + 4*d**3 + 3*d**2 + 5*d. Let p(i) = 5*c(i) - 8*s(i). Factor p(x).
2*x**2*(x - 1)*(x + 1)*(x + 2)
Let r = 41/387 - -5/43. Let 0 + 0*z + r*z**4 + 2/9*z**2 - 4/9*z**3 = 0. Calculate z.
0, 1
Let f = -4 + 6. Let d be -10*f*(-2)/10. Factor -2*x**4 + 0*x**4 + d*x**3 - 4*x - 3 + 5.
-2*(x - 1)**3*(x + 1)
Let k(v) be the first derivative of 0*v**2 + 1/3*v**3 + 1/2*v**4 + 1/5*v**5 - 3 + 0*v. Factor k(m).
m**2*(m + 1)**2
Suppose -2 = 4*d + 14, 4*w = 4*d + 28. Factor 2*o**2 + 2*o**4 + 0 + 1/2*o + 1/2*o**5 + w*o**3.
o*(o + 1)**4/2
Let q be (-22)/(-24) - (-4)/(-128)*8. Let g = -2 - -5. Factor 1/3*u**4 - 2/3*u**g - q*u**2 + 1/3*u**5 + 1/3*u + 1/3.
(u - 1)**2*(u + 1)**3/3
Let k(m) be the third derivative of -25*m**8/1344 - m**7/28 + 3*m**6/40 - m**5/30 - 11*m**2. Let k(s) = 0. What is s?
-2, 0, 2/5
Let z(x) = x**3 + 4*x**2 - x. Let h be z(-4). Suppose -2*n + 21 - 21 - 6*n**2 - h*n**3 = 0. What is n?
-1, -1/2, 0
Let a = -29 + 33. Let k be a/3 + 0/(-3). Factor -k - 2/3*y**2 + 2*y.
-2*(y - 2)*(y - 1)/3
Let t(i) be the first derivative of -1/21*i**6 - 7 + 0*i**4 + 0*i**2 + 0*i + 2/35*i**5 + 0*i**3. Solve t(p) = 0 for p.
0, 1
Let q(s) be the second derivative of -s**7/420 - s**6/300 + 3*s**5/200 + s**4/120 - s**3/30 - 13*s. Suppose q(a) = 0. What is a?
-2, -1, 0, 1
Solve l**4 + 12*l**2 + 64 + 11*l**2 - 35*l**2 + 4*l**3 - 32*l = 0 for l.
-4, 2
Suppose 3*v - 1 = -y, -7*y + 6*y = -v + 7. Suppose 4/9*w + 2/9*w**v + 2/9 = 0. Calculate w.
-1
Let o(f) be the second derivative of f**4/30 + 8*f**3/15 - 9*f**2/5 - f. Factor o(g).
2*(g - 1)*(