/5
Let g(h) be the first derivative of 1/24*h**6 + 0*h + 0*h**4 - 11/2*h**2 + 0*h**3 - 12 + 1/12*h**5. Let i(a) be the second derivative of g(a). Factor i(k).
5*k**2*(k + 1)
Determine z, given that -55/6*z - 2/3*z**3 + 2 + 29/6*z**2 = 0.
1/4, 3, 4
Let x(q) be the first derivative of 13 + 0*q**2 - 2*q**3 + 3/4*q**4 + 0*q. Factor x(r).
3*r**2*(r - 2)
Factor 4*f**2 + 13/2*f + 3 + 1/2*f**3.
(f + 1)**2*(f + 6)/2
Let n(g) be the first derivative of -g**4/3 + 10*g**3/3 + 9*g - 18. Let o(q) be the first derivative of n(q). Factor o(y).
-4*y*(y - 5)
Let n(u) be the second derivative of -5*u**8/336 - u**7/14 + u**5/3 - u**2/2 - 7*u. Let s(z) be the first derivative of n(z). What is a in s(a) = 0?
-2, 0, 1
Find x, given that -3/2*x**3 - 6*x**2 + 15/2*x + 0 = 0.
-5, 0, 1
Suppose 0 = j - 9*j + 56. Determine h, given that j*h + 4*h**2 - h**3 - 6*h - h = 0.
0, 4
Let q(w) be the third derivative of w**6/200 - 7*w**5/100 + w**4/5 + 8*w**3/5 - 7*w**2 - 4*w. Factor q(b).
3*(b - 4)**2*(b + 1)/5
Let t(m) = -7*m - 103. Let z be t(-18). Suppose -10*g = -17 - z. Factor 2/3*w**5 + 0*w**g - 2/3*w**3 + 0*w**2 + 0 + 0*w.
2*w**3*(w - 1)*(w + 1)/3
Suppose 0 = 14*t - 1 + 1. Let z(a) be the first derivative of 5 + 1/4*a**2 + t*a - 1/8*a**4 + 0*a**3. Factor z(q).
-q*(q - 1)*(q + 1)/2
Suppose -37*b = -23*b - 28. Let q(a) be the first derivative of 1/6*a**4 - 1/3*a**b + 2/9*a**3 + 3 - 2/15*a**5 + 0*a. Determine g so that q(g) = 0.
-1, 0, 1
Let j(t) = -100*t - 7597. Let c be j(-76). Factor -1/4*g**c - 343/4 - 21/4*g**2 - 147/4*g.
-(g + 7)**3/4
Factor -306/5 - 304/5*k + 2/5*k**2.
2*(k - 153)*(k + 1)/5
Factor 21*w**2 + 20*w**3 - 33*w**2 - 83*w**2 - 25*w.
5*w*(w - 5)*(4*w + 1)
Let a(z) be the second derivative of -z**4/3 - 52*z**3/3 + 112*z**2 - z + 353. Factor a(l).
-4*(l - 2)*(l + 28)
Let o(p) be the first derivative of -p**6/120 - p**5/20 + 3*p**4/8 + 4*p**3 - 10. Let u(q) be the third derivative of o(q). Determine z so that u(z) = 0.
-3, 1
Let p(j) = -2*j - 6. Let h be p(-5). Let z(v) = -5. Let d(c) = c**2 - 4. Let x(n) = h*z(n) - 5*d(n). Solve x(m) = 0 for m.
0
Factor 3/8 - 1/8*k**2 + 1/4*k.
-(k - 3)*(k + 1)/8
Let i(d) = d**2 - 23*d + 134. Let q be i(10). Let w(l) be the third derivative of 0 + q*l**2 + 1/120*l**5 + 0*l**3 + 0*l - 1/24*l**4. Factor w(v).
v*(v - 2)/2
Let h(y) = -y**2 + 17*y - 31. Let g be h(15). Let a be (g/(-2))/(((-380)/(-24))/19). Factor -4/5*i - 1/5 - a*i**2.
-(i + 1)*(3*i + 1)/5
Let x(j) = 2*j**2 - 6*j - 2. Let z(q) = q - 1. Let t(i) = x(i) - z(i). Let m be t(4). Factor 0 + 1/2*y**5 + 0*y**m - 1/2*y + y**4 - y**2.
y*(y - 1)*(y + 1)**3/2
Let a = -164 + 171. Let l(d) be the third derivative of 0*d + 1/8*d**4 + 0 + 0*d**3 - 3/20*d**5 - 3*d**2 + 3/40*d**6 - 1/70*d**a. Let l(x) = 0. Calculate x.
0, 1
Suppose -41*z + 5*b - 10 = -46*z, -5*z + 12 = 3*b. Factor -1/6*p**5 + 0*p**2 + 0*p**4 - 1/6*p + 0 + 1/3*p**z.
-p*(p - 1)**2*(p + 1)**2/6
Suppose -4*g + 25*g + 2*g = 46. Determine b so that 0 + 0*b - 1/7*b**g + 0*b**3 + 1/7*b**4 = 0.
-1, 0, 1
Let p(v) be the second derivative of 0*v**3 - 7*v + 1/48*v**4 + 0 - 1/8*v**2. Let p(t) = 0. Calculate t.
-1, 1
Let n = -1 + 4. Let 9*b**2 + 3*b**3 - 3*b**4 + 0*b - 18 + 12 + 0*b**n - 3*b = 0. Calculate b.
-1, 1, 2
Let q(f) = 2*f**3 + 30*f**2 - 360*f + 1334. Let k(g) = 5*g**3 + 59*g**2 - 719*g + 2669. Let m(v) = 3*k(v) - 7*q(v). Factor m(w).
(w - 11)**3
Let h(n) be the third derivative of 17*n**2 + 3/10*n**5 + 0 + 1/60*n**6 + 0*n + 5/4*n**4 - 25/3*n**3. Factor h(w).
2*(w - 1)*(w + 5)**2
Let q(d) be the first derivative of -4*d**3/15 + 106*d**2/5 + 28. Factor q(o).
-4*o*(o - 53)/5
Let r(k) be the second derivative of -k**4/21 - 2*k**3/21 + 12*k**2/7 + 2*k + 1. What is w in r(w) = 0?
-3, 2
Let r be 2/6 + (-5)/16. Let g(o) be the second derivative of 4*o + 1/24*o**3 - 1/4*o**2 + 0 + r*o**4. Determine d, given that g(d) = 0.
-2, 1
Let o be 20/6 + (-1)/3. Suppose 7*j**4 + 17*j**3 - 5*j**o + 5*j**4 + 8*j**2 - 8*j**4 = 0. What is j?
-2, -1, 0
Let i(z) = 3*z**2 + z**2 - 2 - z + 1. Let s(a) = 9*a**2 - 2*a - 2. Let h be (-6)/(-33) + (-1141)/(-77) + -5. Let j(x) = h*i(x) - 4*s(x). Factor j(o).
2*(o - 1)*(2*o + 1)
Let l(m) = 12*m**3 + 36*m**2 + 176*m + 148. Let s(y) = -8*y**3 - 35*y**2 - 177*y - 147. Let w(k) = 3*l(k) + 4*s(k). Find a such that w(a) = 0.
-3, -1, 12
Suppose 8*a + 19 - 47 = -3*h, -h = -4. Let q = 21/2 + -10. Suppose -q*w**a - w - 1/2 = 0. Calculate w.
-1
Let x(w) be the second derivative of w**6/225 + w**5/75 - 2*w**4/9 + 8*w**3/15 - 2*w + 65. Determine m so that x(m) = 0.
-6, 0, 2
Suppose -16 - 74 = -12*f - 18*f. Solve -2 - 1/2*t**f + 0*t + 3/2*t**2 = 0.
-1, 2
Suppose 17 = 3*u + 5. Let c be 20/(-8)*16/(-10). Factor -8*a**3 - u*a**c + a + 20*a**3 + a - 12*a**2 + 2*a.
-4*a*(a - 1)**3
Factor 2/9*v**2 + 8/9*v + 2/3.
2*(v + 1)*(v + 3)/9
Suppose 0*q - 3*q = 0. Let d - 3*d - 4*d**2 + 2*d**2 + q*d**2 = 0. What is d?
-1, 0
Let n(o) be the third derivative of -o**8/8400 + o**6/450 + 13*o**3/6 - 23*o**2. Let s(g) be the first derivative of n(g). Determine a, given that s(a) = 0.
-2, 0, 2
Let v(y) be the third derivative of -y**8/40320 - y**7/10080 + y**6/720 + 7*y**5/60 - 19*y**2. Let j(h) be the third derivative of v(h). Factor j(l).
-(l - 1)*(l + 2)/2
Let p(z) be the third derivative of -3/8*z**6 + 125/336*z**8 + 0 + 5/14*z**7 + 0*z**4 + 0*z + 0*z**3 + 1/12*z**5 + 37*z**2. Factor p(f).
5*f**2*(f + 1)*(5*f - 1)**2
Let x(l) be the third derivative of -l**5/270 + 5*l**4/36 + 16*l**3/27 - 125*l**2. Find b such that x(b) = 0.
-1, 16
Factor -3/7*m**3 + 12*m + 0 + 81/7*m**2.
-3*m*(m - 28)*(m + 1)/7
Let s be (-15800)/(-780) + -20 - (-1)/13. Suppose -5*h + u = -16, 5*u + 0*u - 16 = h. Let s*i**5 + 0*i**h + 0 + 0*i + 0*i**2 - 1/3*i**3 = 0. Calculate i.
-1, 0, 1
Suppose -7*w + 36 = 2*w. Factor -20*s**2 + 15*s - 39*s - 777 + 777 - w*s**3.
-4*s*(s + 2)*(s + 3)
Let o(n) be the second derivative of -n**6/54 + n**5/20 - n**4/36 - n**3/54 - 27*n + 1. Factor o(j).
-j*(j - 1)**2*(5*j + 1)/9
Let m(p) = p**3 + p + 2. Let d(t) = 8*t**3 + 4*t**2 - 8*t - 4. Let o(z) = -2*d(z) - 4*m(z). Solve o(q) = 0 for q.
-1, 0, 3/5
Let m(s) = s**2 - s. Let r = -24 - -18. Let h(z) = z**3 + 2*z**2 - 3*z. Let y(k) = r*m(k) + 2*h(k). Factor y(c).
2*c**2*(c - 1)
Let i be (-2369)/92 + 11 + 15. Suppose 0 - 3/4*f + i*f**2 = 0. Calculate f.
0, 3
Factor 2/15*k**2 - 88/15*k + 968/15.
2*(k - 22)**2/15
Let x(j) be the second derivative of -1/2*j**2 - 1/48*j**4 + 0 + 1/6*j**3 + 5*j. Factor x(u).
-(u - 2)**2/4
Let w be (-258)/(-360) - 2/3. Let m(k) be the third derivative of 3/8*k**4 + 0*k + 0 + 0*k**3 - 5*k**2 + w*k**5. Factor m(c).
3*c*(c + 3)
Let f(x) be the first derivative of 0*x**3 + 1/15*x**4 + x + 0*x**2 + 1/50*x**5 + 7. Let s(y) be the first derivative of f(y). Factor s(n).
2*n**2*(n + 2)/5
Suppose -4*j + 9*j = 10. Factor v**2 + 2*v**j + 109 + 108 - 6*v - 226.
3*(v - 3)*(v + 1)
Let x be (-96)/(-434) - 9*(-2)/279. Factor 32/7 + x*i**5 + 22/7*i**4 + 86/7*i**3 + 16*i + 146/7*i**2.
2*(i + 1)**3*(i + 4)**2/7
Let j = 5513 + -22037/4. What is a in 9/2 + 3/4*a**2 + j*a = 0?
-3, -2
Let a(x) be the second derivative of x**5/12 + 5*x**4/6 + 55*x**3/18 + 5*x**2 - 6*x - 2. Factor a(i).
5*(i + 1)*(i + 2)*(i + 3)/3
Let t(j) be the first derivative of 5*j**4/2 - 95*j**3/3 + 95*j**2 + 120*j + 176. Factor t(m).
5*(m - 6)*(m - 4)*(2*m + 1)
Let t(u) be the second derivative of u**5/12 - 5*u**4/12 + 6*u**2 + 4*u. Let v(s) be the first derivative of t(s). Factor v(q).
5*q*(q - 2)
Let y(n) be the first derivative of 1/12*n**4 + 0*n**2 + 2 + 5*n - 1/6*n**3. Let j(x) be the first derivative of y(x). Factor j(d).
d*(d - 1)
What is d in -68*d**3 - 2034*d**4 + 2030*d**4 + 4*d**5 - 5*d - 76*d**2 + 69*d + 80 = 0?
-2, -1, 1, 5
Factor 10*j + 2/3*j**2 + 0.
2*j*(j + 15)/3
Let z(d) be the second derivative of d**8/15120 - d**7/3780 - d**6/1080 + d**5/270 + d**4 - 8*d. Let q(f) be the third derivative of z(f). Factor q(l).
2*(l - 2)*(l + 1)*(2*l - 1)/9
Let r(f) be the first derivative of f**6/10 - 3*f**5/4 + 2*f**4 - 2*f**3 + 17*f + 41. Let b(y) be the first derivative of r(y). Factor b(d).
3*d*(d - 2)**2*(d - 1)
Factor -69168*i**2 - 2944*i - 18 - 8243*i**4 + 242*i**4 - 7997*i**4 - 564*i**4 - 66976*i**3 - 14.
-2*(i + 2)**2*(91*i + 2)**2
Suppose x - 4*q = -13, x + 3*q - 20 = -5. Let t be 2/(-20)*(5 + -22 - -