j) = 7*j**4 - 19*j**3 + 10*j**2 + 4*j - 17. Let l(z) = 5*s(z) - 2*y(z). Factor l(v).
(v - 6)*(v - 1)**2*(v + 1)
Let v(q) be the second derivative of q**6/90 - q**5/30 - 7*q**4/36 - 2*q**3/9 - 16*q. Determine l, given that v(l) = 0.
-1, 0, 4
Let l(j) be the third derivative of j**7/105 + j**6/30 - j**5/2 + j**4/3 + 20*j**3/3 + 3*j**2. Factor l(w).
2*(w - 2)**2*(w + 1)*(w + 5)
Let a = -52 - -470/9. Find q such that 4/9*q - a - 2/9*q**2 = 0.
1
Let z(k) be the second derivative of -2*k + 0*k**3 - 1/10*k**2 + 0 + 1/60*k**4. Factor z(x).
(x - 1)*(x + 1)/5
Let v = -14 - -11. Let y be (-3)/(-18) - v/18. Factor 2/3*t**2 + 0 + 1/3*t**3 + y*t.
t*(t + 1)**2/3
Let x be (8/48)/(18/4). Let c(y) be the second derivative of x*y**4 + 4*y + 0 + 0*y**2 - 1/27*y**3. Factor c(g).
2*g*(2*g - 1)/9
Suppose -5*n - 2 + 17 = 0. Let h be 4/(-10) - (-6)/15. Factor -3*m**n + 0*m + m + 4*m**2 + h - 2.
-(m - 1)**2*(3*m + 2)
Suppose 4*q + v + 3*v - 20 = 0, -5*v = -3*q + 7. Solve -5*u**3 + 5*u - 3*u**2 + 2*u**2 + 3*u**q + u - u - 2 = 0 for u.
-1, 2/3, 1
Let k(a) be the third derivative of -a**5/240 + a**4/16 - 3*a**3/8 - 3*a**2. Suppose k(b) = 0. Calculate b.
3
Factor 4*g**3 + 8*g - 12*g + 8*g**2 + 12 - 20*g**2.
4*(g - 3)*(g - 1)*(g + 1)
Let l be (-22)/(-12) + 53/318. Suppose 8/3*y**3 - 2/3*y**4 + 8/3 - 8/3*y - l*y**2 = 0. Calculate y.
-1, 1, 2
Let f(v) be the second derivative of 0 + 0*v**3 + 1/12*v**4 + 1/60*v**5 + 2*v - 2/3*v**2. Factor f(h).
(h - 1)*(h + 2)**2/3
Let b be 6/30 + 13/10. Factor 0 + 3/2*c**3 + 0*c + b*c**2.
3*c**2*(c + 1)/2
Let x = 83 + -79. Factor 4/7*n**3 + 0*n**x + 0*n**2 - 2/7*n + 0 - 2/7*n**5.
-2*n*(n - 1)**2*(n + 1)**2/7
Suppose c = 4*w - 79, -5*w + 71 + 54 = 4*c. Factor -q**4 + 0*q + 0*q**4 - 4*q + 10*q**4 + 16*q**2 - w*q**3.
q*(q - 1)*(3*q - 2)**2
Factor 12*f**2 - 6*f + 1 - 7*f**4 - 5 + 6*f**3 + 4*f**4 - 5.
-3*(f - 3)*(f - 1)*(f + 1)**2
Find h such that 0 + 2/3*h**4 - 2/3*h**3 + 2/3*h - 2/3*h**2 = 0.
-1, 0, 1
Let a = 8258/11 + -750. Let i = 901/11 + -81. Factor -2/11*x**4 + 16/11 - a*x + i*x**3 - 12/11*x**2.
-2*(x - 2)**3*(x + 1)/11
Suppose -j + 8 = 4. Suppose a + s = j*a - 28, -5*a - 3*s + 42 = 0. Factor a*t + 1 - 3 - 2*t - 5*t**2.
-(t - 1)*(5*t - 2)
Let d(y) be the third derivative of y**5/12 + 5*y**4/6 + 5*y**3/2 + 7*y**2. Factor d(s).
5*(s + 1)*(s + 3)
Let b(l) be the first derivative of l**5/20 - l**4/16 - 9. Determine w so that b(w) = 0.
0, 1
Let s(v) be the third derivative of v**8/3528 - 4*v**7/2205 + v**6/315 + v**5/315 - 5*v**4/252 + 2*v**3/63 - 11*v**2. Find j, given that s(j) = 0.
-1, 1, 2
Factor -3 - 81/8*z**2 - 15/8*z**3 - 45/4*z.
-3*(z + 1)*(z + 4)*(5*z + 2)/8
Let y = 143 - 79. Suppose -y = -4*s - 0*s. Factor -5*o**5 - 4*o**5 - s*o**4 - 14*o**3 - 4*o**2 + 3*o**5.
-2*o**2*(o + 1)**2*(3*o + 2)
Let a(t) be the second derivative of -t**7/294 + 2*t**6/35 - 23*t**5/70 + 5*t**4/7 - 25*t**3/42 - 23*t. Factor a(y).
-y*(y - 5)**2*(y - 1)**2/7
Let i(c) be the third derivative of 1/48*c**4 + 0*c**3 + 0 + 5/1344*c**8 - 1/80*c**5 + c**2 - 7/480*c**6 + 0*c + 1/280*c**7. What is a in i(a) = 0?
-1, 0, 2/5, 1
Suppose 3*b - 5*t = -3*t + 3, -2*t + 6 = 0. What is o in 2*o**b - 4*o + 4*o**3 + 4*o**4 - 4*o**2 - 4*o**5 + 5*o - 3*o**3 = 0?
-1, 0, 1/2, 1
Let z = -717 + 43019/60. Let m = z + 27/20. What is w in 2/3 + m*w - 14/3*w**2 + 8/3*w**3 = 0?
-1/4, 1
Let z(h) be the third derivative of h**6/40 - 3*h**4/8 - h**3 + 6*h**2. Factor z(j).
3*(j - 2)*(j + 1)**2
Let t(y) = -y**3 + 2*y**2 + 3*y - 3. Let n be t(2). Solve 8*f**3 - 6*f**3 - 3*f**2 + f**n + 6*f**2 - 3 - 3*f = 0.
-1, 1
Factor 3/7 - 3*m + 36/7*m**2.
3*(3*m - 1)*(4*m - 1)/7
Let a(i) = -3*i**3 - 4*i**2 - 3*i + 2. Let c(l) = -16*l**3 - 21*l**2 - 16*l + 11. Let x(h) = -11*a(h) + 2*c(h). Factor x(t).
t*(t + 1)**2
Let i(r) be the first derivative of 1/16*r**4 + 1/4*r**3 + 1/4*r**2 + 6 + 0*r. Determine k, given that i(k) = 0.
-2, -1, 0
Suppose 26 = o - 4*u, 39 = -o + 5*o - 3*u. Suppose o*g - 7*g = -3. Determine f so that 1/2*f**2 + 0*f + 3/2*f**4 + 2*f**g + 0 = 0.
-1, -1/3, 0
Let y(q) be the third derivative of q**6/60 - q**5/6 + 2*q**4/3 - 4*q**3/3 - 27*q**2. Factor y(m).
2*(m - 2)**2*(m - 1)
Let m(n) = -n**3 + 7*n**2 - 5*n - 4. Let t be m(6). Suppose 0 = s - t. What is c in 0*c + 0 + 1/2*c**s - 3/4*c**3 = 0?
0, 2/3
Let f(j) = -j**3 - 11*j**2 + 13*j + 14. Let a be f(-12). Factor -25/6*t**a - 2/3 - 19/6*t**3 - 7/6*t**4 - 1/6*t**5 - 8/3*t.
-(t + 1)**3*(t + 2)**2/6
Let z = -9 + 14. Solve -z*v + v + 7*v**2 - 4 - 8*v**2 = 0 for v.
-2
Let n(c) be the first derivative of -1/12*c**4 + 1/6*c**2 - 1/15*c**5 + 1 + 0*c + 1/9*c**3. Factor n(j).
-j*(j - 1)*(j + 1)**2/3
What is m in 0*m - 165/4*m**4 + 0 - 24*m**3 - 3*m**2 = 0?
-2/5, -2/11, 0
Let i be 10 + -1 + 2 - -3. Let a = i + -6. Find g, given that -2/3*g**3 - a*g + 4*g**2 + 16/3 = 0.
2
Let i(a) be the second derivative of -2*a**7/147 - 2*a**6/35 + a**5/35 + a**4/3 - 8*a**2/7 - 12*a. Let i(m) = 0. Calculate m.
-2, -1, 1
Let k(t) = 3*t**5 + t**4 + 12*t**3 - 6*t**2 - 4*t + 5. Let u(p) = p**5 + 4*p**3 - 2*p**2 - p + 2. Let d(f) = 4*k(f) - 11*u(f). Factor d(j).
(j - 1)*(j + 1)**3*(j + 2)
Let t = 53 - 49. Let o be t/4 + (-8)/12. Solve -4/3 - o*f**2 - 4/3*f = 0 for f.
-2
Let c(k) be the third derivative of -k**8/10080 + k**6/720 - k**5/360 - 5*k**3/6 - 2*k**2. Let v(z) be the first derivative of c(z). Find p such that v(p) = 0.
-2, 0, 1
Suppose 0 = -4*y - 2*g - 8, -4*y + 4*g = -g - 20. Factor 32/9*j**3 + 4/9*j - 14/9*j**4 - 22/9*j**2 + y.
-2*j*(j - 1)**2*(7*j - 2)/9
Let -9*g**3 - 3*g**4 - 3*g - 7*g**2 - 5*g**2 + 3*g**2 = 0. Calculate g.
-1, 0
Let v(t) be the third derivative of 7*t**5/60 + t**4/8 - 5*t**2. Let r(z) = 8*z**2 + 4*z. Let i(p) = -5*r(p) + 6*v(p). Factor i(s).
2*s*(s - 1)
Let g = 92/205 + -2/41. Solve -g*v**2 + 0*v + 2/5*v**5 + 0 + 2/5*v**4 - 2/5*v**3 = 0.
-1, 0, 1
Let o(a) be the first derivative of -2/9*a - 2/45*a**5 - 4/9*a**2 - 4/9*a**3 + 1 - 2/9*a**4. Factor o(z).
-2*(z + 1)**4/9
Let f(k) be the third derivative of 5*k**2 + 0*k + 1/40*k**4 + 1/5*k**3 - 1/100*k**5 + 0. Suppose f(z) = 0. What is z?
-1, 2
Let g be (-983)/(-4) - (4 - 7). Let r = 252 - g. Factor 0 - 3*a**2 - r*a**3 - 1/4*a**5 - a - 3/2*a**4.
-a*(a + 1)**2*(a + 2)**2/4
Let s(r) = 9*r - 7. Let d be s(1). What is x in -4/7*x + 2/7 + 2/7*x**d = 0?
1
Let o(j) = -84*j**3 - 156*j**2 + 176*j + 64. Let g(t) = 17*t**3 + 31*t**2 - 35*t - 13. Let c(n) = 16*g(n) + 3*o(n). Factor c(q).
4*(q - 1)*(q + 2)*(5*q + 2)
Let q(m) be the second derivative of m**7/84 - m**6/90 - m**5/12 + m**4/6 + m**3 + 2*m. Let h(k) be the second derivative of q(k). Determine o so that h(o) = 0.
-1, 2/5, 1
Let x(o) = -o**2 - 11*o + 16. Let j be x(-12). Let z = 11 + -7. What is p in 2 - 4*p**2 - 2*p**j + 6*p**z - 2*p**4 = 0?
-1, 1
Let s(o) be the first derivative of -o**2/2 - 3*o - 1. Let y be s(-6). Suppose l**y + 0*l + 3*l**2 - 3*l**3 - 2*l - 7*l**2 = 0. Calculate l.
-1, 0
Let y(p) = 10*p**4 + 15*p**3 + 5*p**2 - 5*p. Let j(v) = v**5 + v**4 + v**3 + v**2 - v. Let w(u) = 5*j(u) - y(u). Factor w(d).
5*d**3*(d - 2)*(d + 1)
Let u(v) be the second derivative of v**6/50 - 9*v**5/100 + v**4/20 + 3*v**3/10 - 3*v**2/5 + 6*v. Factor u(n).
3*(n - 2)*(n - 1)**2*(n + 1)/5
Let c(p) be the first derivative of p**5/10 + 27*p**4/32 - 25*p**3/8 + 53*p**2/16 - 9*p/8 + 20. Factor c(l).
(l - 1)**2*(l + 9)*(4*l - 1)/8
Factor -13*z**2 + 2*z**3 + 9*z**2 + 32*z + 16*z**2 + 4*z**2.
2*z*(z + 4)**2
Let i(f) = -f**3 - 4*f**2 - 3*f - 4. Let q be i(-4). Suppose -2*r = -4*r + q. Factor 6*j**4 - 2*j**5 + 8*j**2 - 12*j**3 - 7*j + 2*j + 2*j**r + 3*j.
-2*j*(j - 1)**4
Suppose -5*o - 1 = -11. Let l(i) be the third derivative of 0 - 1/21*i**3 - 5/84*i**4 - 2*i**o + 0*i - 2/105*i**5. Factor l(b).
-2*(b + 1)*(4*b + 1)/7
Suppose -3*a + 2 = -7. Suppose 7*u - 4*u - 31 = -q, -a = -3*q. Let 18/5*l**5 + 42/5*l**3 - u*l**4 - 4/5*l - 6/5*l**2 + 0 = 0. What is l?
-2/9, 0, 1
Let y = 533/9 + -62. Let q = y + 73/9. Factor 0*v - 5*v**3 - 2/3*v**2 - 8*v**4 + q*v**5 + 0.
v**2*(v - 2)*(4*v + 1)**2/3
What is y in -44*y**3 + 10 - 10*y**2 + 1 - 5*y**4 + 4 + 64*y**3 - 20*y = 0?
-1, 1, 3
Let h(j) = j**4 + 9*j**3 + 23*j**2 + 27*j - 4. Let x(a) = a**4 + 9*a**3 + 24*a**2 + 27*a - 3. Let r(f) = 3*h(f) - 4*x(f). Factor r(g).
-g*(g + 3)**3
Let w be 12/(-6)*1/(-5). Factor -w*s**4 + 0 - 2/5*s + 2/5*s**3