5. Factor 85*k**3 + k**5 - 5*k**c + 3*k**4 - 85*k**3 - k + 2*k**2.
k*(k - 1)**3*(k + 1)
Let c(g) be the first derivative of 38/7*g**2 - 20 - 20/7*g + 16/21*g**3. Factor c(a).
4*(a + 5)*(4*a - 1)/7
Let y(p) be the second derivative of -1/6*p**3 + 3/40*p**5 + 0 + 1/2*p**4 - 6*p - 1/120*p**6 + 0*p**2. Let t(i) be the second derivative of y(i). Factor t(m).
-3*(m - 4)*(m + 1)
Let o(t) = -t**3 - 11*t**2 - 3*t - 9. Let w be o(-11). What is l in 4*l**5 - 58*l**2 - 46*l + 12 - w + 4*l**5 - 18*l**3 + 14*l**4 = 0?
-1, -3/4, 2
Suppose -p = -5*w + 14 + 13, 2*p + 4 = 0. Factor 9967 - 10*h**4 - 5*h**w - 9967 - 5*h**3.
-5*h**3*(h + 1)**2
Suppose 0 = -d - 6, -w - 5*d = -2*d + 16. Suppose 6/5*l**3 - 9/5*l + 3/5*l**5 - 6/5*l**w - 3/5 + 9/5*l**4 = 0. Calculate l.
-1, 1
Let a(u) = u + 0*u - 8 + 16. Let l be a(-6). Factor -4*s**l + 1 + 6*s + 7*s**2 + 2.
3*(s + 1)**2
Suppose -32*m = -8*m - 114 - 102. Solve -5/2*t**4 - 27/4*t - 27/2*t**2 + 0 - 1/4*t**5 - m*t**3 = 0.
-3, -1, 0
Let u(i) = i**2 - 1. Let k(w) = -w**3 - 5*w**2 - 5*w - 2. Let c be k(-4). Let s(g) = -6*g**3 - 14*g**2 - 8*g - 2. Let l(y) = c*u(y) - s(y). Factor l(x).
2*x*(x + 2)*(3*x + 2)
Suppose 5*q = 4*u + 36, 5*q - 5*u = 23 + 17. Factor 2*a**q + 2*a**4 + 36*a - 39*a - 9*a**3 - a**4 + 9*a**2.
3*a*(a - 1)**3
Let i = 15611 - 15607. Let 0 + 15/8*z**2 - 3*z**3 + 3/2*z**i - 3/8*z = 0. Calculate z.
0, 1/2, 1
Solve -2/3*p**5 + 0*p - 2/3*p**4 + 2/3*p**3 + 0 + 2/3*p**2 = 0 for p.
-1, 0, 1
Suppose -8*j - o = -7*j + 6, j = -3*o - 16. Let f be 5/(-50)*54*j. Find n, given that 12/5*n**2 + 6/5 + f*n = 0.
-2, -1/4
Let j(a) = -3*a**3 + 6*a**2. Let h(z) = z**4 + 2*z**3 - 6*z**2 + 1. Suppose 5*l - 10 = 5. Suppose -4 + 10 = l*u. Let d(c) = u*j(c) + 3*h(c). Factor d(t).
3*(t - 1)**2*(t + 1)**2
Suppose 225 = 5*f + 4*p, 0 = f - 0*p + 4*p - 45. Let t = f + -45. Factor t + 0*b - 3/7*b**2.
-3*b**2/7
Let q(i) = 2*i**3 + 9*i**2 - 3*i + 3. Let f(g) = 4*g - 6*g**3 + 2*g + 12 - 20 - 26*g**2 + 2*g. Let x(m) = 3*f(m) + 8*q(m). Solve x(w) = 0.
-3, 0
Let v(y) = 7*y**3 - y**2 + 1. Let h(k) = 11*k**3 + 35*k**2 - 136*k + 97. Let q(j) = -h(j) + v(j). Factor q(f).
-4*(f - 2)*(f - 1)*(f + 12)
Suppose -4*j = 4*k - 116, 3*j = -7*k + 2*k + 147. Let p be 1 + 1*(-12)/k. Factor 9/5*r + p*r**2 + 6/5.
3*(r + 1)*(r + 2)/5
Let a(q) be the first derivative of -1/2*q**6 + 3/5*q**5 - 10 + 3/4*q**4 + 0*q**2 - q**3 + 0*q. Factor a(h).
-3*h**2*(h - 1)**2*(h + 1)
Let c(f) be the third derivative of -f**7/7560 - f**4/12 - 7*f**2. Let d(a) be the second derivative of c(a). Factor d(v).
-v**2/3
Factor 1/3*y**2 - 14/3*y + 0.
y*(y - 14)/3
Let w(s) be the second derivative of -s**8/336 + s**7/168 + s**6/72 - s**5/24 - s**3/2 + 5*s. Let v(y) be the second derivative of w(y). Factor v(a).
-5*a*(a - 1)**2*(a + 1)
Solve 0 + 10/9*i**4 - 8/9*i**2 - 2/9*i**3 + 0*i = 0 for i.
-4/5, 0, 1
Let i = 2 - 1. Let p(a) be the first derivative of 2/9*a**3 + 0*a + i - 1/3*a**2. Factor p(u).
2*u*(u - 1)/3
Suppose -6*x = -1041 - 3399. Factor 736*h - x*h - 4 + 4*h**2 + h**3 + 3*h**3.
4*(h - 1)*(h + 1)**2
Let x(o) be the third derivative of -o**6/60 + o**5/3 - 23*o**4/12 + 14*o**3/3 + 367*o**2. Factor x(q).
-2*(q - 7)*(q - 2)*(q - 1)
Let c(n) be the third derivative of 4*n**6/75 + n**5/15 - 7*n**4/60 - n**3/15 - 83*n**2 + 3. Suppose c(x) = 0. Calculate x.
-1, -1/8, 1/2
Let x(h) be the first derivative of -6 - 1/24*h**6 - 1/4*h**4 - 1/2*h + 5/8*h**2 - 1/6*h**3 + 1/5*h**5. Factor x(p).
-(p - 2)*(p - 1)**3*(p + 1)/4
What is q in -3*q**2 - 9/2*q - 1/2*q**3 + 0 = 0?
-3, 0
Let l be 14284/(-770) - (-30)/(-105). Let p = 96/5 + l. Determine o, given that p*o**4 + 4/11 - 4/11*o**3 + 2/11*o**5 + 2/11*o - 8/11*o**2 = 0.
-2, -1, 1
Let s(n) be the first derivative of n**3/21 + 25*n**2/7 + 625*n/7 - 97. Factor s(w).
(w + 25)**2/7
Let s(y) = 11*y - 13. Let m be s(-10). Let o be m/(-4) - 3/4. Factor 4*x**3 - o*x**5 + 28*x**5 - 2*x**3.
-2*x**3*(x - 1)*(x + 1)
Let -1/2*h**5 - 3*h**3 - h**2 - 3/2 + 7/2*h + 5/2*h**4 = 0. What is h?
-1, 1, 3
Let n = -134 - -433/3. Solve -4/3 + 35/3*k**4 + 4*k**3 + 4*k**5 - n*k**2 - 8*k = 0.
-2, -1, -2/3, -1/4, 1
Let k(m) = -m**3 - m**2 + 2*m + 8. Let w(o) = o**2 + o. Let z(u) = -k(u) + 4*w(u). Let z(h) = 0. Calculate h.
-4, -2, 1
Suppose -6*x = -4*x - 40. Let i be (94/x)/(21/14) - 3. Factor 0 + i*b**2 + 0*b.
2*b**2/15
Let c(j) be the third derivative of -1/840*j**8 + 0*j + 0 + 0*j**3 - 10*j**2 + 0*j**4 + 1/150*j**5 - 1/525*j**7 + 1/300*j**6. Factor c(m).
-2*m**2*(m - 1)*(m + 1)**2/5
Let x(a) be the first derivative of a**6/9 - 2*a**5/5 - 11*a**4/3 - 76*a**3/9 - 9*a**2 - 14*a/3 + 757. Factor x(z).
2*(z - 7)*(z + 1)**4/3
Let t(n) be the first derivative of 1/5*n**2 - 2/15*n**3 + 2/5*n - 39 - 1/10*n**4. Suppose t(a) = 0. What is a?
-1, 1
Let n(t) be the second derivative of t**4/48 + t**3/12 + 12*t - 1. Factor n(d).
d*(d + 2)/4
Let s(k) = 3*k**3 - 4*k + 3. Let h be s(1). Let j(a) be the third derivative of 0*a + 1/20*a**5 - 1/2*a**3 + 0*a**4 - 3*a**h + 0. Factor j(n).
3*(n - 1)*(n + 1)
Suppose 9*j = 11*j + y - 9, 31 = 3*j + 5*y. Let -2/17*u**3 + 0 + 4/17*u**j + 6/17*u = 0. What is u?
-1, 0, 3
Let c = -12 - -43. Let k(i) = -i**2 - 18*i + 4. Let g be k(-18). What is a in -9*a**2 - 12*a**3 - 13*a**g - 14*a**4 + c*a**2 - 8 + 8*a + 9*a**4 = 0?
-1, 2/3
Suppose 280 = 3*h + h. Let g be (1*-4*1)/(h/(-10)). Factor 2/7*r**4 + g*r**3 + 0*r + 0*r**2 + 0.
2*r**3*(r + 2)/7
Let m(b) be the first derivative of -10*b**2 + 2 - b**4 - 16/3*b**3 - 8*b. Factor m(n).
-4*(n + 1)**2*(n + 2)
Let o(a) = 4*a**4 + 4*a**3 - 76*a**2 - 36*a + 56. Let p(s) = -s**4 - s**3 + 15*s**2 + 7*s - 11. Let m(y) = -3*o(y) - 16*p(y). Suppose m(l) = 0. What is l?
-2, -1, 1
Let y = 58 - 48. Let l = y - 7. Find o such that -2/3*o + 0 + 11/3*o**l - 4/3*o**4 - 5/3*o**2 = 0.
-1/4, 0, 1, 2
Let c(r) be the first derivative of 4 + 1/20*r**5 + 1/6*r**3 - 1/6*r**4 + 3*r + 0*r**2. Let k(x) be the first derivative of c(x). Solve k(q) = 0 for q.
0, 1
Let i(v) be the second derivative of v**7/315 - v**6/360 - v**4/12 - 8*v. Let y(x) be the third derivative of i(x). What is j in y(j) = 0?
0, 1/4
Factor 4*i**3 - 7*i**3 + 4*i**3 + 21*i + 6 + 5*i**3 + 21*i**2.
3*(i + 1)*(i + 2)*(2*i + 1)
Suppose 2*s = 26 - 22. Let h(o) be the second derivative of 0*o**3 - s*o + 1/40*o**6 + 0*o**2 + 0*o**5 - 1/16*o**4 + 0. Factor h(t).
3*t**2*(t - 1)*(t + 1)/4
Let l be (-4)/14 + (3/(-21))/(32/(-512)). Factor -1/3*j**l - 1 - 4/3*j.
-(j + 1)*(j + 3)/3
Let k be (-5)/(-10*(-4)/(-16)). Let n be (k*3)/((-14)/(-21)). Factor -4*t - 3 - 4*t**2 + 0 + 2 + n.
-4*(t - 1)*(t + 2)
Let p(l) be the second derivative of -2*l**6/5 + 87*l**5/20 - 55*l**4/4 + 6*l**3 + 250*l. Find k, given that p(k) = 0.
0, 1/4, 3, 4
Let w(l) be the first derivative of l**6/75 - l**5/50 - l**4/15 - 5*l - 6. Let z(h) be the first derivative of w(h). Factor z(u).
2*u**2*(u - 2)*(u + 1)/5
Let r(q) be the second derivative of 2*q**7/231 - 23*q**6/33 + 167*q**5/110 + 59*q**4/66 - 169*q**3/33 + 56*q**2/11 - 3*q - 30. Suppose r(d) = 0. Calculate d.
-1, 1/2, 1, 56
Let w(n) be the second derivative of n**7/14 - 9*n**6/10 + 24*n**5/5 - 14*n**4 + 24*n**3 - 24*n**2 - 44*n + 1. Let w(s) = 0. What is s?
1, 2
Let z(g) be the third derivative of -16/45*g**4 + 0*g - 1/75*g**6 - 1/1575*g**7 + 0*g**3 - 10*g**2 - 8/75*g**5 + 0. Factor z(v).
-2*v*(v + 4)**3/15
Suppose 6*z**2 - 6*z**4 + 0 - 45/4*z**3 - 3/4*z**5 + 12*z = 0. What is z?
-4, -1, 0, 1
Let t(j) be the first derivative of 2/27*j**3 + 32/9*j + 8/9*j**2 + 2. Factor t(v).
2*(v + 4)**2/9
Let g be (4/(0 + 8))/((-13)/((-208)/20)). Suppose 2/5*u**2 + 2/5*u**5 + 0*u + 0 - 2/5*u**3 - g*u**4 = 0. Calculate u.
-1, 0, 1
Let n(b) be the first derivative of -4*b**5/5 + 13*b**4 + 268*b**3/3 + 46*b**2 - 408*b - 54. Solve n(m) = 0 for m.
-3, -2, 1, 17
Let n(v) be the second derivative of -v**6/210 - 3*v**5/35 - 9*v**4/14 - 18*v**3/7 + 9*v**2/2 - v. Let m(d) be the first derivative of n(d). Factor m(c).
-4*(c + 3)**3/7
Let z(y) be the first derivative of 27*y**4/4 - 43*y**3 + 39*y**2 + 24*y + 73. Determine r, given that z(r) = 0.
-2/9, 1, 4
Determine i so that 25/3*i - 8/3 - i**2 = 0.
1/3, 8
Let z(r) = 4*r**2 + 103*r + 78. Let k be z(-25). Let -30*h - 15/2*h**k + 18 - 69/2*h**2 = 0. Calculate h.
-3, -2, 2/5
Let j(v) be the first derivative of 3*v - 5 - 1/2*v**3 + 1/9*v**4 +