Let c(x) be the third derivative of x7⁄42 + 5*x6⁄24 + 3*x5⁄8 - x3⁄3 - 18*x**2 - 2*x. Let t(v) be the first derivative of c(v). Factor t(y).

5y(y + 3)*(4*y + 3)

Let u(s) = -4*s2 + 20*s + 416. Let m(w) = 4*w2 - 19*w - 418. Let p(a) = -8*m(a) - 7*u(a). Factor p®.

-4(r - 12)(r + 9)

Let m(w) be the third derivative of 2⁄13*w3 - 1⁄390*w5 + 2*w2 + 0*w + 5⁄156*w4 + 33. Factor m(g).

-2(g - 6)(g + 1)/13

Suppose -2761*o = -2751*o. Let r(m) be the third derivative of 12*m2 + 1⁄40*m6 + 0*m3 + 3⁄20*m5 + 0*m + 0 + o*m**4. Let r(q) = 0. Calculate q.

-3, 0

Let x be 1 + (-16)/(-6) + 6⁄18. Suppose -q + 1 = x*q - 3*o, 4*o = -5*q + 22. Factor -k2 + q*k2 + k**2 + k.

k*(2*k + 1)

Let j be (6⁄10)/(((-2484)/345)/(16/(-2))). Factor 20⁄3*z + 0 + j*z**2.

2z(z + 10)/3

Suppose -2*b = -0*b - d - 10, -d = -5*b + 25. Factor -u2 - u2 - 10*u4 + 4*u - b*u3 + 12*u4 + u3.

2u(u - 2)(u - 1)(u + 1)

Let c(l) = -l2 - 20*l + 20. Let j(y) = -y2 - 21*y + 16. Let p(k) = -10*c(k) + 8*j(k). Factor p(g).

2(g - 2)(g + 18)

Factor -8*n2 + 10*n + 8*n - 6*n + 3*n2 + 18*n.

-5n(n - 6)

Let j = -1019 + 15287⁄15. Let f(g) be the second derivative of 5⁄9*g3 - 4*g - 4⁄9*g4 + j*g5 - 1⁄3*g2 + 0. Determine k so that f(k) = 0.

1⁄2, 1