(i).
-2*i*(i + 1)**2*(2*i - 1)/15
Factor 3/8*y**3 + 5/8*y**2 + 0 + 1/4*y.
y*(y + 1)*(3*y + 2)/8
Suppose 2*p = -2*c + 8, p + 2*c = 5*c. Determine j, given that -4*j**2 - 6*j**3 - 3*j**p - 8*j**2 - 3*j = 0.
-1, -1/3, 0
Let m(j) be the third derivative of -29*j**5/12 + 155*j**4/24 - 5*j**3/3 + 2*j**2 + 5*j. Determine p, given that m(p) = 0.
2/29, 1
Let w be 2 + 12/4 + (-1 - 0). Let l(o) be the second derivative of -1/3*o**2 + 0 - 4*o - 1/9*o**3 + 1/30*o**5 + 1/18*o**w. Determine r so that l(r) = 0.
-1, 1
Let s be (-16)/(-40)*1/(2/10). Let g(m) be the first derivative of -2/9*m**3 - s*m**2 + 8/3*m - 3 + 1/4*m**4. Determine w so that g(w) = 0.
-2, 2/3, 2
Suppose -2*n = 4*w + 8 + 36, w + 20 = -5*n. Let v be (w/6)/((-15)/6) + 0. Factor -2/3*h**3 - v*h**4 + 0 + 0*h**2 + 0*h.
-2*h**3*(h + 1)/3
Let q(w) be the third derivative of -1/60*w**4 + 1/210*w**7 + 0*w**3 - 1/1680*w**8 + 7/300*w**5 - 3/200*w**6 + 3*w**2 + 0*w + 0. Solve q(n) = 0 for n.
0, 1, 2
Let d = 2/423 + 2524/2961. Factor 0*s - 3/7*s**4 + 9/7*s**3 + 0 - d*s**2.
-3*s**2*(s - 2)*(s - 1)/7
Let m(x) be the first derivative of -3/16*x**4 + 27 + 3/8*x**2 - 9/4*x + 3/4*x**3. Factor m(h).
-3*(h - 3)*(h - 1)*(h + 1)/4
Let w(o) be the third derivative of o**8/1512 + 2*o**7/945 - o**5/135 - o**4/108 + 5*o**2 - 4. Factor w(c).
2*c*(c - 1)*(c + 1)**3/9
Suppose -3*k + 10 = -5*c, 5*c = -5*k - 5 - 5. Let q be (-1)/c - (-24)/16. Factor 3*v**2 - 6*v**2 + 0*v**2 + 2*v + 2*v**q.
-v*(v - 2)
Let n = 240 + -302. Let j be (n/279)/((-4)/6). Solve 0*q**3 + j*q**2 + 1/6*q - 1/3*q**4 + 0 - 1/6*q**5 = 0.
-1, 0, 1
Factor -3 + 756*f - 17*f**2 - 375*f - 396*f + 5.
-(f + 1)*(17*f - 2)
Suppose 114 = 11*i + 30*i - 9. Find d such that 3*d**2 + 0*d + 1/2*d**i - 16 = 0.
-4, 2
Factor -6*h**2 - 1/3*h**4 - 8/3*h**3 - 16/3*h - 5/3.
-(h + 1)**3*(h + 5)/3
Let j(t) = -2*t**2 + 5*t - 10. Let b be j(5). Let o be (84/b)/(4/(-10)). Factor x**3 - 3*x**3 - o*x + 8*x + 0*x**3.
-2*x*(x - 1)*(x + 1)
Let w(h) = -45*h**3 + 10*h**2 + 30*h - 30. Let f(r) = 1 + 83*r + 85*r - 169*r. Let s(k) = -30*f(k) - w(k). Determine p so that s(p) = 0.
0, 2/9
Let q(i) be the second derivative of i**4/6 + 71*i**3/3 - 72*i**2 - 278*i. Factor q(t).
2*(t - 1)*(t + 72)
Let s(p) be the second derivative of p**7/7 - 14*p**6/15 - 5*p**5/2 + 56*p**4/3 - 20*p**3 + 931*p. Solve s(z) = 0.
-3, 0, 2/3, 2, 5
Suppose -6*i - 44 = -i - q, -2*q + 7 = -i. Let r be 5/(-5)*i/3. Factor -1/3*n**4 + 0 + 1/3*n**2 + 0*n + 0*n**r.
-n**2*(n - 1)*(n + 1)/3
Let l = 118 + -589/5. Let o(r) be the first derivative of 2/15*r**3 - 2 - 4/5*r - l*r**2. Factor o(k).
2*(k - 2)*(k + 1)/5
Let n(y) = 3*y**3 + 33*y**2 - 58*y. Let f(z) = z**3 + 10*z**2 - 19*z. Let p(d) = 11*f(d) - 4*n(d). Factor p(t).
-t*(t - 1)*(t + 23)
Determine f so that 18/5*f + 27/5 + 3/5*f**2 = 0.
-3
Let u(j) = -4*j**3 + 4*j**2 + 3. Let r(i) = -i**2 - 1. Let c be 36/(-9) - (0 - 1). Let w(z) = c*r(z) - u(z). Factor w(n).
n**2*(4*n - 1)
Factor 0*r + 1935*r**2 - 1931*r**2 + 0*r + 4*r**5 - 15*r**4 + 12*r**3.
r**2*(r - 2)**2*(4*r + 1)
Let h(n) = 2*n**3 - 25*n**2 + 53*n - 21. Let r(v) = -10*v**3 + 126*v**2 - 264*v + 106. Let k(j) = -28*h(j) - 6*r(j). Let k(m) = 0. Calculate m.
1, 12
Let x be (1*2/(-32))/(240/(-64)). Let u(q) be the second derivative of x*q**5 + 2/3*q**2 - 5*q - 1/12*q**4 + 0 + 0*q**3. Determine y so that u(y) = 0.
-1, 2
Factor 2/11*h**2 - 24/11 + 2*h.
2*(h - 1)*(h + 12)/11
Let n(h) be the second derivative of h**6/45 - 3*h**5/10 - 7*h**4/6 - 11*h**3/9 + h + 72. Factor n(c).
2*c*(c - 11)*(c + 1)**2/3
Factor 4*o**4 + 284*o**2 - 8*o**4 + 580*o**3 - 300*o**3.
-4*o**2*(o - 71)*(o + 1)
Let g(p) = -18*p**2 - 3*p + 3. Let x(a) be the third derivative of -17*a**5/60 - a**4/12 + 2*a**3/3 - 9*a**2. Let m(s) = -5*g(s) + 6*x(s). Factor m(j).
-3*(j - 1)*(4*j + 3)
Let g = -3284 + 3284. Factor -1/2*b**2 + g - b.
-b*(b + 2)/2
Let g be 30/(-18) + (-721)/(-420). Let m(b) be the third derivative of 0*b**4 - g*b**5 - 1/140*b**7 + 0*b + 6*b**2 + 3/80*b**6 + 0*b**3 + 0. Factor m(f).
-3*f**2*(f - 2)*(f - 1)/2
Let t(h) be the first derivative of -h**3/3 + 33*h**2 - 319. Find v such that t(v) = 0.
0, 66
Let c(f) = -f**3 - f + 2. Let i(l) be the first derivative of 0*l**3 + 8*l - 3/2*l**2 - 5/4*l**4 + 3. Let d(b) = 9*c(b) - 2*i(b). Factor d(t).
(t - 1)**2*(t + 2)
Suppose -23 = -6*z + 49. Let b = z - 12. Factor -2/5*n**2 + 0 - 1/5*n**5 + b*n + 0*n**4 + 3/5*n**3.
-n**2*(n - 1)**2*(n + 2)/5
Let i(y) = 19*y**3 - 55*y**2 - 124*y + 104. Let x(g) = 75*g**3 - 220*g**2 - 495*g + 415. Let a(c) = -15*i(c) + 4*x(c). Factor a(l).
5*(l - 5)*(l + 2)*(3*l - 2)
Suppose 2*l + 480 = 4*o + 6*l, -4*o = -5*l - 507. Solve o*z**2 - 11*z**5 - z**3 - 115*z**2 - 3*z**3 - 32*z**4 - 9*z**5 = 0 for z.
-1, 0, 2/5
Let b(l) be the third derivative of 0 + 7/40*l**6 + 11/20*l**5 + 4/7*l**4 + 0*l - 6*l**2 + 2/7*l**3. Factor b(y).
3*(y + 1)*(7*y + 2)**2/7
Let r(u) = -33*u + 530. Let h be r(16). Let p(n) be the first derivative of 2/5*n - 1/10*n**4 + 11 - 2/15*n**3 + 1/5*n**h. Factor p(w).
-2*(w - 1)*(w + 1)**2/5
Let q(v) be the first derivative of -1/5*v**5 - 1/6*v**6 + 3*v**2 + 13/3*v**3 + 0*v + 28 + 7/4*v**4. Factor q(y).
-y*(y - 3)*(y + 1)**2*(y + 2)
Determine z so that 360 + 2/5*z**2 + 24*z = 0.
-30
Solve 0 + 0*g**3 + 36/7*g**2 - 48/7*g - 3/7*g**4 = 0.
-4, 0, 2
Let l = 308 + -304. Let q(a) be the first derivative of 2*a**2 + l - 4*a**3 - 4/5*a**5 + 3*a**4 + 0*a. Factor q(g).
-4*g*(g - 1)**3
Factor 145*q - 391*q - 10*q**2 + 5*q**3 + 181*q - 50.
5*(q - 5)*(q + 1)*(q + 2)
Find s such that 19*s**2 - s**4 + 12*s**2 + 26*s**2 - 10*s - 38*s**2 - 8*s**3 = 0.
-10, 0, 1
Let i = -234 - -238. Let m(l) be the second derivative of -1/15*l**6 + 0*l**5 + 1/2*l**i - 2*l + 2/3*l**3 + 0*l**2 + 0. Solve m(s) = 0.
-1, 0, 2
Let r = 765 - 765. Suppose 2/7*z + r*z**3 - 4/7*z**4 + 0 + 4/7*z**2 - 2/7*z**5 = 0. What is z?
-1, 0, 1
Suppose 62*g - 12 = 59*g - z, -g = -4*z - 17. Factor -8/5*m**4 + 0*m**2 + 0 - 4/5*m**g - 4/5*m**3 + 0*m.
-4*m**3*(m + 1)**2/5
Solve 51*i**2 - 3/2*i**3 + 54 + 213/2*i = 0 for i.
-1, 36
Factor 17*z**2 - 10*z**3 + 9*z**3 - 8 + 14 + 16*z + 34 + 42*z.
-(z - 20)*(z + 1)*(z + 2)
Let d(h) = -25*h**3 - h**2 + 16*h + 7. Let t(f) = 3*f**3 - f**2 - 1. Let y(n) = -d(n) - 3*t(n). Factor y(s).
4*(s - 1)*(s + 1)*(4*s + 1)
Let m(q) be the second derivative of q**7/210 - q**5/30 + 5*q**3/6 - 12*q. Let h(p) be the second derivative of m(p). Suppose h(t) = 0. Calculate t.
-1, 0, 1
Let d = 9/350 - -6623/1050. Factor -d*f + 7/3*f**2 - 2.
(f - 3)*(7*f + 2)/3
Suppose 266 = -2*p + 270. Factor 1/7*m**3 + 3/7*m + 3/7*m**p + 1/7.
(m + 1)**3/7
Let r(h) be the second derivative of h**7/63 - 23*h**6/135 + 2*h**5/9 + 40*h**4/27 - 128*h**3/27 + 16*h**2/3 + 10*h - 10. What is u in r(u) = 0?
-2, 2/3, 1, 2, 6
Let k be 9/15 + (-11984)/90. Let g = k + 133. Determine c, given that 2/9*c**4 + g*c**2 + 0 + 0*c - 2/3*c**3 = 0.
0, 1, 2
Determine u, given that -12/7*u - 20/7*u**2 + 16/7 + 12/7*u**3 + 4/7*u**4 = 0.
-4, -1, 1
Suppose 2*a = -3*y - 0*y + 1, y + 3*a = 5. Let p be 0 + (y - (0 + -18)). Factor 19*j - 16*j + 20*j**4 - 4*j**5 - 16*j**3 - 4*j**4 - 8 - 8*j**2 + p*j.
-4*(j - 2)*(j - 1)**3*(j + 1)
Suppose -k + 37 = 4*d - 8, 3*k - 51 = -5*d. What is b in -d*b**2 - 3*b - 12*b**3 - 2*b + b - 4*b**4 = 0?
-1, 0
Factor 315*g - 2*g**2 + 47 - 4*g**2 - 177 + 31*g**2.
5*(g + 13)*(5*g - 2)
Let o(n) be the third derivative of -n**7/280 + n**6/40 - n**5/16 + n**4/16 + 58*n**2 - 2. Solve o(w) = 0.
0, 1, 2
Let k(a) be the first derivative of -a**6/840 + a**5/420 + a**4/84 + 3*a**2/2 - 19. Let x(o) be the second derivative of k(o). Factor x(j).
-j*(j - 2)*(j + 1)/7
Suppose 45/2 - 51/2*k + 3/2*k**2 + 3/2*k**3 = 0. Calculate k.
-5, 1, 3
Suppose 2*c = 3*l - 8*l + 14, -3*l = -4*c + 2. Factor 21/8*o - 3/2*o**c + 3/4.
-3*(o - 2)*(4*o + 1)/8
Let p = 2/6787 - -20351/33935. Let p - 13/10*z - 1/2*z**2 = 0. Calculate z.
-3, 2/5
Suppose -20/3*m - 1/3 - 100/3*m**2 = 0. What is m?
-1/10
Let p(h) = -h**2 - 11*h - 7. Let g be p(-11). Let d be ((-6)/g)/((-2)/(-14)). Solve -15*a**3 + 9 - 42*a**3 + 3 + d*a + 75*a**2 + 21*a**4 - 54*a - 3*a**5 = 0.
1, 2
Let l = 66 + -66. Factor l*i + 6 + 84*i**2 - 87*i**2 + 3*i.
-3*(i - 2)*(i + 1)
Let d(b) be the first derivative of b**7/336 + b**6/72 + b**5/48 - 5*b**3/3 + 11. Let k(x) be the third derivative of d(x). F