b.
-1, 0, 1/2
Let o = -9/10 + 26/15. Let g(l) be the first derivative of o*l**3 + 1/2*l**4 + 1/4*l**2 - 2 + 0*l. Factor g(r).
r*(r + 1)*(4*r + 1)/2
Suppose 35/2*z**2 + 1/2*z**3 + 64*z + 62 = 0. What is z?
-31, -2
Let f be (11/4)/((-2)/(-16)). Let c = -5 + f. Determine t, given that 16*t**2 + 4*t**5 + c*t**4 + 3*t**4 + 0*t**5 + 32*t**3 = 0.
-2, -1, 0
Let h = 199/30 + -35/6. Let m(g) be the first derivative of h*g + 3 + 3/5*g**2 + 2/15*g**3. Factor m(k).
2*(k + 1)*(k + 2)/5
Let a(u) be the first derivative of u**6/15 - 12*u**5/25 - u**4/5 + 8*u**3/5 + u**2/5 - 12*u/5 - 95. What is v in a(v) = 0?
-1, 1, 6
Determine u, given that 5/3*u**3 + 30*u + 0 + 15*u**2 = 0.
-6, -3, 0
Suppose -3*w + 59 + 12 = m, -w + 5*m = -13. Let a = -21 + w. Solve 3/2*b**3 + 2 + 0*b - 7/2*b**a = 0 for b.
-2/3, 1, 2
Let v(h) be the first derivative of -h**6/6 + 4*h**5 - 67*h**4/2 + 340*h**3/3 - 225*h**2/2 - 8. Determine u so that v(u) = 0.
0, 1, 5, 9
Let d = -117 - -52. Let r = d + 65. Factor 2/5*s**2 + 0 + 0*s - 2/5*s**4 + r*s**3.
-2*s**2*(s - 1)*(s + 1)/5
Solve 2312/11 + 2/11*g**2 + 136/11*g = 0 for g.
-34
Let p(b) be the second derivative of -13*b**7/14 - 14*b**6/5 - 51*b**5/20 - b**4/2 + 38*b - 1. Factor p(r).
-3*r**2*(r + 1)**2*(13*r + 2)
Let p(l) = -l**3 + 5*l**2 + 4*l + 20. Let v be p(6). Let -136*a**3 + 0*a**2 + 140*a**3 + 0*a**2 - v*a**2 + 4*a = 0. What is a?
0, 1
Solve -80*s**3 - 31*s**3 + 128*s + 47*s**3 - 2*s**5 - 62*s**3 + 68*s**4 - 68*s**2 = 0.
-1, 0, 1, 2, 32
Let k(q) be the first derivative of -q**5/300 - q**4/120 - q**2 - 10. Let c(v) be the second derivative of k(v). Find x, given that c(x) = 0.
-1, 0
Let y(p) be the first derivative of 1/4*p**4 - p**2 - 6 - 4*p + 5/3*p**3. Let r(b) = -b**3 - 10*b**2 + 3*b + 8. Let h(f) = -2*r(f) - 5*y(f). Factor h(i).
-(i - 1)*(i + 2)*(3*i + 2)
Let m be ((-10)/(-6))/5 + 105/9. Factor -29*g + 2*g**3 + 38*g - m - 23*g.
2*(g - 3)*(g + 1)*(g + 2)
Determine o so that -20*o**2 - 7299 + 5*o + 7299 = 0.
0, 1/4
Let a = -13 - -13. Suppose -6*d = -d - m - 17, 5*m + 10 = a. Factor -o**2 - o**2 - 6*o + 5*o - o**d.
-o*(o + 1)**2
Let p = 9213 + -9210. Factor -3/4*j**3 - p + 3*j**2 + 3/4*j.
-3*(j - 4)*(j - 1)*(j + 1)/4
Factor -155 - 3*o**2 + 0*o**2 + 5 - 4*o**2 - 85*o + 2*o**2.
-5*(o + 2)*(o + 15)
Suppose -8 = j - 5*j. Factor -5*k**2 - 40*k - 2*k**2 + 3*k**j - 105 + 5.
-4*(k + 5)**2
Let b = -69 - -209/3. Let q be (544/(-102))/(6/(-3)). Factor -8/3 - b*w**2 - q*w.
-2*(w + 2)**2/3
Let n = 118 - 111. Let d(b) be the second derivative of -1/105*b**n + 1/30*b**6 + 0 + 1/60*b**4 - 1/25*b**5 + 0*b**3 + 0*b**2 + 5*b. Factor d(m).
-m**2*(m - 1)**2*(2*m - 1)/5
Let x(d) = 13*d**2 - 31*d + 1. Let r(c) = c**2 - c - 1. Let f(h) = 2*r(h) - x(h). Let p(z) = -10*z**2 + 28*z - 4. Let o(g) = 2*f(g) - 3*p(g). Factor o(n).
2*(n - 3)*(4*n - 1)
Let c = -1/42084 + 7436845/42084. Let t = 177 - c. Factor 0*l**2 - 2/7*l**3 + t*l + 0.
-2*l*(l - 1)*(l + 1)/7
Determine a so that 8/5*a - 2/5*a**3 - 6/5*a**2 + 24/5 = 0.
-3, -2, 2
Let i be 46/(-667) - 679/(-1015). Factor v**3 - 2/5*v**2 + 0*v + i*v**4 + 0.
v**2*(v + 2)*(3*v - 1)/5
Let i(w) be the second derivative of 7/4*w**4 - 6*w**2 - 16*w + 0 - 6*w**3. Let i(t) = 0. Calculate t.
-2/7, 2
Suppose 1/2*a**2 - 47/2 + 23*a = 0. What is a?
-47, 1
Let y = 31/8 + -15/4. Let s(m) be the first derivative of -27/4*m**2 + 2 - y*m**4 - 27/2*m - 3/2*m**3. Determine f, given that s(f) = 0.
-3
Let z(d) be the first derivative of -d**4 + 40*d**3/3 - 42*d**2 - 731. Determine g, given that z(g) = 0.
0, 3, 7
Let -5*l**5 + 1058*l**3 - 136*l**2 + 20*l**4 - 214*l**2 - 723*l**3 = 0. Calculate l.
-7, 0, 1, 10
Let n(s) be the first derivative of 9 + 0*s + 5/2*s**2 + 0*s**3 - 1/540*s**6 - 1/135*s**5 + 0*s**4. Let c(g) be the second derivative of n(g). Factor c(p).
-2*p**2*(p + 2)/9
Let k be (-10)/(-35) - (-8)/(-28). Let w(j) be the second derivative of 1/3*j**3 + 5*j + 2/3*j**2 - 1/30*j**5 + k*j**4 + 0. Factor w(m).
-2*(m - 2)*(m + 1)**2/3
Suppose -3*m - 3*v + 19 = -5*v, v = 3*m - 20. Let w(i) be the second derivative of -4*i**3 + 1/4*i**4 + m*i + 24*i**2 + 0. Find h, given that w(h) = 0.
4
Let s(q) = -q**2 - 10*q + 13. Let t be s(-10). Let m(o) = o**2 - 13*o + 3. Let r be m(t). Factor 24*n**2 + 16*n**3 + 4*n**4 + 0*n**r + 3 + 1 + 16*n.
4*(n + 1)**4
Let j be 6 - (-3)/(15/(-362)). Let k = j - -67. Factor -k*d**5 + 0 + 0*d**3 + 6/5*d**4 + 3/5*d - 6/5*d**2.
-3*d*(d - 1)**3*(d + 1)/5
Factor 8/5 + 6/5*i**2 + 1/5*i**3 + 12/5*i.
(i + 2)**3/5
Suppose -180 = 53*w - 27*w - 41*w. Factor w*h - 20/3 - 4*h**2 - 4/3*h**3.
-4*(h - 1)**2*(h + 5)/3
Let i(u) = 11*u**4 - 129*u**3 + 189*u**2 - 9*u. Let r(j) = -3*j**4 + 32*j**3 - 47*j**2 + 2*j. Let v(m) = -2*i(m) - 9*r(m). Let v(c) = 0. What is c?
0, 3
Let n(y) be the first derivative of -2*y**6/3 + 4*y**5/5 + 3*y**4 - 4*y**3/3 - 4*y**2 + 51. Find t such that n(t) = 0.
-1, 0, 1, 2
Let h(p) be the third derivative of 2*p**7/735 - p**6/42 + p**5/35 + 5*p**4/42 - 8*p**3/21 + 42*p**2. Find k such that h(k) = 0.
-1, 1, 4
Suppose -84 = 9*d - 21*d. Let b(y) be the third derivative of 0*y**6 + 0*y**3 + 0*y**4 + 0 - d*y**2 - 1/1680*y**8 + 0*y + 1/1050*y**7 + 0*y**5. Factor b(p).
-p**4*(p - 1)/5
Let l(w) = w**2 + 41*w + 8. Let r(g) = -g**2 - 40*g - 10. Let q(v) = -5*l(v) - 4*r(v). Determine z, given that q(z) = 0.
-45, 0
Let q be 5*(16/88 + 24/110). Factor 0 - 2/11*s - 6/11*s**3 - 2/11*s**4 - 6/11*s**q.
-2*s*(s + 1)**3/11
Factor 19/3*o + 22 - 1/3*o**2.
-(o - 22)*(o + 3)/3
Suppose 2*f - 32 = 5*u + 5*f, -u + 2*f + 4 = 0. Let l be u/(-32)*4*4/4. Factor -l*z**5 + 1/2*z - z**2 + z**4 + 0 + 0*z**3.
-z*(z - 1)**3*(z + 1)/2
Let i be (12/(-10))/(26/(-65)). Factor -2*x**2 - 5*x**i + 2*x**4 - 3*x - x + 9*x**3.
2*x*(x - 1)*(x + 1)*(x + 2)
Let m(r) be the second derivative of -5*r**4/12 - 15*r**3/2 - 20*r**2 + r - 15. Factor m(a).
-5*(a + 1)*(a + 8)
Let x = 50961 - 152882/3. Determine d, given that 0 + 1/2*d + 2/3*d**2 - 1/6*d**5 - x*d**3 - 2/3*d**4 = 0.
-3, -1, 0, 1
Suppose -329*p + 361*p - p**3 - 4 - 32 - 5*p**2 = 0. Calculate p.
-9, 2
Factor 114*y + 2420 + 5*y**2 - 8*y**2 + 0*y**2 + 106*y + 8*y**2.
5*(y + 22)**2
Let w(v) be the first derivative of -v**4/14 - 6*v**3/7 + 12*v**2/7 + 40*v/7 + 32. Determine l, given that w(l) = 0.
-10, -1, 2
Solve -32*u**4 - 40*u**2 - 449*u**3 + 881*u**3 - 4*u**5 - 500*u**3 = 0 for u.
-5, -2, -1, 0
Suppose 6 = 85*i - 82*i. Suppose 8*n + i*n - 40 = 0. Find a such that 0 + 0*a + 3/5*a**5 + 3/5*a**2 - 3/5*a**3 - 3/5*a**n = 0.
-1, 0, 1
Let u(y) be the third derivative of -y**7/140 + 21*y**6/32 - 1297*y**5/80 - 2133*y**4/32 - 729*y**3/8 - 2*y**2 + 24*y. Solve u(a) = 0 for a.
-1, -1/2, 27
Let s = 8224 + -8224. Factor s*a - 2 + 1/2*a**2.
(a - 2)*(a + 2)/2
Let q(n) = 6*n**5 - 24*n**4 - 24*n**3 - 9*n**2 + 30. Let d(o) = o**4 - 2. Let k(i) = -15*d(i) - q(i). Suppose k(v) = 0. What is v?
-1, -1/2, 0, 3
Let a(g) = -3 + 2 + 16*g - 20*g - g**2. Let p be a(-3). Factor -2 - 5*v**2 + 4*v + 3*v**2 + p*v - 2.
-2*(v - 2)*(v - 1)
Let 8*b**3 - 448*b - 40 + 140*b**3 - 312*b**2 - 12*b**4 + 130*b**2 - 118*b**2 + 652*b = 0. Calculate b.
1/3, 1, 10
Suppose 9 = 3*m - 3. What is q in -89*q + 5*q**2 + 89*q - 45*q**m - 45*q**5 + 5*q**3 = 0?
-1, -1/3, 0, 1/3
Factor 25 + 42*r - 89*r**2 + 13 + 92*r**2 + 37 - 3.
3*(r + 2)*(r + 12)
Let x(w) be the second derivative of -10*w**7/147 + 12*w**6/35 - 17*w**5/35 + 8*w**3/21 + 55*w. Determine z so that x(z) = 0.
-2/5, 0, 1, 2
Factor 104/5*v**3 - 72/5*v**2 - 36/5*v**4 - 108/5*v + 4/5*v**5 + 108/5.
4*(v - 3)**3*(v - 1)*(v + 1)/5
Let d(r) be the third derivative of 4/9*r**3 - 1/180*r**6 + 0 - 2/9*r**4 - 15*r**2 + 0*r + 1/18*r**5. Factor d(u).
-2*(u - 2)**2*(u - 1)/3
Let n(g) be the third derivative of 9*g**2 + 0 + 0*g**3 + 0*g - 1/40*g**4 - 1/100*g**5. Factor n(l).
-3*l*(l + 1)/5
Let y(g) be the third derivative of -g**7/490 + g**6/56 - g**5/20 + 3*g**4/56 - 82*g**2. Determine a so that y(a) = 0.
0, 1, 3
Let l(h) be the first derivative of -h**7/168 + h**5/40 - h**3/24 + 20*h - 1. Let m(t) be the first derivative of l(t). Factor m(k).
-k*(k - 1)**2*(k + 1)**2/4
Solve 4 + 58/3*o + 10/3*o**4 + 30*o**2 + 18*o**3 = 0 for o.
-3, -1, -2/5
Factor -66*u + 6*u - 900 + 24*u**2 - 25*u**2.
-(u + 30)**2
Let c be (16 - (-217)/(-7))/(-5). Factor -9/4*z**2 - 27/4*z + 3/4*z**c - 15/4.
3*(z - 5)*(z + 1)**2/4
Let 