8. Let n(h) = 5*k(h) - 18*v(h). Factor n(x).
2*(x + 116)**2
Let d = 225 - -36. Let i = d - 259. Factor 1/12*z**i + z + 3.
(z + 6)**2/12
Let d(p) = 2*p**3 + 2*p**2 + 3. Let v(w) = -12*w**3 + 88*w**2 - 1598*w + 8655. Let r(b) = 10*d(b) + 2*v(b). Factor r(j).
-4*(j - 17)**2*(j - 15)
Factor -2/9*s**2 + 128/3 + 122/9*s.
-2*(s - 64)*(s + 3)/9
Suppose -4*t + 4*d + 40 = 0, 0*t = 3*t + 2*d - 40. Let g = t + -6. Factor 0*b - 6*b**2 + 0*b**3 + g + 3*b**3 - 3*b.
3*(b - 2)*(b - 1)*(b + 1)
Let b be 16/(-80)*(-4 - -5)*(-18 + 9). Factor -1/5*i**4 + 7/5*i - b*i**2 - 2/5 + i**3.
-(i - 2)*(i - 1)**3/5
Suppose w + 2*w - l - 11 = 0, 5*w = -4*l - 10. Let f be 1/5*107 + 6/(-15). Factor 90*y**3 - f*y**4 - 8*y**2 - 89*y**w + 5*y + 10*y**2 + 13*y.
-3*y*(y - 3)*(y - 1)*(7*y - 2)
Let x be ((-12)/(-20))/((-180)/150) - 2/(-4). Factor 6/5*c**2 + x*c + 2/5*c**4 + 2/5*c**5 - 2*c**3 + 0.
2*c**2*(c - 1)**2*(c + 3)/5
Factor -1017267 + 4*r**2 - 6275*r + 1024163 - 625*r.
4*(r - 1724)*(r - 1)
Let s = -41/1500 + 11/250. Let o(c) be the second derivative of 0 + s*c**5 + 4/9*c**3 - 5/36*c**4 - 9*c - 2/3*c**2. Determine v so that o(v) = 0.
1, 2
Suppose -697*m + 669*m = 0. Let y(k) be the third derivative of 0 + 1/180*k**5 - 1/24*k**4 + m*k + 10*k**2 + 1/9*k**3. Suppose y(z) = 0. Calculate z.
1, 2
Factor -54*q**2 + 2/5*q**4 - 128/5*q**3 + 0 + 396/5*q.
2*q*(q - 66)*(q - 1)*(q + 3)/5
Suppose -2*d + 5*d - 12 = 0. Find v, given that 37 + v**2 - 180*v + 35 - 10 - d + 211*v = 0.
-29, -2
Let x be (-44)/(-48) - -10*(-1)/40. Factor 0 - 10/3*a**3 + 0*a + x*a**4 + 8/3*a**2.
2*a**2*(a - 4)*(a - 1)/3
Let t(i) be the second derivative of i**4/32 - 341*i**3/8 - 796*i + 4. Factor t(y).
3*y*(y - 682)/8
Let o = 6504/332855 - 86482033348/2026088385. Let v = 4/2029 - o. Let 2/3*h**2 + v - 32/3*h = 0. Calculate h.
8
Suppose -282/13*s**3 - 2478/13*s - 1826/13*s**2 + 8/13*s**4 + 738/13 = 0. What is s?
-3, 1/4, 41
Let l(y) = 12*y**3 - 276*y**2 + 2101*y - 5398. Let n(o) = 9*o**3 - 207*o**2 + 1576*o - 4048. Let c(w) = 8*l(w) - 11*n(w). Determine s, given that c(s) = 0.
7, 8
Solve -10/9*v**2 + 0 + 0*v + 68/9*v**3 + 14/9*v**4 = 0 for v.
-5, 0, 1/7
Factor 198*v + 37*v + 3*v**2 - 211*v + 45.
3*(v + 3)*(v + 5)
Suppose -672*y - 40*y**2 - 2/3*y**3 - 6272/3 = 0. Calculate y.
-28, -4
Suppose 228/11 - 108/11*p**4 - 6/11*p**5 + 312/11*p**2 + 12*p**3 - 558/11*p = 0. What is p?
-19, -2, 1
Let p(y) = 6*y**2 + 9*y**2 - 10*y + 6*y**3 + 3 - 7*y**4 - 11*y**2. Let d(l) = -2*l**4 + l**3 + l**2 - 2*l + 1. Let h(s) = -12*d(s) + 3*p(s). Solve h(f) = 0.
-1, 1
Factor -114/5*t - 2/5*t**2 + 72.
-2*(t - 3)*(t + 60)/5
Let l(n) be the first derivative of -n**6/6 - 5*n**5/4 - 5*n**4/3 - 309*n + 145. Let x(b) be the first derivative of l(b). Factor x(j).
-5*j**2*(j + 1)*(j + 4)
Let k(w) = 68*w**2 + 4448*w + 1777. Let l(f) = 91*f**2 + 5931*f + 2369. Let s(g) = -9*k(g) + 7*l(g). What is i in s(i) = 0?
-59, -2/5
Let f(m) = -m**2 - 6*m + 21. Let a be f(-8). Find q such that -43 + a*q**2 - 3*q + 43 - 32*q = 0.
0, 7
Suppose -3*y = -c - 2*y + 7, -3*c + 26 = -4*y. Factor 22 + 13*b**2 - 17*b**2 - 17*b + b**3 - 6*b**c + 4*b.
(b - 11)*(b - 1)*(b + 2)
Let u(h) be the first derivative of h**4/26 - 186*h**3/13 + 19599*h**2/13 - 38642*h/13 + 1470. Factor u(w).
2*(w - 139)**2*(w - 1)/13
Suppose 0 = 58168*k - 58247*k. Determine t, given that 3/7*t**5 + 30/7*t**4 + 96/7*t**2 + 0*t + 96/7*t**3 + k = 0.
-4, -2, 0
Let r be (-2)/6*2/(-8)*-12. Let h(x) = 2*x**2 + 2*x**4 + x**5 - 3*x + 3*x - x**3. Let m(w) = -w**5 - w**2. Let b(u) = r*h(u) - 2*m(u). What is j in b(j) = 0?
0, 1
Let i(h) be the first derivative of 43 + 2/5*h**5 - 5/2*h**4 + 0*h + 4*h**3 + 0*h**2. Factor i(c).
2*c**2*(c - 3)*(c - 2)
Factor 543/2*r + 1/4*r**2 + 1085/4.
(r + 1)*(r + 1085)/4
Let z be 4*8/(-32)*0/35. Determine f, given that -56/11*f**2 - 130/11*f**3 + z - 30/11*f**5 - 112/11*f**4 - 8/11*f = 0.
-2, -1, -2/5, -1/3, 0
Let r = -7221 - -7232. Let h(f) be the first derivative of -20/3*f**3 + r + 75/16*f**4 - 25/24*f**6 + 1/2*f**5 + 5/2*f**2 + 0*f. Let h(a) = 0. Calculate a.
-2, 0, 2/5, 1
Find g, given that -115*g**3 - 825*g**2 - 5946*g + 2*g**4 + 6131*g - 70*g**3 + 3*g**4 + 820 = 0.
-4, -1, 1, 41
Suppose 4*l - 5*r = 101, -70*r + 65*r - 5 = 0. Let v(m) be the second derivative of 2/9*m**3 + 1/54*m**4 + 5/9*m**2 + 0 + l*m. Determine i, given that v(i) = 0.
-5, -1
Let f be (-192)/(-2976)*(-124)/(-20). Factor -4/5*u + 4/5*u**3 - f*u**4 + 2/5*u**2 + 0.
-2*u*(u - 2)*(u - 1)*(u + 1)/5
Let s be ((8/(-20))/((-4)/(-5)))/(16082/(-34056)). Factor 0 + 2/17*r**4 - 2*r**2 - 14/17*r**3 - s*r.
2*r*(r - 9)*(r + 1)**2/17
Suppose 0 = -65*h + 286 - 91. Suppose 2*l - 6 + 0 = 0. Suppose -4*o + 4*o - 169*o**h - 80*o**4 - 80*o**2 + 29*o**l - 15*o**5 = 0. What is o?
-2, -4/3, 0
Let i(l) be the third derivative of l**5/60 + 199*l**4/8 - 599*l**3/3 - 957*l**2 - 2*l. Suppose i(a) = 0. Calculate a.
-599, 2
Let d(q) = 28*q**3 - 160*q**2 - 172*q + 80. Let c(a) = -2*a**3 + a - 5. Let j(z) = 16*c(z) + d(z). Factor j(m).
-4*m*(m + 1)*(m + 39)
Let b(r) be the second derivative of -1/20*r**5 + 1/7*r**3 - 1/210*r**6 + 1/294*r**7 + 7 + 2*r + 0*r**2 + 1/84*r**4. Solve b(g) = 0 for g.
-2, -1, 0, 1, 3
Let v(s) be the second derivative of -s**5/90 - 65*s**4/54 - 127*s**3/27 - 7*s**2 - 3*s + 238. Let v(m) = 0. Calculate m.
-63, -1
Factor 0 + 51*r**3 - 1/2*r**4 + 105/2*r**2 - 103*r.
-r*(r - 103)*(r - 1)*(r + 2)/2
Let g(k) be the second derivative of k**10/10080 + k**9/630 + k**8/140 + 19*k**4/12 - 91*k. Let x(u) be the third derivative of g(u). Let x(z) = 0. What is z?
-4, 0
Let o(u) be the third derivative of -u**7/490 - u**6/315 + u**5/210 + 4*u**3 + 4*u**2 - 6. Let x(d) be the first derivative of o(d). What is i in x(i) = 0?
-1, 0, 1/3
Let n(s) = s**3 - 3*s**2 - 3*s - 5. Let j be n(4). Let m(t) = -t - 1. Let d(c) = -4*c**2 - 21*c - 17. Let g(f) = j*d(f) + 5*m(f). Factor g(b).
4*(b + 1)*(b + 3)
Let r(o) be the first derivative of -o**6/90 - o**5/30 + o**4 - 2*o**3 - 5*o**2/2 - 70. Let q(z) be the third derivative of r(z). Let q(y) = 0. What is y?
-3, 2
Let t(d) be the second derivative of -d - 6 + 35/2*d**2 - 20/3*d**3 + 5/12*d**4. Factor t(c).
5*(c - 7)*(c - 1)
Let r(k) be the third derivative of k**7/1260 + k**6/27 + 19*k**5/180 - 11*k**3/6 - k**2 - 3*k. Let p(b) be the first derivative of r(b). What is q in p(q) = 0?
-19, -1, 0
Suppose -1197 = 32*f - 51*f. Suppose 0 = -18*g + 9 + f. Suppose 0 + 8/19*q**3 - 2/19*q**2 - 8/19*q**g + 0*q = 0. What is q?
0, 1/2
Determine q, given that -11*q**3 + 9*q**4 - 2*q**4 + 12*q - 2*q**5 + 477*q**2 + q**5 + 472*q**2 - 956*q**2 = 0.
-1, 0, 1, 3, 4
Factor -3225/4 - 99/4*w**2 - 1215/4*w + 3/4*w**3.
3*(w - 43)*(w + 5)**2/4
Suppose 1679 = -135*f + 2219. Let n(i) be the first derivative of 36/13*i**2 - 8/65*i**5 + 10 + 49/26*i**f + 0*i - 8*i**3. Factor n(a).
-2*a*(a - 6)**2*(4*a - 1)/13
Suppose -2*z = -2*d + 7 - 11, 14 = z + 5*d. Let x be 18/z - (-9 + 17 - 5). Solve -3*c**3 + 0*c - 3/2*c**2 - x*c**4 + 0 = 0 for c.
-1, 0
Let r(k) be the second derivative of -k**4/3 - 152*k**3/3 - 150*k**2 - 2*k + 5134. Solve r(h) = 0.
-75, -1
Factor -5972/3*q**2 + 4*q + 0.
-4*q*(1493*q - 3)/3
Let x(l) be the third derivative of l**5/30 + l**4/4 - 130*l**3/3 - 24*l**2 - 17*l. Let x(o) = 0. What is o?
-13, 10
Let z(a) be the second derivative of a**3 + 1 - 9*a**2 - 1/30*a**5 + 1/6*a**4 + 6*a. Suppose z(x) = 0. Calculate x.
-3, 3
Factor 75/4*m + 0 + 1/4*m**2.
m*(m + 75)/4
Suppose 0 = 6*j + 35 - 59. Solve 43 - 38 - 13 - j*y**2 - 16 - 28*y = 0 for y.
-6, -1
Let z = -349221 - -1047665/3. Find k, given that z*k**3 + 2048*k + 65536/3 + 64*k**2 = 0.
-32
Let o be (-1)/(6/(-5836)) + (11143 - 11153). Factor o + 2/3*m**2 + 152/3*m.
2*(m + 38)**2/3
Let d = 20231 + -20231. Let c(l) be the third derivative of -2/105*l**7 - 1/56*l**8 + 0*l**3 + 1/60*l**6 + 0*l**4 + d*l + 0 + 0*l**5 - 31*l**2. Factor c(g).
-2*g**3*(g + 1)*(3*g - 1)
Let i be (-40)/32*(-64)/20. Let g(t) be the first derivative of t**5 + 30*t**3 + 7 + 35/4*t**i + 40*t + 50*t**2. Factor g(x).
5*(x + 1)*(x + 2)**3
Let b(d) be the second derivative of 0 + 1/10*d**5 + 148*d - 11/3*d**3 - 6*d**2 - 2/3*d**4. Factor b(s).
2*(s - 6)*(s + 1)**2
Find k, given that 173*k + 255*k - 975*k + 5*k**2 - 1350 - 798*k = 0.
-1, 270
Let b(h) = -h**2 + 12*h - 17. Let p = 743 + -741. Let u be b(p