 8. Let w(m) = -c(m) - 13*g(m). Factor w(s).
2*(s + 1)*(s + 2043)
Let y(s) be the first derivative of -s**6/120 - 7*s**5/60 + s**4/3 + 58*s**2 - 90. Let t(v) be the second derivative of y(v). Factor t(p).
-p*(p - 1)*(p + 8)
Let i(y) = 10*y**2 + 48*y + 44. Let o(d) = d - d - 6*d**2 + 17*d**2 - 12*d**2. Let s(t) = i(t) + 6*o(t). Factor s(j).
4*(j + 1)*(j + 11)
Let l(m) be the second derivative of -3*m**6/10 - 33*m**5/4 - 419*m**4/6 - 454*m**3/3 - 140*m**2 + 204*m - 2. Find h such that l(h) = 0.
-10, -7, -2/3
Suppose -3313*g**2 + 1080*g + 1692*g**3 + 20*g**4 - 847*g**2 + 312*g = 0. Calculate g.
-87, 0, 2/5, 2
Let k(b) be the second derivative of -1/45*b**5 - 2/9*b**3 + 45*b + 1/9*b**4 + 2/9*b**2 + 0. Let k(m) = 0. What is m?
1
Let x = -42 + 52. Solve -x + 8*s + 9*s**4 - 15*s**2 - 2*s - 4*s**4 + 19*s - 5*s**3 = 0.
-2, 1
Let m(w) be the second derivative of -w**9/15120 + w**8/2240 - w**6/180 - 7*w**4/2 - w - 3. Let u(g) be the third derivative of m(g). Factor u(v).
-v*(v - 2)**2*(v + 1)
Let n be (-133)/28*4 + 23. Factor -6/5*y**2 + 3*y + 9/5 + 3/5*y**5 - 18/5*y**3 - 3/5*y**n.
3*(y - 3)*(y - 1)*(y + 1)**3/5
Factor -13/4*s**2 + 117 - 1/4*s**3 + 9*s.
-(s - 6)*(s + 6)*(s + 13)/4
Let y be ((-11)/((-11)/(-4)))/(1/(-5)). Let j be (-64)/12*(-15)/y. Let -4*a**5 - 36*a**3 + 3*a**j + 17*a**4 - a - 7*a + 28*a**2 = 0. Calculate a.
0, 1, 2
Let t(l) be the second derivative of -l**6/210 - 227*l**5/140 - 225*l**4/28 - 673*l**3/42 - 16*l**2 + 43*l - 4. Suppose t(k) = 0. Calculate k.
-224, -1
Suppose 52 = 5*d - 3*c, -70 + 36 = -3*d + 2*c. Suppose 175/2*p + 5/4*p**d + 6125/4 = 0. What is p?
-35
Let y(l) be the first derivative of 5*l**6/27 + 94*l**5/45 + 71*l**4/9 + 212*l**3/27 - 49*l**2/3 - 34*l - 5050. Solve y(o) = 0 for o.
-17/5, -3, -1, 1
Suppose 0*w - w = -3. Let n be 42/(-20) - (108/243 + (-53)/18). Factor 0 - 2/5*v**4 + 0*v**w + 0*v + n*v**2.
-2*v**2*(v - 1)*(v + 1)/5
Let a be (100/432*6 - 6/4)*-2. Let a*o**3 - 2/9*o + 10/9 - 22/9*o**2 + 4/3*o**4 = 0. What is o?
-1, 5/6, 1
Let b(z) = -z**2 + 195*z - 2518. Let y be b(14). Factor 7/2*q**3 + 27/2*q**2 + 6 + y*q.
(q + 1)*(q + 2)*(7*q + 6)/2
Let g(c) be the third derivative of c**5/240 + 97*c**4/48 - 65*c**3/8 + c**2 - 115*c - 2. Determine k, given that g(k) = 0.
-195, 1
Let v(f) = 7*f + 5. Let k be v(0). Suppose k*s**4 - 23*s**2 - 24*s - 7*s**2 + 28*s**3 - 31*s**3 - 2*s**4 = 0. Calculate s.
-2, -1, 0, 4
Let y(i) = -9980*i + 89823. Let d be y(9). What is o in 0*o - 6/11*o**4 + 0*o**d + 8/11*o**2 - 2/11*o**5 + 0 = 0?
-2, 0, 1
Suppose 49*q = -29*q. Let r(t) be the first derivative of 9/28*t**4 + 0*t + q*t**2 + 23 + 1/7*t**3. Let r(l) = 0. What is l?
-1/3, 0
Let w(f) be the third derivative of 0*f**3 - 1/20*f**4 + 2 + 31*f**2 - 1/50*f**6 + 1/20*f**5 + 0*f + 1/350*f**7. Factor w(u).
3*u*(u - 2)*(u - 1)**2/5
Suppose -3*h = 4*l - 5, -3*h + 4*h = -5. Suppose j - 2*i + 36 = l*j, -2*j - 5*i + 26 = 0. Let -j*m - 7*m + m**2 + 2 + 18*m = 0. What is m?
-2, -1
Let r(p) be the third derivative of p**7/8820 - p**6/630 - p**5/35 - 3*p**4 - 29*p**2. Let n(v) be the second derivative of r(v). Factor n(j).
2*(j - 6)*(j + 2)/7
Let b(s) be the second derivative of -s**4/60 + 32*s**3/5 + 194*s**2/5 - 5*s + 390. Factor b(c).
-(c - 194)*(c + 2)/5
Factor 4 - 30/7*m**3 + 26/7*m - 32/7*m**2.
-2*(m + 1)**2*(15*m - 14)/7
Factor 40*h**2 - 10*h**2 - 2304324 + 6072*h - 34*h**2.
-4*(h - 759)**2
Suppose -37*f + 27*f + 30 = 0. Determine v, given that -6 - 6 + v**2 - 6*v + 2*v**3 - v**f - 2*v = 0.
-2, 3
Let l be (22/112 - (-40)/(-320))*80/20. Find z such that -12/7*z + l*z**2 - 2 = 0.
-1, 7
Let d(h) be the third derivative of -h**5/60 + 221*h**4/12 + 443*h**3/6 + 12*h**2 - 2*h. Let d(i) = 0. What is i?
-1, 443
Factor -2/9*g**3 + 20/9*g - 16/9 - 2/9*g**2.
-2*(g - 2)*(g - 1)*(g + 4)/9
Let t = 101323/7506 - -4/3753. Suppose 3/4*n**3 + 99/4*n + t*n**2 + 12 = 0. Calculate n.
-16, -1
Suppose -2*u = -q - 23, 3*u + 13 = 4*u - 2*q. Suppose u*f - 20*f + 108 = 0. Solve -16*h + f*h**3 + 0*h**4 - 4*h**4 + 8*h**4 = 0 for h.
-2, 0, 1
Let y(s) = s**2 + 2 + 23*s + 0*s**3 - 13*s**2 - 12*s + s**3. Let j be y(11). Suppose 0*v**j + 1/2*v**3 - 1/2*v + 0 = 0. Calculate v.
-1, 0, 1
Let r = -79 - -96. Suppose r*n**3 - n**4 - 33*n**3 - 3*n**4 = 0. What is n?
-4, 0
Let y = 7/12 - 1/4. Let u = -7023 - -7023. Suppose u*k**2 + 1/6*k**3 + y - 1/2*k = 0. What is k?
-2, 1
Suppose -4*s**5 + 8*s**4 + 820973*s**3 - 820873*s**3 + 32*s**4 - 96*s - 40*s**2 = 0. Calculate s.
-2, -1, 0, 1, 12
Let p be (2 - -3)*68/238. Let i(s) be the first derivative of -38 - 17/7*s**2 - 3/14*s**4 - 12/7*s - p*s**3 + 2/35*s**5. Suppose i(u) = 0. Calculate u.
-1, 6
Find q, given that -1704*q**3 - 2*q**5 + 419*q**3 - 1585*q**2 - 118*q**4 - 217*q**4 - 366*q - 264*q - 3*q**5 = 0.
-63, -2, -1, 0
Let h(u) be the second derivative of 17*u**7/1120 - u**6/240 - 71*u**3/6 - u - 8. Let v(x) be the second derivative of h(x). Suppose v(j) = 0. Calculate j.
0, 2/17
Suppose 4*i = 4*k - 76, 4*k + k + i - 107 = 0. Let c be (63/k)/(6/4). Suppose -1/4*u + 0 - 1/4*u**c = 0. What is u?
-1, 0
Let i = -1451146/3 - -483719. Determine g so that -1/3*g**2 - i*g - 28/3 = 0.
-7, -4
Suppose 9*s = 45*s - 432. Suppose 4*l + 10 = 5*i, s*i - 7*i = -5*l + 10. Factor 0 + 1/3*b**i + 0*b.
b**2/3
Let f(u) = 2*u**2 + 7*u - 27. Let w be f(-6). Determine c, given that -2*c**5 + 2*c**3 + 2*c**4 - 8*c**2 + 0*c**3 + 7*c**3 - c**w = 0.
-2, 0, 1, 2
Find d, given that -10935 + 18787*d + 2*d**3 - 21622*d - 91*d**2 - 7*d**3 - 134*d**2 = 0.
-27, -9
Factor -209952/11 + 1/11*b**3 + 106272/11*b - 650/11*b**2.
(b - 324)**2*(b - 2)/11
Let i be 21*((-16)/3 - -7). Suppose 0 = -i*t - 0*t + 140. Solve 5/6*v**3 + 4/3 - 1/6*v**t - v**2 - 2/3*v = 0 for v.
-1, 2
Suppose 186*a - 105*a - 67*a = 0. Factor a*u**2 + 0 - 3/2*u**3 + 6*u.
-3*u*(u - 2)*(u + 2)/2
Factor -635/7*s + 1/7*s**2 + 1266/7.
(s - 633)*(s - 2)/7
Let y be -1 - ((-81)/27 - 0/1). Factor 0*m**4 - m + 16*m**2 + 0*m + 7*m**3 + 4*m**4 - 14*m**y.
m*(m + 1)**2*(4*m - 1)
Suppose i = -4*o - 3*i + 48, 5*i - 28 = -3*o. Suppose o = -50*l + 54*l. Solve -100 - 140*a - 14*a**3 + 7*a**4 + 10*a**4 - 69*a**2 - 18*a**l = 0 for a.
-5, -2
Let l(r) be the first derivative of -2*r**3/51 - 310*r**2/17 - 48050*r/17 + 224. Factor l(a).
-2*(a + 155)**2/17
Let a = -442 - -449. Factor 3*y + 39*y - y**2 + 21*y + a*y - 1225.
-(y - 35)**2
Let b = 86 + -83. Let k = -1100 - -1100. Factor k*p**2 + 0 - 1/3*p**5 - 2/3*p**4 + 0*p + 0*p**b.
-p**4*(p + 2)/3
Suppose 2214*p**2 - 8 - 1104*p**2 - 1120*p**2 + 14*p**3 - 32*p = 0. What is p?
-1, -2/7, 2
Factor 56/11*q - 490/11 + 2/11*q**2.
2*(q - 7)*(q + 35)/11
Let i = 3908 + -832402/213. Let y = 278/639 + i. Factor -y*t**2 + 2/9*t**3 - 8/9 - 14/9*t.
2*(t - 4)*(t + 1)**2/9
Suppose -28*k + 21*k = -56. Let x be (2 + (-6)/(-8) + -2)*k. Factor 2*o**4 - 9*o**5 + x*o**3 - 12 + o**4 + 12.
-3*o**3*(o - 1)*(3*o + 2)
Suppose -3*f + 8 = 4*x, -3*x + 4*x - 3*f - 2 = 0. Let a be 0/(x*((-18)/(-4) - 3)). Factor a*h - 1/6*h**4 + 1/6*h**2 - 1/6*h**3 + 1/6*h**5 + 0.
h**2*(h - 1)**2*(h + 1)/6
Let u(l) = 2*l**2 + 60*l + 34. Let w be u(-29). Let t(p) = p - 3. Let r(o) = 4*o**2 - 144*o - 52. Let f(x) = w*t(x) - r(x). Solve f(y) = 0.
-1, 31
Let r(u) be the first derivative of 32/5*u**2 - 31 - 64/5*u - 7/10*u**4 + 4/5*u**3 + 2/25*u**5. Factor r(x).
2*(x - 4)**2*(x - 1)*(x + 2)/5
Let b(v) be the third derivative of -1/120*v**6 - 9*v + 0*v**5 - 1/3*v**3 + 0 + 1/8*v**4 + 2*v**2. Factor b(g).
-(g - 1)**2*(g + 2)
Let k(x) be the third derivative of -x**8/84 - 16*x**7/35 - 17*x**6/6 - 34*x**5/5 - 20*x**4/3 + x**2 + 2. Solve k(r) = 0.
-20, -2, -1, 0
Let b = -177756 + 1244332/7. Solve -2/7*z**3 - b*z**2 + 86/7*z - 44/7 = 0 for z.
-22, 1
Let v(p) be the first derivative of -5*p**6/6 + 32*p**5 - 390*p**4 + 4480*p**3/3 - 1960*p**2 + 1056. Factor v(a).
-5*a*(a - 14)**2*(a - 2)**2
Let j(p) be the second derivative of 0*p**2 + 0*p**4 - 10*p - 1/50*p**6 + 0*p**5 + 0 - 1/70*p**7 + 0*p**3. Suppose j(d) = 0. What is d?
-1, 0
Find u such that -2/3*u**2 + 1090/3*u + 0 = 0.
0, 545
Suppose 0 = z + 12*z - 897. Let x = -66 + z. Find u such that -3/4*u**x + 0 - 1/4*u - 1/4*u**4 - 3/4*u**2 = 0.
-1, 0
Let f(k) be the first derivative of 324*k - 92 + 1/3*k**3 - 18*k**2. Factor f(z).
(z - 18)**2
Let h(f) be the first derivative of 10*f + 86 + 15/4*f**4