8. Solve n(w) = 0 for w.
-5, 2
Factor -25520*g**2 - 35 + 672*g + 25521*g**2 - 638.
(g - 1)*(g + 673)
Factor 0 + 24/11*w**3 + 100/11*w - 2/11*w**4 - 90/11*w**2.
-2*w*(w - 5)**2*(w - 2)/11
Let f(l) be the second derivative of -l**5/5 - 3*l**4 - 46*l**3/3 - 30*l**2 - 3343*l. Suppose f(d) = 0. Calculate d.
-5, -3, -1
Let h be (-4 + 2 - 47)*8760/(-420). Let l = h - 10219/10. Factor 1/10*z**3 - l*z**5 + 0*z + 0 - 1/10*z**4 + 1/10*z**2.
-z**2*(z - 1)*(z + 1)**2/10
Let g(u) be the first derivative of -u**4/10 - 67*u**3/15 - 128*u**2/5 + 29*u - 1831. Determine f, given that g(f) = 0.
-29, -5, 1/2
Let n(k) be the first derivative of -10*k + 5/2*k**2 - 129 + 5/3*k**3. Factor n(f).
5*(f - 1)*(f + 2)
Factor 0 + 4/17*d**4 - 2/17*d**5 + 6/17*d**3 - 8/17*d**2 - 8/17*d.
-2*d*(d - 2)**2*(d + 1)**2/17
Suppose 2708*q - 2701*q - 420 = 0. Let f be ((-45)/(-6))/(210/q). Factor 12/7 + 24/7*d - f*d**2.
-3*(d - 2)*(5*d + 2)/7
Suppose 2286*s + 6145149/8*s**3 - 145161/2*s**2 - 24 = 0. Calculate s.
4/127
Let y(v) be the first derivative of v**4/10 + 38*v**3/15 + 31*v**2/5 - 102*v/5 - 241. Factor y(j).
2*(j - 1)*(j + 3)*(j + 17)/5
Let c(d) = -5*d**2 + 657*d + 698. Let l(v) = 14*v**2 - 1972*v - 2082. Let k(f) = 8*c(f) + 3*l(f). Find q, given that k(q) = 0.
-1, 331
Factor 36/7 - 38/7*b + 2/7*b**2.
2*(b - 18)*(b - 1)/7
Let z be (-7)/4 - (-180)/(-80). Let i be z/(-2) - (0/3)/5. Factor 2/3*s**4 + i*s + 2/3*s**2 - 2*s**3 - 4/3.
2*(s - 2)*(s - 1)**2*(s + 1)/3
Suppose 19*a = 32*a - 39. Suppose -2*c = -5*c + 4*n - 11, 2*c + 4*n = 26. Factor -c*o**a - 13 + 0*o**3 + 11*o - 3*o**2 + o**4 + 13 - 6.
(o - 3)*(o - 1)**2*(o + 2)
Suppose 23 + 9 = 4*o. Factor -26 - 5*c**2 + 35*c + 18 + o.
-5*c*(c - 7)
Let r(h) = -59*h**2 - 128*h + 835. Let k(t) = 25*t**2 + 64*t - 417. Let x(i) = -7*k(i) - 3*r(i). Factor x(w).
2*(w - 23)*(w - 9)
Let q(a) = -a**3 + 4*a**2 - 5*a + 23. Let h be q(4). Let x(n) be the first derivative of -13 + 0*n + 2/11*n**h - 18/11*n**2. Factor x(i).
6*i*(i - 6)/11
Let f = 263 - 277. Let u be 0/((-8)/f*7/2). Suppose u + 2/13*a**3 + 0*a + 0*a**2 = 0. Calculate a.
0
Let r(b) = -b**2 + 6*b + 42. Let i be r(10). Find x such that -2*x**i - 26083 + 26083 + x + x**3 = 0.
0, 1
Let l(n) be the second derivative of n**5/50 - 53*n**4/30 + 2*n - 437. What is m in l(m) = 0?
0, 53
Determine i, given that 4783*i**3 + 716*i**3 - 21904*i**2 + 180*i**4 + 100*i**4 - 1207*i**3 + 4*i**5 = 0.
-37, 0, 4
Let m(d) be the second derivative of -d**6/200 + 3*d**4/40 + d**3/5 - 35*d**2 - 95*d. Let k(t) be the first derivative of m(t). Factor k(c).
-3*(c - 2)*(c + 1)**2/5
Let k be 10/100*6 + 7/5. Suppose -150 = -37*c - k. Factor 89*w - 2 + 29435/4*w**3 - 2697/2*w**2 - 24389/4*w**c.
-(w - 1)*(29*w - 2)**3/4
Let l(x) be the first derivative of x**6/36 - 56*x**5/15 + 185*x**4 - 3600*x**3 - 4500*x**2 + 1080000*x - 2114. Factor l(n).
(n - 30)**4*(n + 8)/6
Let y(a) be the third derivative of -2*a**7/15 + 403*a**6/30 + 587*a**5/15 + 59*a**4/2 + 131*a**2 - 10*a. What is l in y(l) = 0?
-1, -3/7, 0, 59
Let p(i) be the first derivative of -3*i**4/28 - 47*i**3/7 + 1860*i**2/7 - 20100*i/7 - 6869. Solve p(m) = 0.
-67, 10
Factor -102152/3 - 2/3*u**2 + 904/3*u.
-2*(u - 226)**2/3
Let r(m) be the third derivative of -m**5/210 - 23*m**4/84 + 26*m**3/7 - 3576*m**2. Solve r(z) = 0 for z.
-26, 3
Let z(s) be the third derivative of -s**7/6300 - 13*s**6/450 - 169*s**5/75 - 119*s**4/24 - 8*s**2 + 3*s. Let x(a) be the second derivative of z(a). Factor x(g).
-2*(g + 26)**2/5
Let x be ((-4488)/440)/((2/(-20))/1). Let x*j**4 + 27*j**3 + 15*j**5 + 6*j**2 - 188*j**4 + 122*j**4 = 0. Calculate j.
-1, -2/5, 0
Let 33*k**2 + 191/2*k + 1/2*k**3 + 63 = 0. What is k?
-63, -2, -1
Let i = -1 + 1. Suppose 4*m + r + 2*r = -7, r = 2*m - 9. Solve -4*n - 7*n**2 + 75*n**3 - n**4 + 7*n + i*n**m - 70*n**3 = 0 for n.
0, 1, 3
Suppose 0 = -v - 2*l + 6, -3*v + 5*v = l + 2. Factor 0*n**3 + 2*n**4 + 2*n**3 - 4*n**v - 71*n**5 - 64*n**5 + 134*n**5 - n + 2.
-(n - 2)*(n - 1)**2*(n + 1)**2
Factor -106/5*p**2 + 2/5*p**3 - 40 + 304/5*p.
2*(p - 50)*(p - 2)*(p - 1)/5
Solve 546*q - 51*q**2 + 3/2*q**3 - 1764 = 0.
6, 14
Let v(f) be the second derivative of 3*f**6/5 + 8*f**5/5 - 38*f**4/3 + 16*f**3/3 + 288*f - 18. Solve v(o) = 0.
-4, 0, 2/9, 2
Let f(m) be the first derivative of -4107/16*m**2 + 0*m + 142 - 3/32*m**4 - 37/4*m**3. Factor f(z).
-3*z*(z + 37)**2/8
Let x(b) be the second derivative of b**5/25 - 167*b**4/15 - 674*b**3/15 - 338*b**2/5 - 6*b + 45. Factor x(z).
4*(z - 169)*(z + 1)**2/5
Factor -32*f**3 + 3070/9*f + 128/9 + 6128/3*f**2.
-2*(f - 64)*(12*f + 1)**2/9
Let m(d) be the third derivative of -d**5/150 - d**4/3 + 25*d**3/3 + 720*d**2. Let m(g) = 0. What is g?
-25, 5
Let l(t) = 15*t**3 + 969*t**2 - 1026*t - 6. Let w(i) = -43*i**3 - 2908*i**2 + 3070*i + 17. Let a(m) = 17*l(m) + 6*w(m). Factor a(r).
-3*r*(r - 1)*(r + 326)
Suppose 4*l = -2*p - 48, 240*l - 69 + 4 = 245*l. Solve 1/9*i**3 - 5/9*i**p - 4/9*i + 20/9 = 0.
-2, 2, 5
Let y = 1219 + -1217. Let h(v) be the second derivative of 1/60*v**5 + 13*v - 1/6*v**3 + 0 + 1/3*v**y + 0*v**4. Find a such that h(a) = 0.
-2, 1
Let t(z) be the first derivative of -z**4/6 + 494*z**3/9 - 487*z**2/3 - 490*z - 6352. Find v, given that t(v) = 0.
-1, 3, 245
Suppose 14*y = 4122 - 3912. Let g be (-3)/y*6/(120/(-25)). Find z such that -g*z**4 + 0 + z**2 + 0*z**3 + 0*z = 0.
-2, 0, 2
Factor 7/5 + 2673/5*d - 382/5*d**2.
-(d - 7)*(382*d + 1)/5
Let g be 30/(-42) + (-235)/1120*-4. Solve 0 + g*b + 1/4*b**2 - 3/8*b**3 = 0 for b.
-1/3, 0, 1
Let y(x) be the second derivative of -x**6/30 + 87*x**5/100 + 371*x**4/60 + 51*x**3/10 - 63*x**2/5 + 1741*x - 2. Solve y(s) = 0.
-3, -1, 2/5, 21
Let m be -1 - (-10)/(750/(-6055)). Let j = -407/5 - m. Suppose -j*a**2 - 2/3*a + 1 = 0. Calculate a.
-3, 1
Let v(i) = 37*i + 1 + 35*i**2 - 8 - 27*i + 87*i - 21. Let g(j) = 70*j**2 + 195*j - 55. Let q be 8/6*(-6)/(-4). Let u(n) = q*g(n) - 5*v(n). Factor u(r).
-5*(r + 3)*(7*r - 2)
Factor 30 + 8364*p**2 - 140 - 4178*p**2 - 27*p - 4187*p**2.
-(p + 5)*(p + 22)
Let f(y) be the second derivative of -y**6/6 + 12*y**5 - 455*y**4/12 - 40*y**3 + 230*y**2 - 147*y - 7. Suppose f(t) = 0. What is t?
-1, 1, 2, 46
Let q(z) be the third derivative of z**7/105 + 7*z**6/20 - 33*z**5/5 - 253*z**4/3 - 360*z**3 + 2*z**2 + 873. Solve q(u) = 0.
-27, -2, 10
Let t be 17/2 + 10/(-20). Let i be 1/t - (-506)/176. Factor 2/3*j**2 - 8/3 + 2/3*j**i - 8/3*j.
2*(j - 2)*(j + 1)*(j + 2)/3
Suppose -7*l = -3*a - 2*l + 21, 7 = -4*a - 5*l. Factor 21*u**a - 24*u**3 - 22*u - 23*u**3 - 8*u - 3*u**4 + 59*u**3.
-3*u*(u - 5)*(u - 1)*(u + 2)
Let j be (-6468)/8316*24/(-14). Suppose 0*l - 6 = -3*l. Solve l*c**2 - j*c + 0 - 2/3*c**4 + 0*c**3 = 0.
-2, 0, 1
Suppose q = -6*p + 3*p - 10, 0 = -3*p - 12. Factor -397*n + 0*n**q + 370*n + n**2.
n*(n - 27)
Let s = -77 - -81. Let c be (-12)/2*(3 - s). Factor 3*t**2 - t**2 - c*t**2 + 2*t + 2*t**2.
-2*t*(t - 1)
Find q such that -44*q**2 + 16*q**3 - 124 + 6*q**3 - 494*q**2 - 170 + 1946*q + 16*q**3 = 0.
3/19, 7
Let s(c) = 5*c**2 + 480*c + 463. Let o(l) = 70*l**2 + 6720*l + 6485. Let z(f) = 4*o(f) - 55*s(f). Factor z(j).
5*(j + 1)*(j + 95)
Let m(u) = 66*u**2 - 15*u. Let h be m(0). Let a(i) be the second derivative of -3*i + h - 8*i**3 - 3/20*i**5 - 2*i**4 + 0*i**2. Factor a(j).
-3*j*(j + 4)**2
Let b be (13/(-65))/((-85)/50) + 43/68. Solve -9/2*v**2 + 9/4*v + 15/2 + b*v**3 = 0.
-1, 2, 5
Let b(x) = -1. Let u(w) = -2. Let v(j) = -7*b(j) + 4*u(j). Let g(d) = -4 + 6*d**2 + d**3 - 3*d**2 - d - 2*d**2 - 2. Let q(n) = -g(n) + 5*v(n). Factor q(z).
-(z - 1)*(z + 1)**2
Let f(m) be the first derivative of m**4/12 + 7*m**3/6 + 3*m**2 - 10*m - 186. Let z(j) be the first derivative of f(j). Determine o, given that z(o) = 0.
-6, -1
Let q = 1027465/19 - 54077. Factor 2/19 + q*u**2 - 4/19*u.
2*(u - 1)**2/19
Let u(m) be the first derivative of -2*m**2 + 0*m + 4/21*m**3 + 49. Determine g, given that u(g) = 0.
0, 7
Suppose 5*w = 3*y - 6, 6 = y + 2*y + 2*w. Let -1059 - 75*z + 45*z**y + 5*z**3 + 934 - 10*z**3 = 0. What is z?
-1, 5
Let d be ((-2040)/2380)/(2 - 8). Factor d*y**2 - 6/7*y + 9/7.
(y - 3)**2/7
Let u(r) be the first derivative of r**5/20 - 15*r**4/8 + 77*r**3/3 - 585*r**2/4 + 891*r/4 + 757. Solve u(l) = 0.
1, 9, 11
Solve 6/11*o**2 + 0 - 438/11*o = 0 for o.
0, 73
Let n = -992667 - -992669.