 8. Let g(m) = -7*m**4 + m**3 - 2*m**2 - 8*m. Let l(i) = 5*g(i) + 40*w(i). Factor l(s).
5*s**2*(s - 1)*(s + 2)
Let z be 5*(-4)/(-20) + 2. Factor -7*u + 31*u**4 + u**z - 3*u**3 - 7*u**3 - 15*u**2 - 32*u**4.
-u*(u + 1)**2*(u + 7)
Find a, given that -8132304 + 11936*a - 4*a**2 + 2355800 - 3127752 = 0.
1492
Solve 282/5*c**4 - 852/5*c**2 + 4089*c - 13254/5 - 3/5*c**5 - 6618/5*c**3 = 0.
-2, 1, 47
Suppose -131*m - 120 = -21 - 73 - 288. Suppose -38/13*v**m + 40/13*v - 2/13*v**3 + 0 = 0. Calculate v.
-20, 0, 1
Let v(p) = 28*p**2 - 283*p + 197. Let z(w) = 9*w**2 - 94*w + 66. Let i be 38/(-1 + 3) - (-16)/(-8). Let d(u) = i*z(u) - 6*v(u). Determine h so that d(h) = 0.
2/3, 6
Let f(c) be the first derivative of -3*c**3 - 372*c**2 - 15376*c - 1223. Let f(s) = 0. Calculate s.
-124/3
Factor -83*p**3 + 621*p**2 + 1360 - 1620*p + 38*p**3 - 41*p**2 - 5*p**4.
-5*(p - 4)*(p - 2)**2*(p + 17)
Let s(i) be the third derivative of -i**7/630 + 23*i**6/360 + 49*i**5/180 + 25*i**4/72 - 26*i**2 + 36*i - 1. Factor s(o).
-o*(o - 25)*(o + 1)**2/3
Let o be 45/105*28/180. Let r(t) be the second derivative of -1/25*t**6 - 21*t + 0*t**2 + 0 + o*t**4 - 1/50*t**5 + 0*t**3. Factor r(l).
-2*l**2*(l + 1)*(3*l - 2)/5
Let p(o) be the third derivative of o**5/105 + o**4/3 - 138*o**3/7 + 360*o**2. Factor p(h).
4*(h - 9)*(h + 23)/7
Let p(w) be the first derivative of 2*w**3/15 - 4796*w**2/5 + 11500808*w/5 - 918. Solve p(t) = 0.
2398
Let l(o) = -o**2 + 15*o - 36. Let r be l(12). Factor 4*s**2 + 32*s**5 + 53*s**3 + 34*s**4 + r*s**2 + 4*s**2 + 68*s**4 + 13*s**5.
s**2*(3*s + 1)**2*(5*s + 8)
Let y = 1299/340 - 6/85. Let n(s) be the second derivative of -s**4 + 22*s + 6/5*s**5 + 0 - y*s**3 + 27/4*s**2. Solve n(k) = 0 for k.
-1, 3/4
Let b(z) = -17*z**4 + 217*z**3 + 593*z**2 + 592*z + 193. Let t(m) = 4*m**4 - 2*m**3 + 2*m**2 + m + 1. Let y(v) = b(v) + 5*t(v). Factor y(w).
3*(w + 1)**3*(w + 66)
Let m = 81340 + -81338. Factor 3/8*v**4 - 143/8*v**m + 0 + 29/4*v + 41/4*v**3.
v*(v - 1)*(v + 29)*(3*v - 2)/8
Suppose -20*v + 22*v = 65130. Factor 100*m - 32565 + 6*m**3 + 154*m**2 + v.
2*m*(m + 25)*(3*m + 2)
Let q be 2/(-9) + (-320)/(-144) - -9. Suppose 3*g + 3*g**2 + 5 + g - 11 + 4*g - q*g = 0. Calculate g.
-1, 2
Let r(c) be the first derivative of c**5/90 + 4*c**4/3 + 64*c**3 - 73*c**2/2 - 25. Let b(z) be the second derivative of r(z). Factor b(u).
2*(u + 24)**2/3
Let b(h) be the third derivative of -h**6/30 + 116*h**5/15 - 10*h**2 + 114*h. Solve b(u) = 0 for u.
0, 116
Suppose -4*y + 2*f = -7439 + 133, 0 = -3*y - f + 5472. Let o = y + -5471/3. Suppose 0 + 16/3*g + o*g**2 = 0. What is g?
-4, 0
Let n(x) = 2*x**2 - 25*x - 151. Let u be n(17). Let f be u/17 + 30/(-2805)*11. Factor 0 + f*z**2 - 1/6*z**4 + 0*z - 1/6*z**5 + 0*z**3.
-z**4*(z + 1)/6
Factor -133*d + 57*d + 104*d**3 - 28*d + 4*d**4 - 147*d**2 + 35*d**2 + 108.
4*(d - 1)**2*(d + 1)*(d + 27)
Suppose 133*d - 27 + 27 = 0. Let b(h) be the first derivative of 0*h - 1/6*h**6 - 4 - 1/3*h**3 - 3/5*h**5 - 3/4*h**4 + d*h**2. Suppose b(f) = 0. Calculate f.
-1, 0
Suppose -62*l + 93*l - 2232 = 0. Let j be (-1 + 2)/((-2)/(-4)). Factor 5*u**2 - l*u + 5*u**4 - 63*u - 270 + 40*u**j + 35*u**3 + 0.
5*(u - 2)*(u + 3)**3
Let a(q) = -2*q**2 - 169*q + 167. Let j(g) = -3*g - 1. Let n(d) = -a(d) + j(d). Factor n(m).
2*(m - 1)*(m + 84)
Let y(v) be the second derivative of v**4/54 - 32*v**3/9 - 196*v**2/9 + 2*v - 966. Solve y(w) = 0.
-2, 98
Let m(d) be the second derivative of 5*d**4/12 + 25*d**3 + 1125*d**2/2 - 11257*d. Suppose m(j) = 0. Calculate j.
-15
Suppose 2*d - 14 = -m, 27*d = 29*d - 12. Let b(v) be the first derivative of -21/4*v**4 + 3*v**m - 1 - 5*v**3 + 0*v. Factor b(h).
-3*h*(h + 1)*(7*h - 2)
Let v(o) be the first derivative of 34 - o**2 - 12/7*o - 2/21*o**3. Solve v(s) = 0.
-6, -1
Solve -10/9*y**2 + 58/9 + 16/3*y = 0.
-1, 29/5
Let h = -2/6797 - -6827/101955. Let w(y) be the first derivative of 0*y + 0*y**2 + h*y**3 + 12. Factor w(j).
j**2/5
Let p(x) be the first derivative of 1/75*x**6 - 3/5*x**2 + 6 + 1/15*x**4 - 4/15*x**3 - 8*x + 2/25*x**5. Let v(s) be the first derivative of p(s). Factor v(k).
2*(k - 1)*(k + 1)**2*(k + 3)/5
Suppose -3*s + 11 = -5*p, 5*s - 4*p = 17 - 3. Let 76*h**2 - 4*h**3 - 28*h**2 - 27*h**2 - 25*h**s = 0. What is h?
-1, 0
Factor -5261*c - 7254075 - 8174*c + 2716*c + 3440*c**2 + 1389*c - 3443*c**2.
-3*(c + 1555)**2
Let s = -309779/60 + 5163. Let t(k) be the third derivative of 0*k + 0 + s*k**5 + 5/24*k**4 - 26*k**2 + 2/3*k**3. Factor t(r).
(r + 1)*(r + 4)
Let x(o) be the first derivative of 3*o**4/28 + 12*o**3 + 5031*o**2/14 - 11094*o/7 - 1192. Let x(t) = 0. What is t?
-43, 2
Solve 3*p**2 + 1489*p + 3*p**2 + 240 - 1613*p + 0*p**2 - 4*p**2 = 0 for p.
2, 60
Let l(b) be the third derivative of -b**7/840 + 13*b**6/160 - 343*b**5/240 + 335*b**4/32 - 175*b**3/6 + 2*b**2 - b - 696. Factor l(d).
-(d - 28)*(d - 5)**2*(d - 1)/4
Let j(y) be the second derivative of -y**7/84 + 7*y**6/90 + y**5/20 + y**3/3 - 11*y**2/2 - 8*y + 3. Let d(l) be the second derivative of j(l). Factor d(u).
-2*u*(u - 3)*(5*u + 1)
Let p(f) be the third derivative of f**6/270 + 2*f**5/27 + 19*f**4/54 - 20*f**3/9 + 12*f**2 - 117. Factor p(l).
4*(l - 1)*(l + 5)*(l + 6)/9
Let 0 - 1378*j**2 + 1/4*j**5 + 26*j**4 + 1299/2*j**3 + 2809/4*j = 0. Calculate j.
-53, 0, 1
Let f be (-2)/(-4)*0*38/950. What is u in -3/2*u + f + 1/4*u**2 = 0?
0, 6
Let c(d) be the first derivative of -3*d**4/16 + 4405*d**3/4 - 1819953*d**2 + 3636603*d - 3237. Factor c(v).
-3*(v - 2202)**2*(v - 1)/4
Let q(v) be the second derivative of -v**6/180 + v**5/120 + v**4/36 + 1632*v. Factor q(x).
-x**2*(x - 2)*(x + 1)/6
Let p = -163 + 176. Let w(y) = 11*y**4 + 19*y**3 + 2*y**2 - 19*y + 13. Let d(u) = 5*u**4 + 9*u**3 + u**2 - 9*u + 6. Let c(x) = p*d(x) - 6*w(x). Factor c(j).
-j*(j - 3)*(j - 1)*(j + 1)
Let y(k) be the third derivative of -4*k**6/75 + 356*k**5/75 - 353*k**4/60 + 44*k**3/15 - 2*k**2 - 44. Factor y(b).
-2*(b - 44)*(4*b - 1)**2/5
Let n(f) be the second derivative of -f**5/4 - 265*f**4/12 + 560*f**3/3 - 570*f**2 - 104*f. Determine a so that n(a) = 0.
-57, 2
Let f(n) be the first derivative of -2*n**3/39 + 270*n**2/13 - 839. Factor f(l).
-2*l*(l - 270)/13
Suppose -4*m + 460*k - 463*k - 36 = 0, 4*m + 5*k + 60 = 0. Suppose 0 + 18/7*h**2 + 27/7*h**3 + 1/7*h**5 + m*h + 10/7*h**4 = 0. What is h?
-6, -3, -1, 0
Let w(o) be the second derivative of o**9/1512 + o**8/140 + o**3/2 + o**2/2 - 50*o. Let t(h) be the second derivative of w(h). What is q in t(q) = 0?
-6, 0
Factor -14*d**4 + 3*d**3 - 20*d**4 - 2*d**2 - 4*d**3 - 15*d**4 + 50*d**4.
d**2*(d - 2)*(d + 1)
Let j(k) = 2*k**4 + 112*k**3 + 432*k**2 + 322*k. Let c(t) = 2*t**4 + 112*t**3 + 430*t**2 + 320*t. Let i(y) = -5*c(y) + 4*j(y). Find w such that i(w) = 0.
-52, -3, -1, 0
Let d = 3/223 - -7115/1561. Let f be -26*9/(-2574)*11*(1 + 2). Find q such that -324/7*q**4 + 16/7*q + 72*q**2 + 396/7*q**f - d = 0.
-2/3, -1/3, 2/9, 2
Let f(n) = -2*n**3 - 7*n**2 - 2*n + 5. Let p be f(-3). Factor -3*s**5 + 34*s - 18*s**3 + 12*s**p + 6*s - 15*s**4 - 16*s.
-3*s*(s - 1)*(s + 2)**3
Suppose -191 = -21*l - 128. Let u(o) be the first derivative of -l*o - 9*o**4 + 6*o**2 - 27/5*o**5 - 20 + 2*o**3. Suppose u(d) = 0. Calculate d.
-1, 1/3
Solve 5/2*a**4 + 8*a - 1/4*a**5 - 8 - 31/4*a**3 + 11/2*a**2 = 0 for a.
-1, 1, 2, 4
Let z be 9 + (4840/1375)/((-10)/25). Factor z*o**2 + 1/5*o - 2/5.
(o - 1)*(o + 2)/5
Let y = -525 + 539. Suppose 5*d = -24*d - y*d. What is k in 0*k - 1/11*k**4 + 1/11*k**3 + 2/11*k**2 + d = 0?
-1, 0, 2
Let n = 244 - 234. Suppose w = n*u - 6*u + 18, 0 = -4*w + u + 12. Let 1/2*t**w + 1/2*t**3 + 0 + 0*t = 0. What is t?
-1, 0
Let n(o) be the first derivative of -o**4/26 + 14*o**3/13 + 96*o**2/13 + 200*o/13 + 5575. Factor n(x).
-2*(x - 25)*(x + 2)**2/13
Let w(c) = c**3 + 7*c**2 + 4*c - 1. Let u(v) = -5*v**4 - 44*v**3 + 102*v**2 + 74*v - 61. Let g(a) = -u(a) + 6*w(a). Determine s so that g(s) = 0.
-11, -1, 1
Suppose 0 = 3*s - 8*s, 4*u - 96 = s. Let b be 10/((-3)/u*-1). Let b*g + 32*g + 5*g**2 - 318 - 22*g + 723 = 0. What is g?
-9
Suppose z = 37 - 27. Suppose 0 = -18*x + 23*x - z. Determine f so that f**2 - 2*f**x - 13*f + 14*f + 0*f**2 = 0.
0, 1
Let g(t) = -3*t**2 - 54*t + 144. Let c(w) = -3*w**2 - 51*w + 144. Let r(b) = -b**2 + 95. Let z be r(-10). Let q(k) = z*c(k) + 4*g(k). Fact