8)
Suppose -159*b - 673*b + 3137 + 1023 = 0. Let -3/4*t + 0 + 1/4*t**b + t**2 + 1/2*t**3 - t**4 = 0. Calculate t.
-1, 0, 1, 3
Let a be (-172 - -76) + 104 - (6 - 1). Factor 5/3*l**a + 25/3*l**2 + 5 + 35/3*l.
5*(l + 1)**2*(l + 3)/3
Suppose -2*l = -y - 284, 3*l + y - 198 = 223. Let i be 0 + -3 + l*(-8)/(-360). Factor 0*h**3 + 0*h + 0*h**2 - i*h**4 + 0.
-2*h**4/15
Let d(h) be the second derivative of -h**5/4 + 10*h**4/3 - 95*h**3/6 + 30*h**2 - 240*h. Factor d(t).
-5*(t - 4)*(t - 3)*(t - 1)
What is f in -2*f**4 + 0*f**4 - 3*f**4 - 4*f**4 - 159*f**3 + 12*f**4 + 156*f**2 = 0?
0, 1, 52
Let c be 3 + -1 - (-5 - (-318)/20). Let t = -17/2 - c. Determine o so that -12/5*o - t*o**2 - 2 = 0.
-5, -1
Let d(t) be the third derivative of -t**6/280 + 641*t**5/140 - 80*t**4/7 - 796*t**2 - t. Find y, given that d(y) = 0.
0, 1, 640
Let w(t) = t**3 - 6*t**2 + 5*t + 3. Let d be w(5). Suppose 0 = -4*b - 2*s + 22, 20 = -3*b - d*s + 44. Solve 2/5*n**b + 0 + 28/5*n**2 + 98/5*n = 0.
-7, 0
Let q be (-1)/(-10 + 12) + 64/120. Let f(v) be the third derivative of 0 - 3*v**3 - 27*v**2 + 0*v + q*v**5 + 2/3*v**4. Factor f(y).
2*(y - 1)*(y + 9)
Solve -3/4*y + 0 - 27/2*y**2 = 0.
-1/18, 0
Let j(u) be the first derivative of u**6/36 + u**5/10 - u**4/3 - 4*u**3/3 + 4*u**2/3 + 8*u + 1056. Suppose j(z) = 0. What is z?
-3, -2, 2
Let t(y) be the second derivative of -y**6/6 + 9*y**5/2 + 455*y**4/12 - 40*y**3 - 990*y**2 + 15*y + 51. Let t(k) = 0. Calculate k.
-3, 2, 22
Let p(b) be the second derivative of 0*b**2 - 1/3*b**3 - 3/10*b**5 - 1/2*b**4 - 1/15*b**6 + 0 - 49*b. What is l in p(l) = 0?
-1, 0
Let g(o) be the third derivative of -7*o**5/60 + 61*o**4/24 + 3*o**3 + 414*o**2. Determine k, given that g(k) = 0.
-2/7, 9
Factor 192*t + 960 - 3/4*t**3 + 3*t**2.
-3*(t - 20)*(t + 8)**2/4
Let y(f) be the second derivative of 16/3*f**3 - 2/5*f**5 - 30*f + f**4 + 8*f**2 - 2 - 2/15*f**6. Factor y(t).
-4*(t - 2)*(t + 1)**2*(t + 2)
Let c(f) = f**3 - f**2 - 2*f + 3. Let g(l) = -3*l**3 - 2713*l**2 + 916*l + 1794. Let w(p) = -6*c(p) - g(p). Factor w(h).
-(h - 906)*(h - 1)*(3*h + 2)
Suppose -40 + 0 = -8*g. Solve 14*f**g - 25*f**4 - 31*f**3 - 19*f**5 + 36*f**3 + 25*f**2 = 0 for f.
-5, -1, 0, 1
Let f = 45 - 41. Suppose -f*o = o + m - 13, -2*o - 5*m + 19 = 0. Let -15*a**2 + 2*a + 5 + 13*a**2 + o*a + 1 = 0. Calculate a.
-1, 3
Factor -23*p**3 - 15*p**3 + 2*p**4 - 2*p**3 - 2*p**3 - p**4 + 41*p**2.
p**2*(p - 41)*(p - 1)
Let f(c) be the first derivative of -5*c**7/42 + c**6/3 + 19*c**5/12 + 5*c**4/4 + 5*c**2/2 - 6*c - 46. Let w(t) be the second derivative of f(t). Factor w(o).
-5*o*(o - 3)*(o + 1)*(5*o + 2)
Let n be (-4 - 368/52) + 260/3380 + 25504/14. Suppose -3/7*g**2 - n + 390/7*g = 0. Calculate g.
65
Let q(v) be the third derivative of -v**5/54 - 49*v**4/36 - 58*v**3/27 + v**2 - 3*v + 110. Factor q(a).
-2*(a + 29)*(5*a + 2)/9
Let l(p) be the second derivative of -9/40*p**5 + 1/4*p**4 + 5/4*p**3 + 0*p**2 + 71 - 2*p. What is u in l(u) = 0?
-1, 0, 5/3
Let u = -29/47 - -743/1128. Let x(p) be the second derivative of -u*p**4 + p - 1/6*p**3 + 0*p**2 + 0. Factor x(j).
-j*(j + 2)/2
Let p be -6*(-4)/8 - 6. Let v be ((-4)/(-8))/((6/(-52))/p). Find n, given that -v*n - n**2 - 67 - 7*n - 33 = 0.
-10
Let i(v) be the first derivative of -4*v + 1/3*v**3 - 103 - 3/2*v**2. Factor i(w).
(w - 4)*(w + 1)
Solve 410 + 613/3*s - 1/3*s**2 = 0 for s.
-2, 615
Let t be (-2 - (-1 + 7/(-28)))*-8. Let z be (-4)/14 + ((-552)/(-28))/t. Find m, given that 0*m**2 - 3/4*m**z - 9/8*m**5 + 0 + 0*m + 15/8*m**4 = 0.
0, 2/3, 1
Let x(l) be the second derivative of l**5/70 - 467*l**4/21 + 72384*l**3/7 + 438048*l**2/7 - 1267*l. Determine r so that x(r) = 0.
-2, 468
Factor -27/7*z**2 + 12/7 - 9/7*z**3 + 4/7*z.
-(z + 3)*(3*z - 2)*(3*z + 2)/7
Factor 0 - 54/11*c**2 + 0*c + 2/11*c**3.
2*c**2*(c - 27)/11
Let x(v) be the first derivative of -v**3/6 + 28*v**2 - 1568*v + 2675. Solve x(d) = 0 for d.
56
Let d = -14797/2 - -7186. Let b = d + 1295/6. Suppose 55/3*n**2 - 15*n**4 - 20*n**3 - b*n + 0 = 0. What is n?
-2, 0, 1/3
Let w be (600/12)/(-5)*2*3/(-78). Factor -2/13*q**2 - 12/13*q - w.
-2*(q + 1)*(q + 5)/13
Let x(s) be the second derivative of s**6/30 + 39*s**5/10 + 56*s**4/3 - 13*s**3 - 225*s**2/2 - 92*s - 1. Let x(w) = 0. What is w?
-75, -3, -1, 1
What is n in -290*n**2 + 1323*n**3 - 2641*n**3 + 1323*n**3 = 0?
0, 58
Let j be 7/(-35) - 94/5. Let y = j - -22. What is l in -13 + 13 - 6*l**3 + 20*l**2 - 15*l + l**y = 0?
0, 1, 3
Let n(t) = 0*t**3 + 2*t**2 + t**3 - 3*t**2. Let d(z) = -z**2 + 392*z + 391. Let y be d(-1). Let a(i) = 3*i**3 - i - 2. Let c(v) = y*n(v) + a(v). Factor c(l).
(l - 1)*(l + 1)*(l + 2)
Factor 0 - 84/5*t**2 - 288/5*t + 2/5*t**4 + 2*t**3.
2*t*(t - 6)*(t + 3)*(t + 8)/5
Let l = -17076 - -17078. Let u(x) be the first derivative of -2/15*x**3 + 2/5*x - 1/15*x**l + 1/30*x**4 - 17. Factor u(q).
2*(q - 3)*(q - 1)*(q + 1)/15
Let f = 15/2 + -7. Let w be (-1)/(-540)*15 + 6/27. What is m in -1/4*m - f*m**2 + 0 - w*m**3 = 0?
-1, 0
Let t(m) be the second derivative of m**4/78 + 2*m**3/3 + 25*m**2/13 - 1095*m. Factor t(w).
2*(w + 1)*(w + 25)/13
Let b(x) be the first derivative of 11*x**3 + 4227*x**2 + 1536*x - 5087. Factor b(w).
3*(w + 256)*(11*w + 2)
Let d(o) be the third derivative of -o**5/45 - 995*o**4/9 - 1980050*o**3/9 - 336*o**2. Factor d(j).
-4*(j + 995)**2/3
Let c(b) = 2*b**4 - 14*b**3 + 17*b**2 - 15*b + 10. Let w(q) = q**4 - 7*q**3 + 9*q**2 - 7*q + 4. Let z(t) = 2*c(t) - 5*w(t). Suppose z(r) = 0. Calculate r.
0, 1, 5
Suppose v - 105 = 5*a - 111, 2*a + 7*v - 32 = 0. Suppose 11/9*w + 0 - 1/9*w**a = 0. What is w?
0, 11
Find k such that 2/7*k**2 - 30/7 + 4*k = 0.
-15, 1
Let t(a) be the third derivative of -1/168*a**8 + 0*a**5 + 0*a**3 + 0*a + 0 + 0*a**4 + 61*a**2 - 1/30*a**6 - 1/35*a**7. Factor t(f).
-2*f**3*(f + 1)*(f + 2)
Let n = 1867909/4 + -466977. Factor -1/2*t**3 + 0*t**2 + n*t**4 + 1/2*t - 1/4.
(t - 1)**3*(t + 1)/4
Suppose 2 = 2*h + 16. Let z(j) = 6*j**3 + 479330*j + j**2 - 479366*j - 2*j**2. Let c(y) = -9*y**3 + 2*y**2 + 54*y. Let q(t) = h*z(t) - 5*c(t). Factor q(x).
3*x*(x - 3)*(x + 2)
Let a(b) be the first derivative of -2*b**3/3 - 2*b**2 + 48*b - 1090. What is h in a(h) = 0?
-6, 4
Factor 11*p**3 + 9*p**3 + 45025*p**4 - 45030*p**4 - 15*p**2.
-5*p**2*(p - 3)*(p - 1)
Let r be (-13)/(-1) - (-2813295)/(-216450). Let p(i) be the third derivative of 0 + 0*i - 11*i**2 + 1/13*i**4 + r*i**5 + 12/13*i**3. Factor p(u).
2*(u + 6)**2/13
Let n be 12/30 + 714/16065. Factor 0*k + 0 + 8/9*k**3 + 4/9*k**4 - n*k**5 + 0*k**2.
-4*k**3*(k - 2)*(k + 1)/9
Let z be (-3)/(-4*(-108)/230464). Let p = -1600 - z. Factor -2/3*l**2 + 0 + 2/9*l**4 - p*l + 0*l**3.
2*l*(l - 2)*(l + 1)**2/9
Suppose -6*z + 4*z + 3*w = -7, -2*z = -5*w - 9. Let y be ((-18)/21)/((-11)/(308/8)). Factor 2*p + 1/2*p**4 - 3*p**2 + 5/2 - z*p**y.
(p - 5)*(p - 1)*(p + 1)**2/2
Let s(b) = 4*b + 44. Let w be s(10). What is v in 98*v + 294 + 34*v**2 + 104*v**3 - 102*v**3 + w*v = 0?
-7, -3
Suppose -172/5 + 2/5*m**2 - 34*m = 0. Calculate m.
-1, 86
Let j(v) = 45*v**2 - 1565*v + 5505. Let m(t) = 5*t**2 - 174*t + 612. Let f(w) = -4*j(w) + 35*m(w). Let f(l) = 0. Calculate l.
4, 30
Let u(v) be the first derivative of v**4/12 - 2*v**2 - 87*v - 158. Let b(n) be the first derivative of u(n). Determine o, given that b(o) = 0.
-2, 2
Let r(m) be the first derivative of -5*m + 10/3*m**3 + 8 - 5/2*m**2. Determine a, given that r(a) = 0.
-1/2, 1
Let b(g) be the third derivative of -g**7/735 - g**6/105 + g**5/35 + g**4/21 - 5*g**3/21 + 2500*g**2 - 1. Suppose b(s) = 0. What is s?
-5, -1, 1
Let a(c) = 54*c + 434. Let y be a(-8). Let x(s) be the first derivative of 36/7*s - 3/7*s**y - 2/7*s**3 - 22. Factor x(f).
-6*(f - 2)*(f + 3)/7
Let 204 - 3/5*q**2 - 9/5*q = 0. Calculate q.
-20, 17
Let o(t) be the first derivative of -t**6/24 - 5*t**5/6 - 35*t**4/6 - 20*t**3 + 11*t**2 + 33. Let m(z) be the second derivative of o(z). Factor m(v).
-5*(v + 2)**2*(v + 6)
Suppose b = -3*o + 142, -2*o + 186 = 2*o + 2*b. Let w be o/343 - 79/(-35). Factor -8/5 - 4/5*s**2 - w*s.
-4*(s + 1)*(s + 2)/5
Let w(q) = q**2 + 1. Let c be w(1). Let h be (-4)/(-1) - ((-6)/27)/(1/(-9)). Factor 3 + 1/3*i**c + h*i.
(i + 3)**2/3
Suppose 1/4*s**2 + 1873/4*s + 468 = 0. Calculate s.
-1872, -1
Let x(y) be the first derivative of -y**5/30 + y**4/2 - 23*y**3/9 + 5*y*