6 - 202. Factor j(f).
-f**2*(f - 1)*(f + 46)/4
Suppose -1 = 2*s - 9. Let x(o) = -7*o**4 + 5*o**3 + 4*o**2 - 7. Let v(h) = -6*h**4 + 4*h**3 + 4*h**2 - 6. Let c(k) = s*x(k) - 5*v(k). Factor c(m).
2*(m - 1)**2*(m + 1)**2
Let k(o) = -o**3 - o**2 - o + 1. Let s(u) = 2*u**4 - 6*u**3 - 24*u**2 - 20*u + 4. Let m(i) = 4*k(i) - s(i). Factor m(d).
-2*d*(d - 4)*(d + 1)*(d + 2)
Let m be (((-1830)/(-1525))/(14/(-5)))/((-8)/14). Determine b so that 1/4*b**3 + 7/4*b - m - 5/4*b**2 = 0.
1, 3
Factor 4/7*u**4 + 320/7*u**2 + 0 + 76/7*u**3 - 400/7*u.
4*u*(u - 1)*(u + 10)**2/7
Let j(q) = -q**3 + 2*q**2 + 3*q - 1. Let f be j(3). Let o = f - -3. Factor -4*n**3 + 7*n**3 - 5*n**2 - 6*n**2 + 5*n**o.
3*n**2*(n - 2)
Let z be 581/49 + 4 + (-54)/14. Factor z + 1/3*u**2 + 4*u.
(u + 6)**2/3
Let v(l) = l**5 - 2*l**4 + 3*l**3 - 2*l**2 - l - 1. Let t(u) = -u - 1 + u**4 - u**2 - 19*u**3 + 19*u**3. Let r(h) = -2*t(h) + 2*v(h). Factor r(i).
2*i**2*(i - 1)**3
Let l(m) be the second derivative of m**6/3 - 5*m**5/8 + 5*m**4/24 - 7*m + 24. Factor l(x).
5*x**2*(x - 1)*(4*x - 1)/2
Let i(d) be the first derivative of -d**6/900 + d**5/100 + 9*d**3 + 8. Let h(z) be the third derivative of i(z). Factor h(p).
-2*p*(p - 3)/5
Suppose -s + 4 = -0, -3*x + 18 = 3*s. Factor -l**2 - 6 + 3*l**x + 136*l - 132*l.
2*(l - 1)*(l + 3)
Suppose 57*o**4 - 25*o**2 - 45*o**3 + 52*o + 6*o**4 - 26*o**4 - 5*o**5 - 2*o**5 - 12 = 0. Calculate o.
-1, 2/7, 1, 2, 3
Let d(n) = -n**5 - 10*n**4 - 12*n**3 - 16*n**2 - 7*n + 3. Let u(a) = a**4 - a**3 + a**2 + a - 1. Let c(f) = 5*d(f) + 15*u(f). Find l such that c(l) = 0.
-4, -1, 0
Let f = -92 - -95. Let b be (f/(-3))/(-1 - 2). Determine l so that 0 - b*l**4 - 4*l**2 - 8/3*l - 2*l**3 = 0.
-2, 0
Suppose 36*q - 1119 + 3*q**3 + 66*q**2 + 343*q + 255 - 91*q = 0. Calculate q.
-12, 2
Determine u, given that u**2 + 3*u**3 + 0 + 0*u + 5/4*u**4 = 0.
-2, -2/5, 0
Let z(n) = -2*n**2 - 33*n - 22. Let o(w) = 15*w**2 + 265*w + 175. Let c(a) = 5*a + 15. Let m be c(-8). Let d(v) = m*z(v) - 3*o(v). Factor d(b).
5*(b + 1)*(b + 5)
Let v be (-3)/(-2)*(-28)/(-21). Suppose -2*f - v*f = -12. Solve 3*g**f + 69 - 69 + g**3 + 8*g**2 = 0.
-2, 0
Let d(q) = -6 + 4*q**2 - 11*q**2 + 3*q**2 + 5*q + 5*q**2. Let f be d(-6). Determine o so that -2/3*o + f + 7/3*o**2 = 0.
0, 2/7
Let t = 186 + -184. Factor 2/3 + 0*a**3 + 16/9*a + 4/3*a**t - 2/9*a**4.
-2*(a - 3)*(a + 1)**3/9
Let j(o) = 2*o**4 - 109*o**3 - 2806*o**2 + 3*o + 6. Let m(v) = -5*v**4 + 219*v**3 + 5611*v**2 - 7*v - 14. Let c(h) = 7*j(h) + 3*m(h). Let c(x) = 0. What is x?
-53, 0
Suppose 5*b + h = 70, -2*h + 1 - 4 = -b. Factor 4*i**3 + 5*i**2 + 4*i - 5*i + 3*i - b*i**4 + 14*i**4.
i*(i + 1)**2*(i + 2)
Let b(n) be the first derivative of n**6/1260 + n**5/140 + 7*n**3/3 - 3. Let s(u) be the third derivative of b(u). Factor s(r).
2*r*(r + 3)/7
Let a(w) = w**5 - w**4 - w**3 + w. Let b(v) = -8*v**5 + 2*v**4 + 6*v**3 - 6*v. Let o(q) = 6*a(q) + b(q). Factor o(u).
-2*u**4*(u + 2)
Suppose 245/2 - 45/4*f**5 - 1495/2*f**3 + 545*f**2 + 2555/4*f + 345/2*f**4 = 0. Calculate f.
-1/3, 2, 7
Suppose 15 = -3*k - 2*k. Let u(a) = 12*a**3 + 144 - 2*a**3 - 108*a**2 - 2*a**3. Let t(m) = m**3 - 12*m**2 + 16. Let q(b) = k*u(b) + 28*t(b). Factor q(g).
4*(g - 2)**2*(g + 1)
Solve 7/2*v**3 + 1/2*v**4 + 9/2*v + 15/2*v**2 + 0 = 0 for v.
-3, -1, 0
Let p be 5/15*3*1 + -16. Let m be (-2)/p + (-1456)/(-780). Factor -3 - 6*c**m + 3/2*c**3 + 15/2*c.
3*(c - 2)*(c - 1)**2/2
Let b(v) = 50*v - 200. Let c be b(4). Factor c + 4/11*k - 2/11*k**2.
-2*k*(k - 2)/11
Suppose 15 = -7*u + 29. Let w(i) be the first derivative of -3/10*i**u + 3/20*i**4 - 6/5*i + 2/5*i**3 - 5. Let w(a) = 0. Calculate a.
-2, -1, 1
Find k such that 16*k**2 - 13*k + 13*k**2 + 8 + 15*k**2 + k - 40*k**2 = 0.
1, 2
Suppose -24 = -3*x - 0. Suppose -2 - x = -5*b. Solve -z + z**2 - 4*z**b + z = 0 for z.
0
Factor 45*i**3 + 9*i**2 - 41*i**2 - 78*i**2 + 5*i**4.
5*i**2*(i - 2)*(i + 11)
Let r(b) = -33*b - 293. Let l be r(-9). Solve 33/4*t**3 + 3*t + 2 - 23/2*t**2 - 7/4*t**l = 0.
-2/7, 1, 2
Let s(v) be the third derivative of -v**8/1344 + v**7/1512 + 3*v**4/8 + 10*v**2. Let x(d) be the second derivative of s(d). Factor x(o).
-5*o**2*(3*o - 1)/3
Let o(j) be the first derivative of 1/2*j**3 + 3/4*j**2 - 9*j - 34. Factor o(d).
3*(d - 2)*(d + 3)/2
Find s such that 0*s + 2/3*s**2 - 8/9 + 2/9*s**3 = 0.
-2, 1
Let r = 7613 - 7609. Suppose 1/6*l**r + 0*l**3 + 0 - 1/6*l**2 + 0*l = 0. What is l?
-1, 0, 1
Let z(d) = 155*d + 2172. Let h be z(-14). Let -s**4 - 4/3*s - 16/3*s**3 + 0 - 17/3*s**h = 0. Calculate s.
-4, -1, -1/3, 0
Let i = 38 - 36. Suppose 8*q = c + 7*q + 1, -3*q + 3 = i*c. What is u in c*u + 0 - 1/3*u**2 = 0?
0
Suppose 5*r + 7 = -8, -q + 12 = -3*r. Suppose -q*t + t = -5*t. Factor -2/3*d**3 + t - 2/3*d**2 + 4/3*d.
-2*d*(d - 1)*(d + 2)/3
Let h be 0/((-1)/(-2) - 83/(-166)). Factor 9/2*l**2 + 3*l**3 + 1/2*l**4 + 2*l + h.
l*(l + 1)**2*(l + 4)/2
Find x such that -68/5*x**3 + 512/5 + 642/5*x**2 + 2/5*x**4 - 1088/5*x = 0.
1, 16
Factor -108/7*t + 972/7 + 3/7*t**2.
3*(t - 18)**2/7
Suppose -4 + 16 - 4*n**2 - 12 - 4*n - n**3 = 0. What is n?
-2, 0
Let p(n) be the second derivative of n**6/15 + 9*n**5/10 - 7*n**4/2 + 11*n**3/3 - 83*n. Suppose p(h) = 0. What is h?
-11, 0, 1
Let q(k) = 2*k**2 - 12*k + 34. Let f be q(5). Let i be 6/f + (-33)/(-12). Factor -5/2*v**2 + 1/2*v**i + 7/2*v - 3/2.
(v - 3)*(v - 1)**2/2
Suppose -6*g + 2*g**2 - 36 + 36*g + 2*g + 2*g**2 = 0. What is g?
-9, 1
Factor -27902800*q + 3504395*q + 393*q**4 - 26011*q**3 - 7*q**5 + 2*q**5 - 40259*q**3 + 2076460*q**2 + 547*q**4.
-5*q*(q - 47)**4
Let a(f) = 5*f**4 - f**3 - 5*f**2 + f. Suppose -6*o = -o - 20. Let y(r) = 4*r**4 - r**3 - 4*r**2 + r. Let s = -1 - 2. Let c(z) = o*y(z) + s*a(z). Factor c(p).
p*(p - 1)**2*(p + 1)
Let u(z) = -5*z**4 - 11*z**3 + 28*z**2 - 12*z - 8. Let q(g) = 3*g**4 + 12*g**3 - 27*g**2 + 12*g + 6. Let n(k) = -4*q(k) - 3*u(k). Let n(l) = 0. Calculate l.
0, 1, 2
Let i(d) = d**2 + d + 12. Let y(o) = 5*o**2 + 70*o - 280. Let u(z) = 20*i(z) + y(z). Factor u(n).
5*(n + 4)*(5*n - 2)
Let o be 3*(52/12 - 5) + 22. Suppose 4*h + 0*h + 3*y = o, 8 = -2*h + 3*y. Factor 0*t**h - 1/5 + 1/5*t**4 - 2/5*t + 2/5*t**3.
(t - 1)*(t + 1)**3/5
Suppose 8 = -37*n + 41*n. Factor 4/5*q**3 + 12/5*q**n + 0*q - 16/5.
4*(q - 1)*(q + 2)**2/5
Suppose 4*o = -5*x + 3, -7*x - 12 = -5*o - 5*x. Let a be (-1 - -2) + 1 + 1. Determine m so that a*m**3 - 4*m**o - 2*m + 7*m - 7*m - 5*m**3 = 0.
-1, 0
Factor -10*t**3 + 12*t**2 - 86*t**4 + 32*t**4 + 28*t**4 + 28*t**4.
2*t**2*(t - 3)*(t - 2)
Factor -14*w**2 - 2*w**3 + 50*w + 2*w**2 - 122*w + 56*w.
-2*w*(w + 2)*(w + 4)
Let o(x) be the first derivative of 2/3*x**3 + 0*x - 27 + 0*x**2 + 1/3*x**4 + 2/45*x**5. Suppose o(y) = 0. Calculate y.
-3, 0
Suppose 2*h + 4*f = -4, 5*h - 7*f + 10*f = 11. Factor -4/3*k**2 + 1/3*k - 4/3*k**h + 2*k**3 + 0 + 1/3*k**5.
k*(k - 1)**4/3
Suppose 0 = -z + x - 3*x + 4, 13 = 5*z + 3*x. Suppose 3*b + 34 = 4*d + d, -25 = -z*d + 5*b. Factor 0*k**2 + 0*k - 4/9*k**4 - 2/9*k**d - 2/9*k**3 + 0.
-2*k**3*(k + 1)**2/9
Let b(n) be the first derivative of n**6/2 + 3*n**5 + 6*n**4 + 4*n**3 - 199. Factor b(a).
3*a**2*(a + 1)*(a + 2)**2
Let x be (1/2)/(31/186). Let b(y) = -2*y**2 + 4*y**2 + 1 - y**2. Let i(p) = 8*p**2 - 7*p + 5. Let d(u) = x*b(u) - i(u). Factor d(s).
-(s - 1)*(5*s - 2)
Solve 512/3*c**3 - 448*c**2 - 343/3 + 392*c = 0 for c.
7/8
Find x such that -22/5*x**5 + 0 - 48/5*x**2 + 8/5*x + 48/5*x**4 + 14/5*x**3 = 0.
-1, 0, 2/11, 1, 2
Let b(p) = p**4 - p**3 + p + 2. Let x(w) = 7*w**4 - 19*w**3 + 22*w**2 - 5*w + 10. Let o(y) = 5*b(y) - x(y). Factor o(q).
-2*q*(q - 5)*(q - 1)**2
Let t(v) = 4*v**2 + 41*v + 10. Let c be t(-10). Let r(x) be the first derivative of 2 - 1/5*x**3 - 9/10*x**2 + c*x. Let r(u) = 0. Calculate u.
-3, 0
Suppose 18 = 2*r + 3*u, -2*r = -7*r - 2*u + 34. Let x = r - 2. Factor 6 - 12*w + 12 + x*w**2 - 2*w**2.
2*(w - 3)**2
Factor 0 + 1/2*k**2 - 3/2*k.
k*(k - 3)/2
Let l(r) = -9*r**4 + 5*r**3 + 20*r**2 - 5*r - 33. Let g(q) = -2*q**4 + q**3 + 4*q**2 - q - 6. Let s(x) = -33*g(x) + 6*l(x). Factor s(y).
3*y*(y - 1)*(y + 1)*(4*y - 1)
Let v(q) be the first derivative of 3*q**6/8 - 29*q**5/20 - 3*q**4/16 + 29*q**3/12 - 3*q**2/4 + 177. Solve v(b) = 0.
-1, 0, 2/9, 1, 3
Let v(z) be the first derivative of 9*z**5/35 - 51*z**4/28 - 6*z**3/7 + 277. Determi