426. Let u(q) = -q**3 - 3*q**2 + q. Let x(a) = -3*u(a) + v(a). Factor x(w).
-3*(w - 142)*(w - 1)**2
Let h(w) be the third derivative of w**8/672 - w**7/30 + 7*w**6/80 + w**5/3 - 11*w**4/12 - 4*w**3 + 9*w**2 + 7*w. Suppose h(d) = 0. What is d?
-1, 2, 12
Suppose -3*d = -5*n + 50316 + 57143, -2*n + 42968 = 4*d. Determine v so that -n*v**2 - 12*v**3 - 3*v**4 + 21490*v**2 = 0.
-4, 0
Let g(k) = -k**3 + 6*k**2 + k + 4. Let i be g(6). Let z be (9/(-5))/((-45)/(-75)) - 18/(-3). Factor i*q**3 - 15*q**3 - 4 + 7*q**z - 2*q + 4*q**2.
2*(q - 1)*(q + 1)*(q + 2)
Factor 76 - 37*c**2 - 17*c**3 - 30*c + 18*c**3 - 11*c + c.
(c - 38)*(c - 1)*(c + 2)
Factor 36/5*f**3 + 324/5*f + 243/5 + 162/5*f**2 + 3/5*f**4.
3*(f + 3)**4/5
Let r(c) be the second derivative of -c**5/40 + 35*c**4/24 + 37*c**3/6 - 947*c - 1. Find i such that r(i) = 0.
-2, 0, 37
Let c(a) be the third derivative of 16*a**2 - 2/3*a**3 + 0 - 2*a - 1/72*a**4 + 1/180*a**5. Factor c(j).
(j - 4)*(j + 3)/3
Suppose 0 = -6*h - h + 6279. Solve 1503*x + 35*x**4 + 520*x**2 - 146*x**3 - 214*x**3 + h*x - 720 = 0.
-2, 2/7, 6
Suppose -3*o - 3 = -6*o - 3*u, 5 = -5*u. Factor 6*w**o - 2 - 6 - 2181*w + 2173*w.
2*(w - 2)*(3*w + 2)
Let -909*x**2 + 783 - 1000*x + 220*x - 916*x**2 + 1822*x**2 = 0. What is x?
-261, 1
Let y be 12/(-30) - (1084/(-510) + (-71)/(-1207)). Find w, given that -y - 1/3*w**3 + 1/3*w + 5/3*w**2 = 0.
-1, 1, 5
Let z be ((-1805)/(-420))/(-19) + 1/4. Let c(s) be the second derivative of 0 - 1/12*s**4 + 0*s**3 - 26*s + 3/20*s**5 + 1/8*s**6 + 0*s**2 + z*s**7. Factor c(l).
l**2*(l + 2)**2*(4*l - 1)/4
Let k(a) be the first derivative of -a**4/16 + 73*a**3/4 - 1539*a**2 + 8748*a + 6872. Factor k(x).
-(x - 108)**2*(x - 3)/4
Let i(q) = 23*q**2 - 201*q - 1115. Let f(u) = -6*u**2 + 60*u + 279. Let z(l) = -11*f(l) - 3*i(l). Find y such that z(y) = 0.
-23, 4
Suppose -5*s + s = -5*i + 106, -5*i = -2*s - 98. Let l be (-14)/i*(-1188)/378. Find d such that -2/9*d**2 + l*d + 0 = 0.
0, 11
Let m(v) be the first derivative of 3*v**4/32 - 7*v**3/8 - 387*v**2/16 + 405*v/8 + 324. Factor m(z).
3*(z - 15)*(z - 1)*(z + 9)/8
Let y(o) = -4*o**2 - 540*o + 4578. Let g be y(-143). Find u such that 2/11*u - 2/11*u**g + 0 = 0.
0, 1
Let r(l) be the second derivative of -l**4/9 - 2696*l**3/9 - 908552*l**2/3 + 133*l. Factor r(h).
-4*(h + 674)**2/3
Let f(q) be the first derivative of -2*q**5/5 + 7*q**4 - 136*q**3/3 + 130*q**2 - 150*q + 578. Suppose f(c) = 0. Calculate c.
1, 3, 5
Factor 62*i**4 - 29*i**4 + 513*i**2 + 12*i**3 - 3402*i - 36*i**4.
-3*i*(i - 9)**2*(i + 14)
Suppose -4*f - 8291 = -3*d, 4*f - 9*f = 5*d - 13760. Factor -d*b + 2757*b - b**3 - b**4 + 14*b**3.
-b**3*(b - 13)
Let w(v) be the first derivative of 2*v**6/75 + 2*v**5/25 + v**4/15 + 81*v - 195. Let d(h) be the first derivative of w(h). Determine z so that d(z) = 0.
-1, 0
Let w be ((-402)/51 - (17 + -25)) + (-19)/(20672/(-8440)). Determine q so that 181/2*q**4 + 25 + 355/2*q + 879/4*q**2 - 2455/8*q**3 - w*q**5 = 0.
-2/7, -2/9, 2, 5
Let h(v) be the first derivative of 4*v**3/9 - 82*v**2/3 + 104*v - 678. Factor h(t).
4*(t - 39)*(t - 2)/3
Factor -66869*c - 8260 + 32123*c + 32661*c - 5*c**2.
-5*(c + 4)*(c + 413)
Factor 7*y**4 - 261*y**2 + 0*y**4 - 131*y**2 + 48*y**2 - 9*y**4 - 176*y**3.
-2*y**2*(y + 2)*(y + 86)
Let z = -147714/5 - -29543. Factor -49/5 - 7*h + 13/5*h**2 - z*h**3.
-(h - 7)**2*(h + 1)/5
Let u(x) be the first derivative of -x**6/6 - 18*x**5/5 + 45*x**4/2 + 32*x**3/3 - 273*x**2/2 - 198*x + 6418. Solve u(h) = 0 for h.
-22, -1, 3
Let z be (-2079 - -2083) + 0 + (-2 - 0). Factor 32/5*k**z + 28/5 + 2/5*k**3 + 58/5*k.
2*(k + 1)**2*(k + 14)/5
Let r(x) be the second derivative of -x**5/30 + x**4/18 + 50*x**3/9 + 16*x**2 + 2*x - 65. Factor r(q).
-2*(q - 8)*(q + 1)*(q + 6)/3
Let r(g) = -g**2 + 25*g - 21. Let i be r(6). Suppose -i = -34*t + 9. Suppose 4/3*o**t - 2/3*o**4 + 0*o + 0 + 0*o**2 = 0. Calculate o.
0, 2
Factor -527/4*z + 0 + 1/4*z**4 - 525/4*z**3 - 1053/4*z**2.
z*(z - 527)*(z + 1)**2/4
Let l(j) be the third derivative of 2*j**7/945 - 11*j**6/540 + j**5/30 + 1507*j**2. Solve l(u) = 0 for u.
0, 1, 9/2
Let k = 319/46 - 2503/414. Factor k*y - 2/3 - 2/9*y**2.
-2*(y - 3)*(y - 1)/9
Let o(c) = -12*c**2 + 17*c - 7. Let a(k) = -2*k**2 + k - 1. Let m be (-2)/((-3)/(45/(-10))). Let s(x) = m*a(x) + o(x). Let s(j) = 0. What is j?
1/3, 2
Let l be 232/3857*21/12. Find b, given that 14/19*b + l*b**2 + 0 = 0.
-7, 0
Let n be (353/(-3))/((-30)/(-180)). Let s = n - -708. Factor 2/7*u**3 - 8/7*u**s + 10/7*u - 4/7.
2*(u - 2)*(u - 1)**2/7
Factor -27*a + 46*a**2 + 58*a**2 - 9*a**3 - 9*a**2 - 11*a**2.
-3*a*(a - 9)*(3*a - 1)
Let v(k) be the second derivative of 1/8*k**4 - 1/20*k**5 - 1/2*k**2 + 1 + 3*k + 1/4*k**3. Factor v(x).
-(x - 2)*(x + 1)*(2*x - 1)/2
Let b = -1331/6 - -222. Let s be ((-3)/4)/((-126)/28). Determine n, given that 0 - b*n**3 + s*n - 1/6*n**2 + 1/6*n**4 = 0.
-1, 0, 1
Let g(j) = -48*j - 196. Let h be g(-4). Let a(b) = -4*b**3 + b**2 + b. Let q(r) = 14*r**3 - 20*r**2 + 58*r - 44. Let z(c) = h*a(c) - q(c). Factor z(s).
2*(s - 2)*(s - 1)*(s + 11)
Let n be (-32)/(-2392)*(68 + -3). Let 2/23*m**3 - n + 6/23*m + 12/23*m**2 = 0. What is m?
-5, -2, 1
Let w be 531 - -6*1/2. Suppose 538*v**5 - 19*v**3 + 95*v**3 - 16 - w*v**5 - 26*v**4 - 2*v**4 + 64*v - 100*v**2 = 0. Calculate v.
1, 2
Let d(c) = -4*c**3 + 102*c**2 + 1674*c + 1562. Let k(j) = 11*j**3 - 308*j**2 - 5023*j - 4687. Let w(s) = 17*d(s) + 6*k(s). Find q, given that w(q) = 0.
-28, -1
Let h = 2503 - 2501. Let w(t) be the first derivative of -3/2*t**2 + 19 + h*t + 1/3*t**3. Factor w(d).
(d - 2)*(d - 1)
Let y(x) = 6*x**3 + x**2 + x + 1. Let o(i) = -53*i**3 - 74*i**2 - 297*i + 819. Let z(f) = 2*o(f) + 18*y(f). Factor z(r).
2*(r - 69)*(r - 2)*(r + 6)
Let l be 0 - ((-144)/(-5))/(-2). Let u = -53263 - -266318/5. Suppose l*s + 432/5 + u*s**2 = 0. Calculate s.
-12
Let p(s) be the first derivative of -s**5/300 - 7*s**4/120 - s**3/5 + 39*s**2 + 171. Let f(m) be the second derivative of p(m). Factor f(x).
-(x + 1)*(x + 6)/5
Let k(c) be the third derivative of -c**7/560 + c**6/32 - 37*c**5/160 + 15*c**4/16 - 9*c**3/4 + 11*c**2 + 166. Factor k(q).
-3*(q - 3)**2*(q - 2)**2/8
Let 57/2*o + 3/8*o**2 + 108 = 0. Calculate o.
-72, -4
Let f(y) be the first derivative of -79*y**2 - 1777*y - 189*y + 7*y**2 + 238*y - y**3 - 119. Factor f(m).
-3*(m + 24)**2
Solve 16 + 4/3*x**3 + 12*x**2 + 80/3*x = 0.
-6, -2, -1
Let n = -332 + 377. Factor 69*p + 3*p**3 + n - 9*p**2 - 26*p**2 + 62*p**2.
3*(p + 1)*(p + 3)*(p + 5)
Find l, given that -2023 - 30333 + 30415*l - 775*l**2 + 5*l**3 - 974 + 3685 = 0.
1, 77
Let i = 47 + -44. Let q(b) be the third derivative of 2/195*b**5 - 1/780*b**6 + 0 - 1/39*b**4 + 13*b**2 + 0*b**i + 0*b. Factor q(y).
-2*y*(y - 2)**2/13
Let y(w) = -2880*w**2 - 2890*w**2 - 7*w + 5769*w**2. Let k be y(-6). Solve -3/4*a**4 + 0 - 9/2*a**3 - 9*a**2 - k*a = 0.
-2, 0
Solve -742/5*y - 14/5*y**4 + 348/5 - 1534/5*y**2 - 458/5*y**3 = 0 for y.
-29, -3, -1, 2/7
Let g be (2 + (3 - 7))/(-12). Let i = -7739 + 7741. Let 0*u + g*u**3 + 0 + 0*u**i = 0. Calculate u.
0
Let d(r) be the second derivative of r**7/105 + r**6/15 + r**5/25 - 4*r**4/15 - 1044*r. Find x such that d(x) = 0.
-4, -2, 0, 1
Let r = 614 + -592. Factor -7 - 5 + 21 + 903*z + z**2 + r - 871*z.
(z + 1)*(z + 31)
Let s(f) be the first derivative of -f**2 + 1/4*f**4 + f**3 + 118 - 3/5*f**5 + 0*f + 1/6*f**6. Let s(o) = 0. Calculate o.
-1, 0, 1, 2
Let o = -506 - -508. Factor -5*i - 8*i**3 - 20*i**2 + 9*i**3 - o*i**3 - 11*i - 3*i**3.
-4*i*(i + 1)*(i + 4)
Suppose 3*b = 3*z + 6, 4*b - 2*b - 4 = -2*z. Suppose 0*l - b*h - 16 = -4*l, -2 = -3*l - h. Factor -4*m - 9*m**2 + 9*m**2 - 2*m**3 + 6*m**l.
-2*m*(m - 2)*(m - 1)
Factor -494018/3*t + 994/3*t**2 + 245526946/9 - 2/9*t**3.
-2*(t - 497)**3/9
What is o in 38*o**2 + 918 - 874 - 70*o - 1398*o**3 - 10*o**2 + 1396*o**3 = 0?
1, 2, 11
Suppose 0 = -94*d + 225*d - 108*d - 46. Solve 3/4*u + 3/4*u**d + 1/4 + 1/4*u**3 = 0.
-1
Let l(v) be the first derivative of 4*v**5/5 - 14*v**4 - 128*v**3/3 + 4547. Factor l(r).
4*r**2*(r - 16)*(r + 2)
Let g = -351044 - -351047. Let 0*d - 4/5*d**g + 0 + 52/5*d**2 = 0. What is d?
0, 13
Let w(c) be the first derivative of -c**5/60 - c**4/12 + 4*c**3/3 - 3*c**2/2 - 22*c + 17. Let o(q) be the second derivative of w(q). Factor o(i).
-(i - 2)*(i +