7. Let d(r) be the third derivative of 0*r**a + 0 - 1/600*r**6 + 0*r**5 + 0*r + 1/120*r**4 - 14*r**2. Factor d(j).
-j*(j - 1)*(j + 1)/5
Let r be 19282/88 + 8/32. Let s = r - 219. Find w such that -2/11*w**5 + 6/11*w**4 - 4/11*w**3 - s*w**2 - 2/11 + 6/11*w = 0.
-1, 1
Suppose 0 = -m + 7*d + 35, 0 = m + 3*d - 380 + 395. Factor m*i - 44/3*i**2 + 0 + 14*i**3 + 2/3*i**4.
2*i**2*(i - 1)*(i + 22)/3
Let k be -1 + 1338/864 - (-2)/(-4). Let j(i) be the third derivative of 1/720*i**6 - 1/12*i**3 + 0 - 1/72*i**5 + k*i**4 + 0*i + 7*i**2. Factor j(q).
(q - 3)*(q - 1)**2/6
Let v(l) be the second derivative of l**6/144 - 7*l**5/12 + 245*l**4/12 + 11*l**3/6 - l**2/2 - 88*l. Let g(t) be the second derivative of v(t). Factor g(k).
5*(k - 14)**2/2
Let z(g) be the second derivative of 5*g**4/24 + 965*g**3/6 + 1925*g**2/4 - 391*g - 4. Let z(n) = 0. What is n?
-385, -1
Let t(u) be the third derivative of -u**8/8960 - u**7/1680 + u**4/12 - 2*u**3/3 + 4*u**2 - 10*u. Let h(f) be the second derivative of t(f). Factor h(q).
-3*q**2*(q + 2)/4
Suppose -4*z + 28 + 8 = 0. Let h(n) = -n**3 + 9*n**2 + 3. Let o be h(z). Suppose -2*l**2 + l**5 - 4*l**o - 2 + 4*l**2 + 2*l + l = 0. What is l?
-2, -1, 1
Let b(i) be the third derivative of 0 - 269*i**2 + 1/420*i**6 + 0*i + 2/105*i**5 + 1/21*i**4 + 0*i**3. Determine h, given that b(h) = 0.
-2, 0
Let s(j) = -j**2 - 1. Let v = -4 + 2. Let w(b) = -2*b**3 + 35*b**2 - 234*b + 319. Let d(i) = v*w(i) + 10*s(i). Let d(x) = 0. What is x?
2, 9
Suppose 556 = -7*n + 640. Determine l, given that 4*l**5 + 24*l**4 + 24 - 4*l**2 - 8*l**3 + n*l - 8*l - 44*l**2 = 0.
-6, -1, 1
Find q, given that -99*q**2 - 281*q**2 - 2612*q**3 + 4262*q**3 + 245*q**5 + 25*q - 1540*q**4 = 0.
0, 1/7, 1, 5
Factor -6*q**3 - 18*q**3 - 312*q**2 - 108 + 297*q**2 + 297*q.
-3*(q - 3)*(q + 4)*(8*q - 3)
Let u(g) be the third derivative of -g**5/300 + 83*g**4/20 - 20667*g**3/10 - 1679*g**2. Find n such that u(n) = 0.
249
Let y(t) = 2*t**2 - 67*t - 45. Let x be y(36). Factor 4*p**2 - x*p + 9587 - 9415 - 41*p.
4*(p - 43)*(p - 1)
Factor 73*y + 85*y + 105*y - 94*y + 87616 + y**2 + 423*y.
(y + 296)**2
Let q = -63005 + 63007. Factor 14/5*p - 1/5*p**q - 24/5.
-(p - 12)*(p - 2)/5
Suppose 4*g + 11 = 3, 0 = -3*t - 3*g. Factor -140*x**t - 22 - 27 + 14*x + 139*x**2.
-(x - 7)**2
Let b be 14/924*-12*44/(-48). Let h(i) be the third derivative of b*i**4 + 0*i**3 + 0*i - 2/15*i**5 + 0 + 1/30*i**6 - 19*i**2. Factor h(r).
4*r*(r - 1)**2
Let u(k) be the first derivative of -k**4/6 + 10*k**3/3 - 26*k**2/3 + 316. Factor u(w).
-2*w*(w - 13)*(w - 2)/3
Determine n so that 567*n + 549/4*n**2 + 1/4*n**4 + 729 + 21/2*n**3 = 0.
-18, -3
Let g(z) = z**2 - 8*z + 36. Let h be g(13). Factor 18*y**3 + 9*y**2 + 10*y**4 + h - 101 + 5*y**2 + 2*y**5 + 4*y.
2*y*(y + 1)**3*(y + 2)
Let u(a) be the third derivative of a**5/36 + 385*a**4/72 - 65*a**3/3 + 1785*a**2. Factor u(x).
5*(x - 1)*(x + 78)/3
Solve 60*y**3 + 3/2*y**4 - 141/2*y**2 - 369*y + 0 = 0.
-41, -2, 0, 3
Let u(n) be the third derivative of n**6/180 + n**5/10 + 7*n**4/18 - 8*n**3/3 + 405*n**2 - 1. Find w such that u(w) = 0.
-6, -4, 1
Let w(d) be the first derivative of -4*d**3/3 - 736*d**2 + 1476*d - 4692. What is i in w(i) = 0?
-369, 1
Let a = 2456 + -108059/44. Let y = a - -3/22. Suppose 0 + 0*m + 0*m**3 - y*m**5 + m**2 - 3/4*m**4 = 0. Calculate m.
-2, 0, 1
Let x(u) be the second derivative of 2/225*u**6 + 0 + 0*u**3 + 57*u + 0*u**2 - 1/45*u**4 - 1/50*u**5. Factor x(s).
2*s**2*(s - 2)*(2*s + 1)/15
Let l(a) be the first derivative of -a**4/16 - 21*a**3/4 - 891*a**2/8 + 3267*a/4 - 3944. Factor l(v).
-(v - 3)*(v + 33)**2/4
Let u = -25304 - -202433/8. Let n(w) be the third derivative of 0*w + u*w**4 - 1/20*w**5 - 13*w**2 + w**3 + 0. Solve n(t) = 0.
-1, 2
Let a be 588/(-49) - (-2 + 305/(-30)). Let g(u) be the first derivative of -a*u**4 - 4/3*u**2 + 8/9*u**3 + 0*u + 19. Factor g(y).
-2*y*(y - 2)**2/3
Suppose -192/5 - 3/5*g**2 - 39*g = 0. Calculate g.
-64, -1
Let i(v) be the third derivative of v**8/504 - 26*v**7/315 - 3*v**6/20 - v**2 - 2*v + 96. Find z, given that i(z) = 0.
-1, 0, 27
Suppose -207368/3 + 6440/3*d - 50/3*d**2 = 0. What is d?
322/5
Let j(q) be the first derivative of 5*q**3/3 - 1470*q**2 - 4797. Factor j(s).
5*s*(s - 588)
Let x(p) be the third derivative of p**7/560 + 11*p**6/240 - 3*p**5/20 - 65*p**3/6 - 42*p**2 + 2. Let v(r) be the first derivative of x(r). Factor v(w).
3*w*(w - 1)*(w + 12)/2
Suppose -2*f + 14*f - 240 = 0. Suppose -4*x - 9*i + 15 = -10*i, 0 = -5*x + i + f. Factor -8/3*l**4 + 0 - 2*l**x + 0*l + 2/3*l**3 + 4/3*l**2.
-2*l**2*(l + 1)**2*(3*l - 2)/3
Let u(t) = 58*t + 12. Let y be u(6). Suppose -5*w = -w - y. Factor 28*a**4 - 2*a**5 + 132*a**2 + 122*a**2 - 352*a + 128 - 146*a**3 + w*a**2.
-2*(a - 4)**3*(a - 1)**2
Let z = 35742/3545 - 342/709. Determine d, given that -z*d**2 + 2/5*d**3 - 44/5 + 18*d = 0.
1, 22
Let l(r) be the third derivative of -11*r**6/30 - 967*r**5/15 - 10604*r**4/3 + 3872*r**3/3 - r**2 - 33*r. Factor l(g).
-4*(g + 44)**2*(11*g - 1)
Let h(x) be the second derivative of 44*x + 0 - 1/30*x**4 + 0*x**2 - 9/100*x**5 - 2/75*x**6 + 0*x**3 + 1/14*x**7. Suppose h(m) = 0. What is m?
-2/5, -1/3, 0, 1
Determine w so that 130*w + 6890*w - 1999*w**2 - 3240 + 465*w**3 - 439*w**2 - 25*w**4 - 532*w**2 = 0.
3/5, 6
Factor 6/5*u**3 + 0*u - 54/5*u**2 + 0.
6*u**2*(u - 9)/5
Suppose -i - 3*s + 21 = 0, -s + 55 = -0*i + 3*i. Suppose 17*m - 20*m = -i. Solve 4*j - 5*j**3 - 31 + 83 - m*j**2 - 44 - j**4 = 0 for j.
-2, 1
Let y(x) be the third derivative of 107*x**2 - 3/80*x**5 + 0*x + 0 + 7/960*x**6 - 1/6*x**3 - 1/1680*x**7 + 5/48*x**4. Factor y(g).
-(g - 2)**3*(g - 1)/8
Let q = 10416 + -10416. Let j(x) be the third derivative of 22*x**2 + q*x - 1/24*x**3 + 1/32*x**4 - 1/80*x**5 + 1/480*x**6 + 0. Factor j(n).
(n - 1)**3/4
Let g be (4/(-100))/(-52 - (-18095)/350). Factor -24/5*v - g*v**2 - 216/5.
-2*(v + 18)**2/15
Let w be -18 + -9*3/(-9). Let g be (-36)/w - 15/(-25). Factor 23*l**4 - 20*l**4 + 0*l**g + 3*l - 3*l**2 - 3*l**3.
3*l*(l - 1)**2*(l + 1)
Suppose 1225*z**2 + 21*z - 90 - 114 + 43*z - 180 - 1227*z**2 = 0. Calculate z.
8, 24
Let m(w) = -315*w**3 + 3925*w**2 - 530*w. Let k(t) = -35*t**3 + 436*t**2 - 60*t. Let v(o) = -55*k(o) + 6*m(o). Factor v(b).
5*b*(b - 12)*(7*b - 2)
Let v(n) be the second derivative of n**4/96 + 7*n**3/8 - 43*n**2/16 - n - 16. Factor v(g).
(g - 1)*(g + 43)/8
Let d(c) = -27*c**3 + 182*c - 284*c - 2*c**4 - 413*c + 189*c**2. Let u(g) = -g**4 - 26*g**3 + 190*g**2 - 514*g. Let l(o) = -2*d(o) + 3*u(o). Factor l(b).
b*(b - 8)**3
Let g(c) be the first derivative of 4*c**3 + 56 + 1/30*c**5 - 7/12*c**4 + 64/3*c - 40/3*c**2. What is h in g(h) = 0?
2, 4
Let i = -46/1041 - -6844/13533. Factor -2/13*k + 2/13*k**3 + 6/13*k**2 - i.
2*(k - 1)*(k + 1)*(k + 3)/13
Let g be (1623/4)/3 - (-1)/(-4). Suppose -18*u + 13*u + g = 0. Find b such that -3 + 20*b + 48*b - 50*b - u*b**2 = 0.
1/3
Suppose 48 - g**2 + 5*g**2 - 185*g + 213*g = 0. What is g?
-4, -3
Let y(m) = -m**3 + 4*m + 13. Let g be y(-2). Suppose 71 = -g*z + 110. Suppose -7/2*a**z + 3/2*a + 1/2*a**2 + 2*a**5 - 1/2 + 0*a**4 = 0. Calculate a.
-1, 1/2, 1
Suppose -4*r + 67 = g, -3*g + 25 = r - 0*r. Suppose r*a = 12*a + 16. Let 14*h**3 - 6*h**2 - 13*h**4 + 19*h**a - 15*h**5 + h**3 = 0. What is h?
-1, 0, 2/5, 1
Let g = 5129/20468 + -3/5117. Let m be ((-6)/(-16))/(9/6). Factor 0 + m*c**2 + g*c**3 + 0*c.
c**2*(c + 1)/4
Let 4/7*c**5 + 309104/7*c**3 + 32157432/7 + 16992648/7*c**2 + 1920/7*c**4 + 6977556*c = 0. What is c?
-159, -2, -1
Let j(g) be the second derivative of 3/10*g**5 + 1/63*g**7 - 4/9*g**3 + g + 8/9*g**2 - 16/135*g**6 + 13 - 5/27*g**4. Determine n, given that j(n) = 0.
-2/3, 1, 2
Let b(c) be the third derivative of c**6/30 - 16*c**5/15 - c**4/6 + 32*c**3/3 + 109*c**2 + 3*c. Suppose b(x) = 0. Calculate x.
-1, 1, 16
What is a in -21231*a**3 - 705/2*a**4 - 3/2*a**5 - 40368*a - 61248*a**2 + 0 = 0?
-116, -2, -1, 0
Let c(y) be the third derivative of -3*y**4/2 - 11*y**3/2 - 339*y**2. Let w be c(-1). Suppose -w*x + 3/2*x**2 + 3/2 = 0. Calculate x.
1
Let s be (-16)/(-14) - 228/(-266). Determine c, given that 4 + 12*c**2 - 28*c**3 - 80*c + 39*c**2 - 15*c**2 - 4*c**4 - 36 - 108*c**s = 0.
-2, -1
Let d(a) = -2*a**3 + 15*a**2 - 25*a - 8. Let t be d(4). Suppose 2*u + 3*u = 5*h + 15, -t*u = 4*h + 12