8. Factor y*v**3 - 32/7*v**2 + 30/7*v + 0.
2*v*(v - 15)*(v - 1)/7
Let g(w) be the second derivative of 5*w**7/2016 - w**6/96 - w**4/12 - 21*w**2/2 - 46*w. Let a(b) be the third derivative of g(b). Factor a(c).
5*c*(5*c - 6)/4
Let r(s) = -146*s + 27453. Let t be r(188). What is v in 2/3*v**t - 10/3*v**2 + 2/3*v**4 + 8/3*v - 10/3*v**3 + 8/3 = 0?
-2, -1, 1, 2
Let x(c) be the second derivative of c**5/10 + 21*c**4/2 + 734*c**3/3 + 672*c**2 + 1648*c - 2. Find p, given that x(p) = 0.
-48, -14, -1
Let y(i) = -86*i + 1379. Let x be y(16). Suppose 0*a + 4*a**2 + 0 + 1/3*a**x = 0. What is a?
-12, 0
Suppose 608/13*p**3 + 134/13*p - 496/13*p**2 - 12/13 = 0. What is p?
1/4, 6/19
Let l(b) be the third derivative of b**6/240 + 5*b**5/12 + 703*b**2. Factor l(i).
i**2*(i + 50)/2
Let p(u) = -1824*u - 7125. Let b(y) = -35*y - 137. Let a(h) = 209*b(h) - 4*p(h). Let f be a(-7). Determine q so that -1/2 - 1/2*q**4 + f*q + 0*q**3 + q**2 = 0.
-1, 1
Let o(q) be the first derivative of 4*q**3/3 + 460*q**2 + 52900*q + 1874. Determine k so that o(k) = 0.
-115
Let o be (5285/105 + -15 - 35)*2*6. Factor 16/15*d**2 - 2/3*d**3 + 0 - 8/15*d + 2/15*d**o.
2*d*(d - 2)**2*(d - 1)/15
Let i(o) = 3*o**4 - 263*o**3 - 634*o**2 + 9*o + 864. Let a(n) = 2*n**4 - 258*n**3 - 636*n**2 + 10*n + 864. Let c(t) = -7*a(t) + 6*i(t). Let c(l) = 0. What is l?
-54, -2, 1
Let j(k) = 45*k - 5*k - 2*k**2 + 4*k - 36 - 14*k. Let r(i) = -4*i**2 + 29*i - 37. Let w(z) = -3*j(z) + 2*r(z). Factor w(h).
-2*(h - 1)*(h + 17)
Let 6*q**4 - 7*q**4 + 1453*q**2 - 131072 - 4909*q**2 + 100*q**3 + 21677*q + 23379*q = 0. What is q?
4, 32
Solve -3*c**4 - 172*c**2 + 383*c**2 + 88*c**3 - 175*c**2 - 121*c**3 = 0 for c.
-12, 0, 1
Let f(k) = -3*k - 11. Let u be f(-7). Let b = -107 - -122. Factor -b*q**2 + 8*q**3 + 0*q**3 + 11*q**3 + u*q - 14*q**3.
5*q*(q - 2)*(q - 1)
Let x(v) be the first derivative of -183 - 35*v**3 - 225/2*v**2 + 5/4*v**4 - 115*v. Solve x(s) = 0 for s.
-1, 23
Let l = 203 - 125. Let m = l + -78. Factor 4/5*t**2 + m + 4/5*t.
4*t*(t + 1)/5
Let k be (-20262)/48 + -1 - -7. Let j = -416 - k. Determine n, given that 0 + j*n**2 + 3/8*n = 0.
-3, 0
Let -20*o**4 - 789*o**2 + 136 + 2*o**4 - 231*o**3 + 8 + 222*o - 948*o = 0. Calculate o.
-8, -3, -2, 1/6
Let v be 2/3 - 5220/(-270). Factor v*q + 8*q - 13*q - 4*q + 21*q - 4*q**2.
-4*q*(q - 8)
Let u = 18/941 + 3674/4705. Let l(a) be the first derivative of u*a**5 + 0*a**3 + 0*a - 2 + 3/4*a**4 - 1/4*a**2 + 1/4*a**6. Suppose l(y) = 0. Calculate y.
-1, 0, 1/3
Suppose 27*q + 21 - 4/3*q**2 = 0. Calculate q.
-3/4, 21
Determine k, given that 32/13 - 116/13*k - 6/13*k**4 + 44/13*k**3 + 46/13*k**2 = 0.
-2, 1/3, 1, 8
Let c(u) be the second derivative of -u**6/30 + u**5/4 - u**4/3 - 127*u + 1. Factor c(t).
-t**2*(t - 4)*(t - 1)
Let p(c) be the third derivative of c**5/60 + c**4/6 + c**3/3 - 6*c**2. Let w be p(-4). Determine h, given that -h - 4*h - 17*h**w + 3*h = 0.
-2/17, 0
Let s be (-5)/(-50)*7/238. Let n = s - -677/1020. What is f in 1/2*f + n - 7/6*f**2 = 0?
-4/7, 1
Suppose r = d - r, 0 = 4*d + 2*r - 20. Suppose 4*y + c = 14, -4*y - 4*c = -y - d. Solve 73*i**2 + 12*i**y + 107*i**2 - 100*i**2 + 32*i + 56*i**3 = 0.
-2, -2/3, 0
Solve 3/7*a**2 - 51/7*a + 216/7 = 0 for a.
8, 9
Determine w, given that 56 + 595*w + 97*w**2 - 655*w - 93*w**2 = 0.
1, 14
Let u = -793316 - -3966673/5. Factor -18*v - u + 3/5*v**2.
3*(v - 31)*(v + 1)/5
Suppose 3*y - 9 = 0, 17*y = -2*p + 14*y + 181. Let m + 197*m**4 + 85*m**2 - 392*m**4 + 200*m**4 - p*m + 30 - 35*m**3 = 0. What is m?
1, 2, 3
Let a(w) be the third derivative of -w**8/84 - 2*w**7/315 + 11*w**6/45 + 4*w**5/45 - 20*w**4/9 - 95*w**2 - 5. Suppose a(t) = 0. What is t?
-2, 0, 5/3, 2
Let l(g) = 2704*g**2 - 1430*g + 196. Let q(z) = 13*z. Let p(m) = l(m) - 2*q(m). Find a, given that p(a) = 0.
7/26
Let f = -480 - -488. Determine j so that -46*j + 50 + 325*j - 127*j - 194*j**2 - f*j**3 = 0.
-25, -1/4, 1
Let c(p) = -2*p**2 - 9*p + 1. Let m be c(-4). Suppose 3*x = -15, 5*x + 10 = -m*s - 0*x. Factor 42 + 2*j**s - 19 + 10*j - 8*j**2 - 27.
2*(j - 2)*(j - 1)**2
Factor -16/3*i**3 - 2/3*i**4 - 12*i - 14*i**2 + 0.
-2*i*(i + 2)*(i + 3)**2/3
Let p = -1423273 + 2846587/2. Let -p*i - 1/2*i**2 + 21 = 0. What is i?
-42, 1
Let o(d) = 3*d**3 + d**2 + 10. Let z(v) = -31*v**3 - 4990*v**2 - 8266800*v - 4574296100. Let m(t) = -10*o(t) - z(t). Factor m(x).
(x + 1660)**3
Let w = 1534/1479 + 929906/10353. Determine p so that 128/7*p**4 - 528/7*p**2 + w*p**3 + 6/7*p**5 + 0 - 242/7*p = 0.
-11, -1/3, 0, 1
Suppose -931*x + 1386 = -238*x. Factor 3/8*h**x + 243/4*h + 19683/8.
3*(h + 81)**2/8
Let a = -4312 - -4314. Let y(k) be the third derivative of -1/270*k**5 + 0*k + 1/108*k**4 + 0*k**3 + 0 - 15*k**a. Suppose y(i) = 0. Calculate i.
0, 1
Let l(r) be the third derivative of r**8/672 - 17*r**7/420 + 3*r**6/16 - 43*r**5/120 + 7*r**4/24 - 306*r**2. Factor l(f).
f*(f - 14)*(f - 1)**3/2
Factor 2/13*j**2 + 762/13*j - 764/13.
2*(j - 1)*(j + 382)/13
Let h(f) be the second derivative of -1/6*f**6 - 35/12*f**4 + 0 + 5/2*f**3 + 39*f + 5/4*f**5 + 0*f**2. Factor h(l).
-5*l*(l - 3)*(l - 1)**2
Let s(z) be the first derivative of z**4/32 - 31*z**3/8 - 143*z**2/8 - 24*z - 1320. Let s(i) = 0. What is i?
-2, -1, 96
Let q = -464855/3 - -154952. Find j such that -q*j**2 - 20/3 - 4*j = 0.
-10, -2
Let w(o) be the third derivative of 11/4*o**4 + 1/3*o**5 - 85 + 3*o**3 - 2*o**2 + 0*o. Solve w(i) = 0.
-3, -3/10
Let j be -1 + 161/(42/6). Suppose 2 = -5*f + j. Find q, given that 0 + 6/19*q**f - 4/19*q + 14/19*q**2 - 16/19*q**3 = 0.
0, 2/3, 1
Let z(m) be the first derivative of 0*m - 12 + 1/2*m**4 - 4*m**2 + 0*m**3. Factor z(s).
2*s*(s - 2)*(s + 2)
Let k(x) be the third derivative of -x**7/10080 - 5*x**6/288 - 125*x**5/96 + 49*x**4/6 - 214*x**2. Let p(c) be the second derivative of k(c). Factor p(s).
-(s + 25)**2/4
Let x(c) = -2*c**2 - c + 1. Let r(m) = 2*m. Let t(g) = 19*g - 5. Let w(f) = 6*r(f) - t(f). Let v(u) = -w(u) + x(u). Determine b, given that v(b) = 0.
1, 2
Suppose 2 = -a - 5*u, -5*a - 3*u = -5*u - 17. Find b, given that -9*b**3 + 154 - 148 + 0*b**a + 9*b - 6*b**2 = 0.
-1, -2/3, 1
Factor -2/9*h**4 - 20/3*h**3 - 1352/9*h - 182/3*h**2 + 0.
-2*h*(h + 4)*(h + 13)**2/9
Let s(f) = 21*f**2 - 4*f - 9. Let k(d) = -7*d**2 + 12. Let l(a) = -a**2 + 2. Let w(p) = -k(p) + 5*l(p). Let x(m) = -2*s(m) + 6*w(m). Factor x(t).
-2*(3*t + 1)*(5*t - 3)
Let i(r) = -r**3 - 32*r**2 - 29*r - 21. Let z be i(-31). Let g = -497/6 - z. Factor 0*o + 0 + 1/6*o**3 + 0*o**2 + g*o**4.
o**3*(o + 1)/6
Let t(s) be the third derivative of 20*s**4 + 3*s**2 + 1/80*s**6 + 8 - 19/20*s**5 + 0*s + 200*s**3. Solve t(x) = 0.
-2, 20
Let n(w) = 14553*w + 29127. Let a be n(-2). Factor 4 + a*m - 11/2*m**2.
-(m - 4)*(11*m + 2)/2
Factor -2 - 14*u**3 + 4*u - 4441*u**4 + 46*u + 2 + 4440*u**4 - 35*u**2.
-u*(u - 1)*(u + 5)*(u + 10)
Let f be 1/(2/(-48)*3*-4). Factor 22/5*k - 1/5*k**f + 0.
-k*(k - 22)/5
Factor -35*c + 131*c - 4*c**3 + 25*c**2 - 3*c**2 + 21*c**2 + 49*c**2.
-4*c*(c - 24)*(c + 1)
Let t be 612/144 - 2/8. Factor 499 + 670 - 128*j - 145 + t*j**2.
4*(j - 16)**2
Let m(g) be the third derivative of -14*g**2 + 0*g**3 - 5/6*g**5 - 1/8*g**6 + 0 + 1/42*g**7 + 0*g**4 + 0*g. Factor m(f).
5*f**2*(f - 5)*(f + 2)
Factor -47769 + 3*r**2 - 4*r**2 + 796*r + 42050 - 152685.
-(r - 398)**2
Let h(w) = -w**3 + 18*w**2 - 14*w - 24. Let p be h(17). Find i such that 28*i**5 + p*i**5 - 51*i**5 - 3*i**4 + 19*i**4 + 4*i**3 - 24*i**2 = 0.
-3, -2, 0, 1
Let u(v) be the third derivative of v**6/1980 - v**5/165 + 22*v**3/3 - 2*v**2 + 5*v. Let g(n) be the first derivative of u(n). Factor g(r).
2*r*(r - 4)/11
Let v(o) be the third derivative of o**5/100 - 39*o**4/10 - 157*o**3/10 - 2*o**2 + 317*o. Suppose v(t) = 0. Calculate t.
-1, 157
Let n(s) be the third derivative of -s**6/2520 + 3*s**5/35 - 54*s**4/7 + 161*s**3/6 + 2*s**2 - 226*s. Let d(t) be the first derivative of n(t). Factor d(w).
-(w - 36)**2/7
Let f(u) be the second derivative of -u**6/15 + 13*u**5/30 + 5*u**4/9 - 8*u + 2. What is q in f(q) = 0?
-2/3, 0, 5
Let x(z) be the first derivative of 75/4*z**4 + 13*z**5 - 65/3*z**3 + 0*z - 5/2*z**2 - 35/3*z**6 - 81. Determine v so that x(v) = 0.
-1, -1/14, 0, 1
Suppose m = -4 + 7. What is o in o**3 + 2*o**4 + 18*o**2 - 18*o**m + 4 + 7*o**3 - 14*o = 0?
1, 2
Let n(d) = 3*d**2 + 71