8. Let q(k) = 4*k**2 + 3*k. Let a(p) = n(p) + 4*q(p). Factor a(i).
(i - 8)*(i + 1)
Let u(a) be the first derivative of -16*a**3/57 + 31*a**2/19 + 8*a/19 + 2962. Factor u(t).
-2*(t - 4)*(8*t + 1)/19
Suppose 6*q - 84 = 10*q. Let i = 23 + q. Determine t so that 3 - 2 - 4*t - 4*t**3 + 8*t**i - 1 = 0.
0, 1
Let c(a) be the first derivative of a**5/30 - 83*a**4/12 - 167*a**3/18 + 3618. Factor c(y).
y**2*(y - 167)*(y + 1)/6
Let t(q) be the first derivative of -q**4/20 + 31*q**3/15 - 12*q**2/5 - 36*q - 2536. Factor t(u).
-(u - 30)*(u - 3)*(u + 2)/5
Let f(d) be the second derivative of d**6/720 + 7*d**5/120 + 49*d**4/48 + 41*d**3/6 + d + 8. Let c(q) be the second derivative of f(q). Factor c(s).
(s + 7)**2/2
Let i(p) be the second derivative of 9/5*p**2 - 27*p + 11/30*p**4 + 0 - 19/15*p**3 - 1/50*p**5. Factor i(a).
-2*(a - 9)*(a - 1)**2/5
Let b(h) be the second derivative of -1/3*h**3 + 0 - 5/6*h**4 - 2/5*h**5 - 66*h + 0*h**2. Factor b(z).
-2*z*(z + 1)*(4*z + 1)
Let n(k) be the second derivative of k**5/5 - 13*k**4/6 + 15*k**3/8 + 9*k**2/4 + 3465*k. Determine q so that n(q) = 0.
-1/4, 3/4, 6
Suppose 0*w - 4*w + 12 = 0. Let r = -2/295425 + 689327/295425. Suppose 4/3 + 2/3*i**2 + 1/3*i**w - r*i = 0. What is i?
-4, 1
Let l(q) be the second derivative of -q**5/15 - 11*q**4/18 - 16*q**3/9 - 7*q**2/3 + 10402*q. Let l(f) = 0. What is f?
-7/2, -1
Let i(v) be the third derivative of 2*v**5/65 + 877*v**4/156 + 73*v**3/39 - 10776*v**2. Determine l so that i(l) = 0.
-73, -1/12
Let u be (-258)/(-60) + -22 + 74/4. Factor -2/15*t**2 + 14/15 - u*t.
-2*(t - 1)*(t + 7)/15
Let l(f) be the third derivative of -3*f**6/80 - 4*f**5/5 + 191*f**4/16 - 15*f**3 + 2284*f**2. What is a in l(a) = 0?
-15, 1/3, 4
Suppose 2637 = 993*d + 651. Factor 578/7 + 68/7*n + 2/7*n**d.
2*(n + 17)**2/7
Let a(l) = 3*l**4 + l**3 - 21*l**2 - 11*l + 2. Let c(p) = -10*p**4 - 5*p**3 + 84*p**2 + 44*p - 8. Let t(h) = -9*a(h) - 2*c(h). Find w such that t(w) = 0.
-1, 1/7, 2
Suppose -2*p = 3*d - 164, -3*p + 27 + 30 = d. Let l = d + -52. Factor 7*i**2 - 7*i**l + 6 + 2*i**2 + 8*i.
2*(i + 1)*(i + 3)
Factor 4740*i - 371407 - 242662 - 314297 - 195014 - 5*i**2.
-5*(i - 474)**2
Let f(c) be the third derivative of -c**8/72 + 58*c**7/315 - 13*c**6/36 + 7*c**5/45 - 24*c**2 + 41*c. Let f(h) = 0. Calculate h.
0, 2/7, 1, 7
Let p(f) = -f**4 - f**3 + 3*f**2 - f. Let s(k) = 6*k**4 - 102*k**3 - 336*k**2 + 16*k + 416. Let a(l) = -8*p(l) - s(l). Factor a(g).
2*(g - 1)*(g + 2)**2*(g + 52)
Let k(q) = 17737*q + 620822. Let h be k(-35). Factor -3/4*a**3 + 57/2*a**2 - 219/4*a + h.
-3*(a - 36)*(a - 1)**2/4
Let p be 0/15 - (-2 - 2). Let s be (9 + (p - 10))*(-4)/(-18). Factor s - 5/9*j - 1/9*j**2.
-(j - 1)*(j + 6)/9
Let q(t) be the third derivative of -4*t**2 + 0*t**3 + 0*t**4 + 0*t + 1/240*t**5 + 1/80*t**6 - 2. Solve q(n) = 0 for n.
-1/6, 0
What is k in -66*k - 56*k - 63*k + 186*k - 2*k**3 + k**5 = 0?
-1, 0, 1
Let r(m) be the first derivative of m**4 + 24*m**3 + 66*m**2 + 64*m - 219. Factor r(v).
4*(v + 1)**2*(v + 16)
Suppose -236*x + 13 = -235*x. Suppose -x*s**2 + 23 - 25 + 15*s**2 = 0. Calculate s.
-1, 1
Let l = -11263/3 + 45055/12. Factor 7/4*g**3 - 2 + 9/4*g**2 - l*g**4 - 7/4*g.
-(g - 8)*(g - 1)*(g + 1)**2/4
Let q be (-2 - -6) + (-1827)/36 + 49. Let y be ((-39)/(-26))/(1/2). What is b in 4 - 8*b**y + 14*b**2 + q*b**4 - 1/4*b**5 - 12*b = 0?
1, 2
Let i(z) be the third derivative of -z**8/504 - 73*z**7/189 + 491*z**6/540 - 41*z**5/90 + 51*z**2 + 20*z. Find j such that i(j) = 0.
-123, 0, 1/3, 1
Let v(r) = -r**3 + 27*r**2 + 3*r - 55. Let b be v(27). Factor 20*u**2 - b - 6 - 4*u**3 - 8*u + 0.
-4*(u - 4)*(u - 2)*(u + 1)
Let n be 5/35*(-74 - 14) - (-12 - 1). Suppose n*v + 1/7*v**2 + 0 = 0. What is v?
-3, 0
Let n = -880948 - -880950. Factor -24/11*s**n + 0 - 1/11*s**4 - s**3 + 36/11*s.
-s*(s - 1)*(s + 6)**2/11
Factor 110/9*g + 28/9*g**2 - 1936/9 - 2/9*g**3.
-2*(g - 11)**2*(g + 8)/9
Let l(g) be the first derivative of -g**5/20 + 5*g**4/8 - 7*g**3/12 - 9*g**2/4 + 152. Solve l(x) = 0 for x.
-1, 0, 2, 9
Let n(g) be the third derivative of g**7/105 - 157*g**6/20 + 12402*g**5/5 - 334620*g**4 + 3796416*g**3 + 2670*g**2. Factor n(c).
2*(c - 156)**3*(c - 3)
Suppose -144*v + 138 = 138. Find r, given that v - 10/7*r**2 + 12/7*r - 2/7*r**3 = 0.
-6, 0, 1
Let r(m) = -8*m - 446. Let c be r(-58). Let b be 33/(-594) + 73/c. Factor -1/4*k + k**b + 0 + 0*k**3 - 3/4*k**2.
k*(k - 1)*(2*k + 1)**2/4
Let u(v) be the first derivative of -v**6/1080 - v**5/60 - 5*v**4/72 - 22*v**3/3 + 18. Let w(r) be the third derivative of u(r). What is j in w(j) = 0?
-5, -1
Factor -114 + 112/3*a + 2/9*a**2.
2*(a - 3)*(a + 171)/9
Let q(d) be the third derivative of 1/12*d**5 + 2*d - 3*d**2 + 10/3*d**3 - 25/24*d**4 + 0. Solve q(r) = 0 for r.
1, 4
Let u(o) be the second derivative of 19*o**6/1260 - o**5/210 - 22*o**3/3 - o**2 - 23*o. Let h(d) be the second derivative of u(d). What is g in h(g) = 0?
0, 2/19
What is k in 64 + 31*k**4 + 1875*k**2 + 29*k**4 + 16164115*k - 16164925*k + 51 - 1460*k**3 = 0?
1/3, 1/2, 23
Suppose 2*g = -5*b + 36 - 10, -3*b = -12. Suppose 0 = -g*d - 4*m + 32, 2*d + m - 1 = 3*d. Factor d*o**4 + o**3 + 0 + 0*o + 7/3*o**5 - 2/3*o**2.
o**2*(o + 1)**2*(7*o - 2)/3
Let w(d) = 5*d - 45. Let g be w(12). Find z, given that -5*z + 80*z**2 - g*z + z**4 - 21*z**4 + 5*z**3 + 0*z = 0.
-2, 0, 1/4, 2
Let o(b) = 594*b + 1192. Let n be o(-2). Let f(j) be the second derivative of -1/3*j**n - 8/3*j**3 - 17*j + 0*j**2 + 0. Solve f(i) = 0.
-4, 0
Let p(y) be the first derivative of 3*y**4/4 + 10*y**3 - 48*y**2 - 288*y + 1747. What is m in p(m) = 0?
-12, -2, 4
Let f(u) be the second derivative of -8*u**7/21 + 278*u**6/15 - 98*u**5/5 - 139*u**4/3 + 68*u**3 + 8*u + 372. Solve f(b) = 0 for b.
-1, 0, 3/4, 1, 34
Let i = 43/9300 - 1/775. Let h(a) be the third derivative of -i*a**5 - 49/30*a**3 - 7/60*a**4 + 0 - 12*a**2 + 0*a. Determine m, given that h(m) = 0.
-7
Suppose 721/6*j + 115 - 1/6*j**3 + 5*j**2 = 0. Calculate j.
-15, -1, 46
Let v(i) = 6 - 2*i**4 - 4 + 9*i**4 - 13*i + 3*i**2 + i**3. Let h(b) = 2*b**4 + 2*b**2 - b**4 - 3*b**2 - b + b**3. Let n(s) = 30*h(s) - 5*v(s). Factor n(k).
-5*(k - 2)*(k - 1)**3
Let y be 0*(40/(-240))/(1/(-2) - -1). Let j(z) be the first derivative of -1/5*z**4 + y*z - 21 - 18/5*z**2 - 8/5*z**3. Let j(x) = 0. Calculate x.
-3, 0
Solve 514/7*g - 102/7*g**2 - 20/7 = 0 for g.
2/51, 5
Let a be -54 + 10 - -36 - -4*2. Factor -2*w**2 + 0 - 4/3*w + a*w**3 + 2/3*w**4.
2*w*(w - 2)*(w + 1)**2/3
Let c(d) be the third derivative of d**5/210 - 5*d**4/42 - 48*d**3/7 - d**2 - 210*d. Factor c(q).
2*(q - 18)*(q + 8)/7
Suppose 0 = 2*a, -5*q + 24 + 56 = -3*a. Let c be 0 + (-1 - q/(-4)) + 5. Factor -19*t**3 + 0 - 20*t**2 - 10 + 6*t**3 - 25*t + c*t**3.
-5*(t + 1)**2*(t + 2)
Let s(w) be the second derivative of 0 + 1/3*w**5 + 0*w**3 + 1/3*w**4 - 15*w - 1/2*w**2 + 1/15*w**6. Let u(a) be the first derivative of s(a). Factor u(n).
4*n*(n + 2)*(2*n + 1)
Let x(a) = -10*a**2 + 236*a - 229. Let r(k) = -43*k**2 + 946*k - 916. Let q(z) = 6*r(z) - 26*x(z). Factor q(h).
2*(h - 229)*(h - 1)
Let v = 22441 + -22439. Let s(w) be the third derivative of 0*w + 0 - 5/12*w**3 + 5/24*w**4 - 1/24*w**5 - 13*w**v. Factor s(d).
-5*(d - 1)**2/2
Suppose -4 - 16 = -10*k. Factor -4 + 14 - 13 + 18*d - 3*d**k + 40 + 11.
-3*(d - 8)*(d + 2)
Suppose -9*p - 35 = -16*p. Factor -5*g + 20*g - 30*g**2 - 3*g + 30 - 10*g + p*g**3 - 7*g.
5*(g - 6)*(g - 1)*(g + 1)
Let g(s) = 18*s**2 - 108*s + 156. Let l(i) = -i**3 + 19*i**2 - 103*i + 156. Let v(a) = -3*g(a) + 2*l(a). Find c, given that v(c) = 0.
-13, 2, 3
Let m(c) = -18*c**4 - 26*c**3 + 28*c**2 + 8*c - 48. Let k(j) = -2*j**4 - 3*j**3 + j**2. Let t(v) = 8*k(v) - m(v). Factor t(y).
2*(y - 2)**2*(y + 2)*(y + 3)
Let -14*y**4 - 40/3*y + 38/3*y**3 + 0 + 14*y**2 + 2/3*y**5 = 0. What is y?
-1, 0, 1, 20
Suppose 380*g + 4320 = 385*g. Factor -15802*c + 16378*c + 3*c**3 + 36*c**2 + g + 42*c**2.
3*(c + 2)*(c + 12)**2
Let g be 36/5*(-7)/(14/(-5)). Factor -20*r**2 + g*r - 23*r**2 + 60*r**2 - 20*r**2.
-3*r*(r - 6)
Suppose i = -3*q - 6, -147*q + 142*q + 5*i + 90 = 0. Factor 2/11*p**4 + 0 - 12/11*p**2 - 16/11*p + 6/11*p**q.
2*p*(p - 2)*(p + 1)*(p + 4)/11
Let g(n) be the first derivative of n**7/1400 + 23*n**6/300 + 529*n**5/200 + 109*n**3/3 - 60. Let d(r) be the third derivative of g(r). 