 of 2*f**3/3 - 18*f**2 - 38*f - 1326. Factor d(x).
2*(x - 19)*(x + 1)
Let j(a) be the third derivative of -121/480*a**5 + 251*a**2 - 3*a**3 + 0 + 0*a + 31/8*a**4 + 1/192*a**6. Factor j(n).
(n - 12)**2*(5*n - 1)/8
Let y be 3/(-1*6 - 63/(-9)). Factor 36*n**2 + 3*n**3 - 6*n**3 - 1509 + 48*n**2 + 7*n**y - 219 + 288*n.
4*(n - 3)*(n + 12)**2
Let f(a) = a**3 + 2*a**2 - 5*a - 2. Let u be f(-3). Let c = 4 + u. Let y(k) = -k**2 - 16. Let v(j) = 2*j**2 + 24. Let p(m) = c*y(m) + 5*v(m). Factor p(g).
2*(g - 2)*(g + 2)
Factor 120/7 + 2/7*d**3 + 6/7*d**2 - 128/7*d.
2*(d - 6)*(d - 1)*(d + 10)/7
Let l(b) be the first derivative of -1/42*b**6 + 4050/7*b**3 + 59/35*b**5 - 216 - 645/14*b**4 - 37125/14*b**2 - 50625/7*b. Factor l(f).
-(f - 15)**4*(f + 1)/7
Suppose 0 = 5*k + 5*w - 7*w - 91, 0 = 3*k - 4*w - 63. Factor -27*d + 14*d + 2*d**2 + 12 + 16 - k*d.
2*(d - 14)*(d - 1)
Let m(n) be the third derivative of n**5/90 - 47*n**4/36 + 60*n**3 - 2*n**2 + 2831*n - 2. Suppose m(s) = 0. Calculate s.
20, 27
Let u(y) = -3*y**3 - y**2 + 2*y + 1. Let l(i) = 130*i**3 - 10815*i**2 + 254965*i - 22095. Let p(j) = l(j) + 5*u(j). Factor p(r).
5*(r - 47)**2*(23*r - 2)
Determine c, given that -75*c + 4/3*c**5 - 60*c**2 + 20/3*c**4 + 0 - 11/3*c**3 = 0.
-3, -5/2, 0, 3
Let a(u) = 2*u + 20. Let g be a(-8). Factor 2*q**5 - 98*q - 3*q**4 + 33*q**g + 96*q**3 - 2*q**4 - 28*q**2.
2*q*(q - 1)*(q + 1)*(q + 7)**2
Let m(s) be the second derivative of -1/6*s**4 + 86 - 3/110*s**5 - 2*s + 0*s**2 - 2/11*s**3. Suppose m(r) = 0. Calculate r.
-3, -2/3, 0
Let n(h) be the second derivative of 2/3*h**4 + 0*h**2 + 54 - 2*h - 4/15*h**6 + 0*h**3 - 1/5*h**5 + 2/21*h**7. Factor n(i).
4*i**2*(i - 2)*(i - 1)*(i + 1)
Let h be (-32)/64 - (-34)/8 - 6/8. Let x(z) be the first derivative of 1/3*z**h + 0*z**2 - 16 - z. Suppose x(s) = 0. What is s?
-1, 1
Let l(h) be the second derivative of h**4/4 + 611*h**3 + 1119963*h**2/2 + 935*h. Determine i so that l(i) = 0.
-611
Let m(c) be the first derivative of -c**6/360 - c**5/24 + 2*c**3/3 + 7*c**2 - 24. Let t(f) be the third derivative of m(f). What is v in t(v) = 0?
-5, 0
Let a(l) = l**3 + 2*l**2 - 8*l - 5. Let m be a(4). Let g = m + -55. Factor 14*y**4 - g*y**4 - 2*y**4 - 10*y**3 + 4*y**2 - 2*y**5.
-2*y**2*(y - 2)*(y - 1)**2
Let t(i) be the third derivative of -1/45*i**5 - 1/180*i**6 + 0 + 0*i + 0*i**3 - 93*i**2 + 1/12*i**4. What is l in t(l) = 0?
-3, 0, 1
Let b = -6717 + 80605/12. Let x(l) be the third derivative of -b*l**3 + 0 + 0*l + 17*l**2 - 1/96*l**5 + 1/960*l**6 + 1/24*l**4. Find h such that x(h) = 0.
1, 2
Let k be (-6)/24 + (-179)/4. Let d = 50 + k. Determine i, given that 6*i - 29*i**2 + 192*i**5 - 190*i**d + 9*i**4 + 3*i**2 + 9 = 0.
-3, -1/2, 1
Let u(x) = 3*x**3 - 9*x**2 + 5*x - 10. Let l = 166 - 163. Let a be u(l). Factor 7/2*z**2 + 13/2*z**4 + 0 + 15/2*z**3 + 2*z**a + 1/2*z.
z*(z + 1)**3*(4*z + 1)/2
Let m(f) be the third derivative of 0*f + 1/240*f**5 - 1/4*f**3 - 5/96*f**4 - 6 - 7*f**2. Factor m(g).
(g - 6)*(g + 1)/4
Let l(b) = -2*b**3 + b**2 - 2*b + 1. Let f(h) = -h**4 + 104*h**3 + 111*h**2 - 4*h + 2. Let u(j) = f(j) - 2*l(j). Factor u(n).
-n**2*(n - 109)*(n + 1)
Let s(l) = 4*l**2 - 4*l - 8. Let u(t) = t**2 - t - 2. Let n = -198 + 200. Let k(z) = n*u(z) - s(z). Factor k(b).
-2*(b - 2)*(b + 1)
Factor -880/3*s - 80*s**2 + 0 - 5/3*s**3.
-5*s*(s + 4)*(s + 44)/3
Let l = -4147/215 + 838/43. Factor -v**2 - l*v**3 + 0 - 4/5*v.
-v*(v + 1)*(v + 4)/5
Factor 16 + 4*b**3 + 6*b**3 + 196*b**2 - 182*b**2 - 28*b - 12*b**3.
-2*(b - 4)*(b - 2)*(b - 1)
Let i(z) = 6*z - 69. Let x be i(12). Factor 5671*f**4 + 21*f**2 - 2*f**5 - 18*f**x - f**5 - 6*f - 9*f**3 - 5656*f**4.
-3*f*(f - 2)*(f - 1)**3
Let z = 419 + -447. Let i be -6 + (96/56)/((-8)/z). Solve i*k + 0*k**3 + 2/3*k**2 + 0 - 2/3*k**4 = 0 for k.
-1, 0, 1
Let j(c) be the second derivative of -1/27*c**4 + 2*c - 1/45*c**5 + 0*c**2 + 69 + 4/27*c**3. Factor j(u).
-4*u*(u - 1)*(u + 2)/9
Let x(y) be the first derivative of -9*y**5/35 - 33*y**4/14 - 37*y**3/7 + 33*y**2/7 + 120*y/7 - 2513. What is j in x(j) = 0?
-4, -10/3, -1, 1
Let w(k) be the third derivative of 1/20*k**5 + 1/4*k**4 + 0*k + 0 + 0*k**3 - 3/40*k**6 - 53*k**2. Factor w(o).
-3*o*(o - 1)*(3*o + 2)
Suppose -4*q = 2*t - 42, -4*q + 98 = 3*t - 3*q. Let p(o) be the first derivative of 1/24*o**3 + t + 0*o - 1/16*o**2. Factor p(s).
s*(s - 1)/8
What is o in -12*o**3 - 16*o**3 + 25620 - 25444 - 356*o**2 - 512*o = 0?
-11, -2, 2/7
Let s(x) = 100*x**4 - 370*x**3 + 110. Suppose 904 = -11*o + 299. Let u(z) = -11*z**4 + 41*z**3 - 12. Let y(b) = o*u(b) - 6*s(b). Factor y(a).
5*a**3*(a - 7)
Let h(a) be the third derivative of -a**5/210 + 3*a**4/7 - 33*a**3/7 - 656*a**2. Factor h(u).
-2*(u - 33)*(u - 3)/7
Let m(b) be the first derivative of -2*b**3/15 - 4*b**2 - 102*b/5 - 2729. What is f in m(f) = 0?
-17, -3
Let r be ((-98)/20)/((-109522)/39115). Solve -1/4*u**5 + 2*u**3 + 3/2*u**2 - r*u - 3/2*u**4 + 0 = 0 for u.
-7, -1, 0, 1
Let u(y) be the second derivative of y**6/1440 + 5*y**5/96 - 13*y**4/48 + y**3/6 - 109*y. Let s(a) be the second derivative of u(a). Factor s(r).
(r - 1)*(r + 26)/4
Let v(l) = 12*l + 12. Let a be v(-4). Let k be (a/10)/((-69)/230). Determine r so that -4*r**2 - 17*r - 8*r**3 + 34*r - 17*r + k*r**4 = 0.
-1/3, 0, 1
Let g = 1296 - 1296. Let r(p) be the third derivative of 0 + 0*p**3 - 1/210*p**5 + g*p + 1/84*p**4 + 15*p**2. Factor r(z).
-2*z*(z - 1)/7
Determine a so that 1/2*a**3 + 0 - 2*a**2 + 0*a = 0.
0, 4
Let h(r) be the second derivative of -1/1260*r**6 + 4*r + 0*r**2 + 0*r**4 + 1/420*r**5 + 0 - 1/6*r**3. Let m(f) be the second derivative of h(f). Factor m(c).
-2*c*(c - 1)/7
Suppose -22*k = -4*q - 25*k + 406, -3*q - k + 302 = 0. Suppose 28*w - q = -22*w. Factor 7/4*s**4 - 1/2*s**3 + 0 - 7/4*s**w + 1/2*s.
s*(s - 1)*(s + 1)*(7*s - 2)/4
Let d be 6/8*((-128)/(-3))/16. Let l(i) be the third derivative of 0*i**4 + 0*i + 1/45*i**5 + 0*i**3 + 0 - 3*i**d + 1/90*i**6. Find n such that l(n) = 0.
-1, 0
Let b(y) be the third derivative of 5*y**8/168 - 9*y**7/14 - 55*y**6/24 + 23*y**5/2 + 235*y**4/6 - 100*y**3 + 295*y**2. Find n, given that b(n) = 0.
-2, 1/2, 2, 15
Factor 825*y + 300 + 497*y**2 + 84*y**3 - 31*y**4 + 3*y**5 - 35*y**4 + 181*y**2.
3*(y - 20)*(y - 5)*(y + 1)**3
Let v = 1501/1239 - 225/413. Suppose v*l**3 + 0*l + 0 + 4*l**2 = 0. What is l?
-6, 0
Let k(n) be the third derivative of 100489*n**7/70 + 150892*n**6/15 + 2728423*n**5/180 + 2857*n**4/18 + 2*n**3/3 - 7*n**2 + 151*n. Let k(m) = 0. What is m?
-3, -1, -2/951
Let c(j) be the second derivative of 9/20*j**5 + 21*j**2 + 6*j - 13/2*j**3 - 19 - j**4. Let c(u) = 0. Calculate u.
-2, 1, 7/3
Let t(r) be the second derivative of r**6/105 + r**5/7 + 9*r**4/14 + 6*r**3/7 + 33*r - 1. Factor t(g).
2*g*(g + 1)*(g + 3)*(g + 6)/7
Let n(q) = -2*q**4 - q**3 + 2*q**2 + q + 1. Let o(h) = 45*h**4 + 35*h**3 - 160*h**2 + 120*h - 20. Let j(k) = 20*n(k) + o(k). Factor j(f).
5*f*(f - 2)**2*(f + 7)
Suppose -3*d + 3 = -3. Let v(m) = 11*m + 68. Let g be v(-6). Factor -z**g + 3*z**4 + d*z**3 + 3*z**4 - 5*z**2 - 4*z + 2*z**5.
2*z*(z - 1)*(z + 1)**2*(z + 2)
Let -160/3*h**3 + 0*h + 16*h**4 + 0 - 2/3*h**5 + 0*h**2 = 0. What is h?
0, 4, 20
Let d(l) be the first derivative of 7/12*l**3 + 5/4*l**2 + 0*l + 148. Factor d(f).
f*(7*f + 10)/4
Let 294/11 + 2/11*u**2 + 56/11*u = 0. What is u?
-21, -7
Let d(p) = 2*p**2 - 74*p - 300. Let u(b) = 3*b**2 - 75*b - 300. Let f(i) = 5*d(i) - 4*u(i). Factor f(r).
-2*(r + 5)*(r + 30)
Let g(p) be the first derivative of 25*p + 15*p**2 + 7/4*p**3 + 1/16*p**4 - 32. Find v such that g(v) = 0.
-10, -1
Let y(p) be the third derivative of 7*p**6/60 + 4*p**5/5 - 75*p**4/4 - 350*p**3/3 - 4*p**2 + 3*p + 37. Factor y(b).
2*(b - 5)*(b + 7)*(7*b + 10)
Let m(i) be the second derivative of i**5 + 114*i**4 + 272*i**3/3 + 10771*i. What is c in m(c) = 0?
-68, -2/5, 0
Suppose 939/2*k + 1875/4 + 3/4*k**2 = 0. What is k?
-625, -1
Let d(f) be the second derivative of 1/6*f**4 + 0*f**2 + 4/15*f**3 + 1/100*f**5 + f - 1/150*f**6 - 37. Find c, given that d(c) = 0.
-2, -1, 0, 4
Let s = -7 + 10. Let q(t) = t**2 - 7*t - 25. Let o be q(-3). Factor 4*p**s - 2*p**4 - 5*p**4 - 2*p**o + 5*p**4.
-2*p**3*(p - 1)*(p + 2)
Find k such that 2/15*k**2 + 456968/15 + 1912/15*k = 0.
-478
Suppose 120 = -4*n - n + 65*n. Let z(m) be the first derivative of -40 +