ative of -4*k**6/3 + 3*k**5 - 3*k**4/2 - k**3/3 - 222. Factor r(d).
-d**2*(d - 1)**2*(8*d + 1)
Determine s, given that -63/5 + 66/5*s - 9/5*s**4 + 174/5*s**3 + 312/5*s**2 = 0.
-1, 1/3, 21
Let m(n) = -5*n + n + 5*n + 16. Let t be m(-11). Determine y, given that 138*y**4 + 2*y - 24*y**2 + 2*y - 75*y**t - 18*y**4 - 7*y - 18*y**3 = 0.
-1/5, 0, 1
Let f(b) be the first derivative of -b**5/4 + 5*b**4/12 + 5*b**3/6 - 5*b**2/2 - 35*b + 26. Let r(q) be the first derivative of f(q). Let r(z) = 0. Calculate z.
-1, 1
Let k = -76/13 + 688/91. Suppose 4/7*i**5 + k*i**3 - 12/7*i**4 + 0*i - 4/7*i**2 + 0 = 0. Calculate i.
0, 1
Let 18/5 - 6/5*h**3 + 3/5*h**5 + 3/5*h - 36/5*h**2 + 18/5*h**4 = 0. Calculate h.
-6, -1, 1
Let g be (-3)/22*26/(-351). Let r = 19/99 - g. Determine d, given that -r*d**2 - 4/11 + 6/11*d = 0.
1, 2
Suppose 0 - 1/3*x**4 + 1/3*x**2 + 0*x + 0*x**3 = 0. What is x?
-1, 0, 1
Let n(x) be the third derivative of -x**6/120 - x**5/12 - x**4/6 + x**3/3 - 5*x**2. Let g be n(-4). What is v in 0 + 2/7*v**4 - 2/7*v + 2/7*v**3 - 2/7*v**g = 0?
-1, 0, 1
Factor -1/4*b**4 + 1/4*b + 1/4*b**5 - 1/2*b**3 + 1/2*b**2 - 1/4.
(b - 1)**3*(b + 1)**2/4
Factor -156*f - 38*f**2 - 410*f**3 - f**2 + 414*f**3 - f**2.
4*f*(f - 13)*(f + 3)
Suppose 5*h - 23 = 2*w - 6, 7 = -2*w + 3*h. Let p(i) be the first derivative of 5/9*i**3 + 4/3*i**2 - w + 1/12*i**4 + 4/3*i. Determine d, given that p(d) = 0.
-2, -1
Let x = -64494/7 - -9214. Factor x*d**2 + 0*d - 2/7*d**3 + 0.
-2*d**2*(d - 2)/7
Let a be (17/51)/(20/18 + -1). Factor 40*p - 18*p**a + 5*p**4 - 15*p**3 - 50*p**2 + 38*p**3.
5*p*(p - 2)*(p - 1)*(p + 4)
Let k = 11/106 - -10/159. Let r(v) be the first derivative of -1/4*v**4 + 10 + 0*v**3 + 0*v - 2/5*v**5 - k*v**6 + 0*v**2. Find s such that r(s) = 0.
-1, 0
Let n(t) be the third derivative of -4*t**5/15 - 5*t**4/24 - 11*t**3/6 + 51*t**2. Let o(s) = -3*s**2 - s - 2. Let c(w) = -2*n(w) + 11*o(w). Factor c(l).
-l*(l + 1)
Let k(z) = -z**2 - 16*z - 10. Let u be k(-15). Suppose 5*y - 14 = 3*m, -u*y + 16 = -m - m. Let 1 - 1 + 4*f**2 - m*f**2 - 2*f**3 = 0. Calculate f.
0, 1
Let l(s) be the third derivative of s**6/300 + s**5/30 - 7*s**4/30 + 383*s**2. Factor l(d).
2*d*(d - 2)*(d + 7)/5
Let q be (52/(-48) + 1)*(-117)/26. Factor 3/8*c - 1/8*c**2 - 1/8*c**4 - q*c**3 + 1/4.
-(c - 1)*(c + 1)**2*(c + 2)/8
Let l(p) = -21*p + 67. Let k be l(3). Let f(x) be the third derivative of 0*x + 6*x**3 + 6*x**2 + 0 + 1/15*x**5 + x**k. Find g, given that f(g) = 0.
-3
Let z(c) = -8*c**2 - 302*c - 11552. Let h(d) = 19*d**2 + 603*d + 23104. Let v(q) = 2*h(q) + 5*z(q). Let v(x) = 0. Calculate x.
-76
Let y(g) = g**2 - g - 1. Let x = -110 - -107. Let s(m) = -4 - 6*m**2 + 3 + 4. Let w(v) = x*y(v) - s(v). Factor w(a).
3*a*(a + 1)
Suppose -w - 1 = 0, 10 - 1 = 3*k - 3*w. Let f(z) be the first derivative of 4 + 0*z**3 + 1/2*z**4 + 0*z**k + 0*z - 1/5*z**5. Factor f(s).
-s**3*(s - 2)
Let u(r) be the first derivative of 2*r**5/5 + 3*r**4 + 6*r**3 + 100. Factor u(j).
2*j**2*(j + 3)**2
Let g(j) = -3*j**3 - 42*j**2 - 45*j. Let v(h) = 3*h**3 + 43*h**2 + 45*h. Let p(w) = -5*g(w) - 6*v(w). Factor p(n).
-3*n*(n + 1)*(n + 15)
Let o(p) be the third derivative of 0 - p - 200/9*p**3 - 10/63*p**7 - 230/9*p**4 + 23/9*p**6 - 25*p**2 - 143/15*p**5. Let o(n) = 0. What is n?
-2/5, 5
Let r = -143 + 146. Suppose 5*l + 2*x = 4*l - 2, -r*l = 4*x. Factor -4/7*y**2 + 0*y - 80/7*y**l - 32/7*y**5 + 0 - 34/7*y**3.
-2*y**2*(y + 2)*(4*y + 1)**2/7
Suppose 4*q = -3*p - 5 + 33, q = p. Factor 3/2*o**p + 0 + 6*o**3 + 0*o + 6*o**2.
3*o**2*(o + 2)**2/2
Let z(d) be the second derivative of 0 + 0*d**2 - 2/15*d**3 - 1/75*d**6 + 1/25*d**5 + 13*d + 1/30*d**4. Factor z(j).
-2*j*(j - 2)*(j - 1)*(j + 1)/5
Let o(j) be the second derivative of j**6/20 + 177*j**5/20 + 3709*j**4/8 + 3363*j**3 + 9747*j**2 + 415*j. Factor o(q).
3*(q + 2)**2*(q + 57)**2/2
Suppose 1445*u - 1431*u = 56. Let a(v) be the second derivative of 0 - 9/4*v**2 + 1/2*v**3 - v - 1/24*v**u. Let a(p) = 0. What is p?
3
Factor 4/5*y**5 + 0*y + 256/5*y**2 - 12*y**4 + 192/5*y**3 + 0.
4*y**2*(y - 8)**2*(y + 1)/5
Factor 4*z**2 - 30*z - 85*z - 24*z**2 - 75.
-5*(z + 5)*(4*z + 3)
Let f = -17/1236 + 10/103. Let j(o) be the third derivative of 1/9*o**3 - o**2 + 1/30*o**5 + 0 + f*o**4 + 0*o + 1/180*o**6. Let j(m) = 0. What is m?
-1
Suppose -2*w - 14 = -3*i + 14, i + 4*w = 0. Suppose -10*n + i = -6*n. Factor -1/4 + 1/4*d - 1/4*d**3 + 1/4*d**n.
-(d - 1)**2*(d + 1)/4
Let v(p) be the second derivative of -p**7/294 - p**6/210 + p**5/28 + 5*p**4/84 - 2*p**3/21 - 2*p**2/7 - 54*p. Determine s so that v(s) = 0.
-2, -1, 1, 2
Let f(b) be the first derivative of -b**8/5880 + b**7/980 + b**6/1260 - b**5/140 + 8*b**3/3 - 15. Let x(g) be the third derivative of f(g). Factor x(q).
-2*q*(q - 3)*(q - 1)*(q + 1)/7
Suppose 224*q - 51 - 25/3*q**4 + 160*q**3 - 974/3*q**2 = 0. What is q?
3/5, 1, 17
Suppose 16 = 9*r - 13*r. Let l(j) = -6*j + 24. Let n(b) = b**2 - 6*b + 24. Let q(p) = r*l(p) + 3*n(p). Factor q(z).
3*(z - 2)*(z + 4)
Suppose 130*z - 13 = -5*i + 131*z, i - 3*z - 11 = 0. Solve 16/3*v + 16/3 + 4/3*v**i = 0 for v.
-2
Let y = -5/3378 + 5077/6756. Let -3/4*n**4 + 3/2 - 15/4*n + 9/4*n**2 + y*n**3 = 0. Calculate n.
-2, 1
Let r(g) = g**2 + 17*g + 52. Let p(y) = -3*y**2 - 52*y - 155. Let o(t) = 2*p(t) + 7*r(t). Find z, given that o(z) = 0.
-9, -6
Factor 12/5*v - 9/5 - 3/5*v**2.
-3*(v - 3)*(v - 1)/5
Factor 1/4*t**4 + 9/2 - 3/4*t**3 - 7/4*t**2 + 15/4*t.
(t - 3)**2*(t + 1)*(t + 2)/4
Factor -12 + 3*d**3 - 24*d**2 - 6 - 6 + 51*d - 6.
3*(d - 5)*(d - 2)*(d - 1)
Let q(p) = -245*p**3 + 1598*p**2 - 864*p + 116. Let j(c) = -490*c**3 + 3199*c**2 - 1727*c + 233. Let o(d) = -4*j(d) + 7*q(d). Factor o(f).
5*(f - 6)*(7*f - 2)**2
Suppose -204 = -7*v - 176. Let y(x) be the second derivative of 0*x**2 + 3*x - 1/9*x**3 + 0 + 1/36*x**v + 1/60*x**5. Factor y(r).
r*(r - 1)*(r + 2)/3
Let h(l) be the first derivative of -l**4/38 - 46*l**3/57 + 49*l**2/19 - 50*l/19 + 403. Factor h(k).
-2*(k - 1)**2*(k + 25)/19
Let l(m) be the first derivative of m**5/4 + 5*m**4/12 - 5*m**3/6 - 5*m**2/2 + 12*m + 6. Let q(f) be the first derivative of l(f). Determine g so that q(g) = 0.
-1, 1
Let o(u) be the first derivative of u**6/180 + u**5/10 + 5*u**4/12 + 7*u**3/9 - 25*u**2/2 + 8. Let f(x) be the second derivative of o(x). Solve f(d) = 0 for d.
-7, -1
Let y(q) be the first derivative of 2*q**3/21 + 87. Determine j, given that y(j) = 0.
0
Let b(a) be the second derivative of 0*a**2 + 15*a + 1/147*a**7 + 0*a**3 + 0 - 1/105*a**6 + 1/42*a**4 - 1/70*a**5. Solve b(j) = 0 for j.
-1, 0, 1
Suppose 0 = -b + 1, -b - 770 = -2*s - 767. Factor -1/4*u**4 - 17/4*u**s + 7/4*u**3 - 3/2 + 17/4*u.
-(u - 3)*(u - 2)*(u - 1)**2/4
Let a(j) be the second derivative of -j**5/120 + 5*j**4/24 - 25*j**3/12 - 2*j**2 + 12*j. Let n(x) be the first derivative of a(x). Factor n(f).
-(f - 5)**2/2
Suppose 3*x + 12 = 7*x. Let w(h) = h**2 + h. Let v(j) = -j**4 + j**3 + j**2 - 3*j - 2. Let c(p) = x*v(p) + 6*w(p). Factor c(l).
-3*(l - 2)*(l - 1)*(l + 1)**2
Let k(b) be the first derivative of -b**5/5 - 5*b**4/6 - b**3 - b**2/3 - 161. Determine l so that k(l) = 0.
-2, -1, -1/3, 0
Let y(w) be the third derivative of w**8/11760 + w**7/4410 - w**6/630 + w**4/4 + 9*w**2. Let t(v) be the second derivative of y(v). Factor t(f).
4*f*(f - 1)*(f + 2)/7
Let l(g) be the third derivative of -g**8/84 - 2*g**7/35 + 4*g**5/15 - 4*g**2. Factor l(w).
-4*w**2*(w - 1)*(w + 2)**2
Let m(q) be the second derivative of 2*q**6/15 + 88*q**5/5 + 1846*q**4/3 - 2640*q**3 + 4050*q**2 + 148*q. Solve m(a) = 0 for a.
-45, 1
Let r(d) be the third derivative of -d**5/60 + 8*d**3/3 - 2*d**2 + 29. Factor r(f).
-(f - 4)*(f + 4)
Let k(s) be the second derivative of s**6/180 + s**5/120 - s**4/72 - s**3/36 + 110*s. Solve k(g) = 0.
-1, 0, 1
Determine v so that -203 + 135*v**2 + 57*v**2 + 5*v**3 + 33*v**2 + 203 + 220*v = 0.
-44, -1, 0
Suppose s - 4 = -4*q, 0 = -q - s - 19 + 23. Find x, given that -4/7*x**4 - 8/7*x**3 + 4/7*x**2 + q + 6/7*x + 2/7*x**5 = 0.
-1, 0, 1, 3
Let b be (-6 - -5)*(16 - 16). Let -6*k**2 + b*k + 3/2*k**5 + 9/2*k**4 + 0*k**3 + 0 = 0. Calculate k.
-2, 0, 1
Suppose -5*a = -4*v - 400, -a = -v + 30 - 109. Let y = a + -82. Factor 2/7*m**5 + 4/7*m**y - 2/7 - 4/7*m**3 - 2/7*m**4 + 2/7*m.
2*(m - 1)**3*(m + 1)**2/7
Let x(c) be the second d