e the first derivative of 0*l**2 - 14/5*l**5 + l**4 + 36 + 0*l + 0*l**3 - 4/3*l**6. Factor y(k).
-2*k**3*(k + 2)*(4*k - 1)
Let h(c) be the first derivative of c**4/8 + 41*c**3/3 + 161*c**2/4 + 40*c - 297. Let h(b) = 0. Calculate b.
-80, -1
Let z = 26 + -22. Find y such that -588*y**5 - 1889*y**4 - 300*y - 1374*y**2 - 358*y**z - 2757*y**3 - 18 - 6 = 0.
-2, -1, -2/7, -1/4
Suppose 5*n + 295*v = 294*v + 9, -3*n = 4*v - 2. Solve 6*h**4 - 1/2 - 7/2*h + 7/2*h**3 - 11/2*h**n = 0.
-1, -1/3, -1/4, 1
Let s(f) be the second derivative of 24*f + 7/20*f**4 + 3/100*f**5 + 0 + 27/10*f**2 + 3/2*f**3. Factor s(v).
3*(v + 1)*(v + 3)**2/5
Let k(y) = -y**3 - 5*y**2 + 9*y - 33. Let p be k(-7). Let -16/3*g**p + 4*g + 0 + 4/3*g**3 = 0. Calculate g.
0, 1, 3
Let o = 28 + -21. Let a(u) = -u**2 + 10*u - 14. Let z be a(o). Factor 0*s**2 + 9*s**3 - 4*s**2 + 2*s - z*s**2.
s*(s - 1)*(9*s - 2)
Factor -9 - 459 - 62*s**2 + 77*s**2 + 1164*s.
3*(s + 78)*(5*s - 2)
Let q(g) be the first derivative of g**8/4200 + g**7/1050 + 7*g**3/3 + 11. Let f(p) be the third derivative of q(p). Factor f(c).
2*c**3*(c + 2)/5
Let i(v) = -v**2 + 1. Let z(r) = -3*r**2 - 8*r - 14. Let x be 1 + -6 + -3 + 2. Let f(d) = x*i(d) + 3*z(d). Factor f(u).
-3*(u + 4)**2
Let t(s) be the second derivative of s**8/1008 + 14*s**2 - 25*s. Let c(o) be the first derivative of t(o). Solve c(w) = 0 for w.
0
Let j(v) = v**3 - 4*v + 5. Let a be j(1). Suppose 4*l + 5*n + a = -5, 4*l - 23 = 5*n. Factor 0 - 1/3*o**5 + 0*o**3 + 0*o + 0*o**l + 1/3*o**4.
-o**4*(o - 1)/3
Determine x so that -422*x**3 - 257*x**3 + 460*x**2 - 104*x + 12*x**5 + 212*x**4 + 91*x**3 + 8*x**5 = 0.
-13, 0, 2/5, 1
Let k be -19 - -18 - (1/(-1) - 2). Let b(j) be the third derivative of 0 + 0*j**3 - 2*j**k - 1/120*j**5 - 1/96*j**4 + 0*j - 1/480*j**6. Factor b(g).
-g*(g + 1)**2/4
Let y(g) = -2*g**4 + g**3 + g**2 + 2*g. Let d(o) = -6*o**4 - 18*o**3 + 74*o**2 - 42*o. Let h(z) = d(z) - 4*y(z). What is u in h(u) = 0?
0, 1, 5
Let p = -8 + 10. Suppose 1 = -5*n + 2*r + 5, -p*r + 4 = -n. Factor -2*i + 0*i**3 - 9*i**3 + n*i + 3*i**2.
-3*i**2*(3*i - 1)
Let y(a) be the third derivative of a**11/887040 + a**10/201600 + 3*a**5/10 - 20*a**2. Let g(w) be the third derivative of y(w). Factor g(p).
3*p**4*(p + 2)/8
Let u(t) be the first derivative of t**6/24 - t**5/4 + t**4/16 + 17*t**3/12 - 11*t**2/4 + 2*t - 112. Factor u(b).
(b - 4)*(b - 1)**3*(b + 2)/4
Let q(j) be the second derivative of 0 + 8*j**2 - 38*j + 2*j**3 - 1/3*j**4. Solve q(r) = 0.
-1, 4
Suppose -6*y - 23 = -59. Let n(a) be the third derivative of -2/5*a**5 - 64/3*a**3 - 4*a**4 + 7*a**2 + 0 - 1/60*a**y + 0*a. Solve n(k) = 0.
-4
Suppose 4*v = 2*p + 7*v - 9, p + 2*v - 6 = 0. Suppose 0 = -2*o + 5*k - 16, -k = -4*k + 12. Factor p + 1/5*i**o + 1/5*i.
i*(i + 1)/5
Suppose 2*y + 2*x - 36 = 0, 4*y + x - 117 = 6*x. Suppose 0 = 4*z + 5*a - 12, 5*z + 8 = a + y. Determine n, given that -17/2*n**2 + 10*n**z + 1 - 5/2*n = 0.
-2/5, 1/4, 1
Let c(s) be the third derivative of s**6/24 - s**5/6 + 8*s**2. Suppose c(x) = 0. What is x?
0, 2
Suppose t = 9*t - 928. Let v = -346/3 + t. Factor -4/9*c**3 + 0 + 0*c**2 + 0*c - v*c**4 - 2/9*c**5.
-2*c**3*(c + 1)*(c + 2)/9
Factor -r**3 + 3/7*r + r**2 + 0 - 3/7*r**4.
-r*(r - 1)*(r + 3)*(3*r + 1)/7
Factor 1/3*x**2 - 7/3*x - 6.
(x - 9)*(x + 2)/3
Let z(p) = -4*p**3 - 2*p**2 - 3*p + 3. Let b = 57 + -60. Let x(n) = -7*n**3 - 3*n**2 - 5*n + 5. Let i(l) = b*x(l) + 5*z(l). Factor i(y).
y**2*(y - 1)
Let c(t) be the third derivative of t**5/21 + 2*t**4/7 - 11*t**2 - 2*t. Determine b so that c(b) = 0.
-12/5, 0
Factor 9*s**3 + 315*s**4 + 2*s**2 - 3 - s**5 - 1 - s**3 + 0*s**3 - 7*s - 313*s**4.
-(s - 4)*(s - 1)*(s + 1)**3
Let y(v) be the third derivative of 0*v**3 + 12*v**2 + 0*v - 1/30*v**5 + 0*v**4 + 0. Factor y(q).
-2*q**2
Let h(d) be the third derivative of 1/60*d**5 + 5/24*d**4 - 10*d**2 + 0*d + d**3 + 0. Let h(k) = 0. Calculate k.
-3, -2
Suppose -4*x + 31 = 3*m, -6 = -3*m + 9. Let p(c) be the first derivative of -c + 1/10*c**5 + 6 + 1/6*c**3 - 3/4*c**2 + 3/8*c**x. Solve p(w) = 0.
-2, -1, 1
Factor 0 - 18/5*x - 6*x**2 + 294/5*x**4 + 154/5*x**3.
2*x*(3*x - 1)*(7*x + 3)**2/5
Let q be (6/10 - -2 - 2)*1. Let y(r) = -r**3 - 8*r**2 - 8*r - 5. Let g be y(-7). Let -3/5*z**g + 0 - q*z = 0. Calculate z.
-1, 0
Let m(g) = -9*g**3 - 35*g**2 - 8. Let q be m(-4). Let r(i) be the first derivative of 2/5*i**2 - q - 2/5*i - 2/15*i**3. Let r(z) = 0. Calculate z.
1
Let 6*f**2 + f + 3*f**2 + 11*f - 3*f**2 - 2*f**2 - 40 = 0. Calculate f.
-5, 2
Let a(g) be the first derivative of g**6/27 + 14*g**5/45 - 17*g**4/6 + 202*g**3/27 - 82*g**2/9 + 16*g/3 + 442. What is s in a(s) = 0?
-12, 1, 2
Suppose 5*s - 2*v - 35 = -5*v, 3*v - 19 = -s. Suppose 20 = s*d + d. Factor 0*t**2 + 2/7*t**5 + 0*t + 0 - 2/7*t**d + 0*t**3.
2*t**4*(t - 1)/7
Determine n so that 9*n**4 - 2*n**4 + 5*n**4 + 27*n**3 + 0*n**4 - 6 - 4*n**2 - 27*n - 2*n**2 = 0.
-2, -1, -1/4, 1
Factor 41/3*j + 7/3*j**2 - 1/3*j**3 + 11.
-(j - 11)*(j + 1)*(j + 3)/3
Determine b, given that 96 + 39*b**4 - 18*b**4 + 24*b**3 - 19*b**4 + 160*b + 96*b**2 = 0.
-6, -2
Factor 4 + 14/3*y**2 - 26/3*y.
2*(y - 1)*(7*y - 6)/3
Let k = -29/13 + 723/91. Factor 4/7*y**2 + 100/7 + k*y.
4*(y + 5)**2/7
Let o(i) be the first derivative of -i**6/21 - 2*i**5/35 + i**4/14 + 2*i**3/21 - 267. Factor o(f).
-2*f**2*(f - 1)*(f + 1)**2/7
Let y = 85 - 8. Factor 5*t**2 - y*t + 41*t + 20 + 56*t.
5*(t + 2)**2
Let r(v) be the third derivative of 8/7*v**4 + 3/280*v**6 + 16/7*v**3 + 10*v**2 + 0 + 0*v + 13/70*v**5. Solve r(b) = 0.
-4, -2/3
Factor 128/11 + 2/11*w**2 + 32/11*w.
2*(w + 8)**2/11
Let b(o) be the second derivative of -o**5/30 + 19*o**4/9 - 8*o**3 + 2*o + 17. Solve b(j) = 0 for j.
0, 2, 36
Find u such that 171/4*u - 1/4*u**2 + 43 = 0.
-1, 172
Suppose 0 = 4*w - c + 10 + 10, 4*w + 36 = 5*c. Let z = -2 - w. Suppose -3*m**2 + 3*m - 2*m**2 - 9*m**3 + 5*m**z - 6*m**4 = 0. What is m?
-1, 0, 1/2
Suppose 5*b + 5 = 4*o, 3*b = 3*o + b - 9. Suppose -f + d = 5, 3*d = -5*f + 2*d + o. Factor i - 1/2*i**4 + f - i**3 + 1/2*i**2.
-i*(i - 1)*(i + 1)*(i + 2)/2
Factor 562*y**2 - 134 + 132*y + 552*y**2 - 1112*y**2.
2*(y - 1)*(y + 67)
Let y(b) = -b**3 - 10*b**2 - 2*b - 16. Let r be y(-10). Suppose 0 = -r*d - 3*d. Determine l so that 0 + 9/4*l**3 + 3/4*l**4 + d*l - 9/4*l**5 - 3/4*l**2 = 0.
-1, 0, 1/3, 1
Suppose 0 = 3*n + 15, 0 = -4*t + 5*n - 24 + 57. Let 2/5*p**5 + 0 + 0*p**t - 4/5*p**4 + 0*p + 2/5*p**3 = 0. What is p?
0, 1
Suppose 0 = -9*a + 108 + 27. Let j be 2/((-70)/a)*-7. Factor -1 - j*c**2 + 7 - 3.
-3*(c - 1)*(c + 1)
Let d(c) be the second derivative of c**6/960 + 3*c**5/320 + c**4/32 - 5*c**3/6 + 9*c. Let n(x) be the second derivative of d(x). Suppose n(f) = 0. What is f?
-2, -1
Let i(u) = u**3 - 11*u**2 + 3*u - 29. Let g be i(11). Suppose 0*k = g*k. Let -1/2*c**3 - 1/2*c + k + c**2 = 0. What is c?
0, 1
Suppose -2*m + m + 4 = 0. Let h(i) be the third derivative of 0 + 1/60*i**5 + 0*i**m + 0*i**3 + 0*i - 2*i**2. Suppose h(n) = 0. What is n?
0
Let z be (-4)/(-12)*(77/(-14) + 7). Let h(k) be the first derivative of 3*k**2 + 9/4*k**4 + 2 - 3/5*k**5 + 0*k + 5*k**3 - z*k**6. Find u such that h(u) = 0.
-1, 0, 2
Let y = 17 - 13. Let g be ((-147)/90 - -4) + y/30. Factor -g*x**2 - 7/6*x**4 - 19/6*x**3 - 1/6*x + 1/3.
-(x + 1)**3*(7*x - 2)/6
Let d(l) be the third derivative of -l**8/53760 + l**6/5760 + l**4/4 - 13*l**2. Let r(q) be the second derivative of d(q). Factor r(f).
-f*(f - 1)*(f + 1)/8
Let h(j) be the third derivative of -2*j**5/105 - 43*j**4/84 + 11*j**3/21 - 494*j**2. Factor h(i).
-2*(i + 11)*(4*i - 1)/7
Find l such that -5/2*l**3 - 1/2*l**4 - 3/2*l**2 + 9/2*l + 0 = 0.
-3, 0, 1
Let g be 1 - (1 - 0 - 1). Suppose 2*q + 4 = -5*d, 43 = 4*d - 71*q + 66*q. Factor -5/4*f**d + 3*f - g.
-(f - 2)*(5*f - 2)/4
Determine d so that 16*d**2 - 5 - 20*d - 12 + 26 - 4*d**3 + 0 - 1 = 0.
1, 2
Suppose 3 - 2*t**2 + 23/2*t = 0. What is t?
-1/4, 6
Let o = -53/35 - -19/7. Factor 1/5*g**4 - 4/5*g + o*g**2 + 1/5 - 4/5*g**3.
(g - 1)**4/5
Let y = -206 - -211. Factor 0 - 3*a**4 + a**2 - 1/2*a**3 + 9/4*a**y + 1/4*a.
a*(a - 1)**2*(3*a + 1)**2/4
Let n(f) be the first derivative of 27*f**5/25 + 21*f**4/4 + 94*f**3/15 - 2*f**2 - 8*f/5 + 180. Suppose n(m) = 0. Calculate m.
-2, -2/9, 1/3
Let p(i) be the first derivative of -i**6/240 + 7*i**4/96 + i**3/8 + 29*i - 