2)
Let q(s) be the second derivative of -s**8/1344 - s**7/840 + s**6/60 - s**5/30 - s**4/3 + 2*s. Let d(y) be the third derivative of q(y). Factor d(f).
-(f - 1)*(f + 2)*(5*f - 2)
Let b(r) be the third derivative of -r**8/168 - r**7/105 + r**6/60 + r**5/30 + 29*r**2. Factor b(q).
-2*q**2*(q - 1)*(q + 1)**2
Let s(m) be the second derivative of -1/60*m**5 + 1/6*m**4 + 0 - 2*m + 4/3*m**2 - 2/3*m**3. Find g such that s(g) = 0.
2
Let z(t) = 5*t**2 - 16*t - 127. Let m(u) = 6*u**2 - 15*u - 128. Let x(q) = -6*m(q) + 7*z(q). Factor x(s).
-(s + 11)**2
Suppose -5*r + 3*i + 2 = -70, -4*r - 5*i + 65 = 0. Let a = r - 10. Factor 1/2*m**a + 5*m**3 + 5/2*m + 1/2 + 5*m**2 + 5/2*m**4.
(m + 1)**5/2
Let 4*w - 1/3*w**4 - 3 + 2/3*w**2 - 4/3*w**3 = 0. What is w?
-3, 1
Suppose -2*a - a - 24 = 0. Let g be (a/10)/(8/(-20)). Factor 6*v**2 + 6*v - 6*v**4 - 2*v**5 + 0*v**5 - g*v**2 - 4*v**3 + 2.
-2*(v - 1)*(v + 1)**4
Let z(g) = g**3 - 9*g**2 - g + 9. Let l be z(9). Let o(h) be the third derivative of 1/90*h**5 + 1/36*h**4 + 0*h**3 + 0*h - 2*h**2 + l. Factor o(t).
2*t*(t + 1)/3
Suppose -5*p - 11 = -46. Determine i so that 5*i**2 - 4*i**2 + 4*i + p*i**2 = 0.
-1/2, 0
Let k = -98 - -589/6. Factor 0 - 1/6*g - k*g**2.
-g*(g + 1)/6
Let z(u) be the second derivative of 0*u**2 + 0 - 1/40*u**5 - 1/6*u**4 - 1/3*u**3 + 3*u. Solve z(f) = 0 for f.
-2, 0
Let o be 2/8 + 4/112. Factor 2/7*s + 0 - 4/7*s**2 + o*s**3.
2*s*(s - 1)**2/7
Suppose 4*s - s = 48. Let w = -47/3 + s. Factor c**4 + 1/3*c - w*c**3 - c**2 + 0.
c*(c - 1)*(c + 1)*(3*c - 1)/3
Let h(y) = -4*y**4 + 8*y**3 + y**2 - 8*y + 3. Let o(s) = -4*s**4 + 8*s**3 + 2*s**2 - 8*s + 2. Let j(u) = -2*h(u) + 3*o(u). Let j(k) = 0. Calculate k.
-1, 0, 1, 2
Factor -12*a - a - 3 + 18*a**2 - 2*a.
3*(a - 1)*(6*a + 1)
Let h be (0/10)/(1 - 0). Factor 0*l + 1/3*l**4 + h + 1/3*l**2 - 2/3*l**3.
l**2*(l - 1)**2/3
Let r(y) be the second derivative of y**7/126 + y**6/90 - y**5/60 - y**4/36 - 20*y. Factor r(o).
o**2*(o - 1)*(o + 1)**2/3
Solve -40/7*w + 100/7 + 4/7*w**2 = 0 for w.
5
Suppose -7*q = 4*q - 33. Let u(k) be the second derivative of -1/42*k**4 + k - 2/21*k**q + 0 - 1/7*k**2. Factor u(x).
-2*(x + 1)**2/7
Let h(v) be the first derivative of -2/5*v**2 - 9 - 1/20*v**4 + 0*v - 4/15*v**3. Factor h(n).
-n*(n + 2)**2/5
Let b be 2/((-3)/(93/(-10))). Let z = b - 119/20. What is s in -1/4*s - 3/4*s**3 + 0 - z*s**4 - 3/4*s**2 = 0?
-1, 0
Let i(q) be the second derivative of -q**5/40 + q**4/12 + 7*q. Suppose i(o) = 0. Calculate o.
0, 2
Let j(u) = -2*u - 6. Let x be j(-5). Factor 16*f**3 - f**x - 7*f**2 - 9*f**2 - 3*f**4 + 0*f**2.
-4*f**2*(f - 2)**2
Let z = 44/3 - 349/24. Let o(m) be the first derivative of 1 + 1/3*m**3 - z*m**4 + 0*m + 0*m**2. Factor o(a).
-a**2*(a - 2)/2
Suppose -2*s + 13 = 3*o, -7*o - s = -3*o - 14. Suppose p**3 - 3*p**2 - 2*p - 5*p**o - p**4 + 0*p**3 - 2*p**2 = 0. Calculate p.
-2, -1, 0
Let y(o) = o**2 + 8*o + 5. Let a be y(-8). Factor 2 - a + q - q**2 + 0*q**2 + 5.
-(q - 2)*(q + 1)
Let a(i) be the second derivative of -1/72*i**4 - 1/18*i**3 - 3*i + 0 - 1/12*i**2. Factor a(f).
-(f + 1)**2/6
Let g(k) be the third derivative of -k**8/168 - k**7/15 - 2*k**6/15 + 8*k**5/15 - 25*k**2. Factor g(o).
-2*o**2*(o - 1)*(o + 4)**2
Let g = 2 - -1. Let 3*i**g + 2*i**5 + 2*i**5 + 5*i**4 - 2*i**3 = 0. What is i?
-1, -1/4, 0
Suppose -5*v + 12 - 2 = 0. Let d(c) = -c + 6. Let w be d(5). Factor -3*q**4 + q**5 - w - 4*q**4 + 6*q**4 + v*q**2 + q - 2*q**3.
(q - 1)**3*(q + 1)**2
Let w be 2/4 + 18/(-40). Let p(k) be the second derivative of w*k**5 + 1/6*k**3 + 1/6*k**4 + 2*k + 0*k**2 + 0. Factor p(y).
y*(y + 1)**2
Let g be (-9 + 8)*(-6)/2. Let r = g - 0. Determine y, given that -1/4*y - 5/4*y**2 - 3/4*y**r + 1/4 = 0.
-1, 1/3
Factor 588*j**2 + 11 - 686*j**3 - 168*j + 2 + 9 - 6.
-2*(7*j - 2)**3
Let l(j) = j**3 + j - 4. Let c(y) = -3*y**3 + y**2 - 4*y + 13. Let n = 2 + -6. Let g(p) = n*c(p) - 14*l(p). Factor g(q).
-2*(q - 1)*(q + 1)*(q + 2)
Suppose h - 2*h = -4. Let g = -4 + h. Let -1/3*n**3 + g + 1/3*n + 0*n**2 = 0. Calculate n.
-1, 0, 1
What is r in -13*r + 10 + 3*r**2 + 43*r + 65 = 0?
-5
Let j(w) be the first derivative of -w**6/15 - 4*w**5/25 + 4*w**3/15 + w**2/5 - 4. Determine m, given that j(m) = 0.
-1, 0, 1
Let j be ((-3)/4)/((-30)/16). Factor 2/5 - 2/5*q**2 - 2/5*q**3 + j*q.
-2*(q - 1)*(q + 1)**2/5
Let d be (-1)/5 + (-11)/(-5). Determine l so that 8*l + 3*l**2 - d*l + 5*l**2 + 1 + 0*l = 0.
-1/2, -1/4
Let g(y) = y**2 + y - 1. Let h be g(2). Let a(f) be the second derivative of 1/2*f**4 + 0 + 1/10*f**h + f**2 - 2*f + f**3. Factor a(c).
2*(c + 1)**3
Suppose 0*i = 3*i. Suppose i = -3*x + 6*x - 6. Factor 2*g - 4*g + 5*g**x + 2*g**3 + 2*g**4 - 7*g**2.
2*g*(g - 1)*(g + 1)**2
Suppose -2*c = 2*c - l - 21, c + 16 = -4*l. Find p, given that 0*p**c + 4/7*p**2 - 6/7*p**3 + 0 + 2/7*p**5 + 0*p = 0.
-2, 0, 1
Let v(f) be the third derivative of -f**7/1890 - f**6/1080 + f**5/108 - f**4/72 + 12*f**2. Factor v(j).
-j*(j - 1)**2*(j + 3)/9
Let g(n) be the second derivative of -n**6/120 + n**5/16 + n**4/8 - 4*n**3/3 - 4*n**2 - 60*n. Factor g(c).
-(c - 4)**2*(c + 1)*(c + 2)/4
Let x be (22/6)/((-40)/(-7)). Let b = x + 1/40. Let 2/3*l**2 + 0 + b*l = 0. What is l?
-1, 0
Let g(n) be the second derivative of -11*n**6/10 + 93*n**5/20 - 27*n**4/4 + 5*n**3/2 + 3*n**2 + 13*n. Factor g(h).
-3*(h - 1)**3*(11*h + 2)
Factor 1/2 + p**4 - 1/2*p**3 + 1/2*p - 3/2*p**2.
(p - 1)**2*(p + 1)*(2*p + 1)/2
Let q be 3/27 - 100/(-45). What is t in -q*t + 1/6 + 49/6*t**2 = 0?
1/7
Let j be (12/(-18) - 2) + (1 - -2). Factor b + b**2 + 1/3*b**3 + j.
(b + 1)**3/3
Let i = 65/4 - 16. Suppose 3/4*x**2 - 1 + 0*x + i*x**3 = 0. Calculate x.
-2, 1
Let y(h) be the third derivative of 0*h + 3/8*h**4 + 0 - 1/40*h**6 + h**3 + 4*h**2 + 0*h**5. Let y(i) = 0. What is i?
-1, 2
Let t(y) be the first derivative of 4*y**3 + 6*y**2 - 2. Let l(x) = -x**2 - x. Let o(z) = 15*l(z) + t(z). Factor o(p).
-3*p*(p + 1)
Let j be (1 + 2/4)*(-4)/(-3). Factor -4/5 + 2*o**j + 6/5*o.
2*(o + 1)*(5*o - 2)/5
Let m(i) be the third derivative of -i**10/151200 + i**9/30240 - i**8/20160 - i**5/20 - 3*i**2. Let q(h) be the third derivative of m(h). Factor q(b).
-b**2*(b - 1)**2
Let k be 968/320 + (-2 - 1). Let q(o) be the second derivative of 0*o**2 + 0 - 1/6*o**3 - 2*o + k*o**5 + 1/24*o**4. Factor q(u).
u*(u - 1)*(u + 2)/2
Let g be 0 - 12/(-18)*(-4)/(-6). Solve -2/3*w**3 + 0*w - 4/9*w**2 + 0 + g*w**4 + 2/3*w**5 = 0.
-1, -2/3, 0, 1
Let n(o) be the first derivative of -9*o**5/10 - 15*o**4/8 - o**3/2 + 3*o**2/4 - 45. Solve n(l) = 0 for l.
-1, 0, 1/3
Let s(b) be the second derivative of -25*b**7/21 - 11*b**6/3 - 19*b**5/10 + 23*b**4/6 + 8*b**3/3 - 4*b**2 + 5*b. Factor s(y).
-2*(y + 1)**3*(5*y - 2)**2
Let c = 15038 + -137956/9. Let i = c + 292. Factor -i*u**2 - 2*u - 4/9.
-2*(u + 1)*(7*u + 2)/9
Let l(d) be the second derivative of -d**4/3 - 16*d**3 - 288*d**2 + 2*d. What is i in l(i) = 0?
-12
Let z(y) = -y + 2. Let o be z(0). Find k, given that -k**2 + k**2 + 4*k**2 + 0*k - o*k = 0.
0, 1/2
Let c = 2/31 - -23/124. Suppose -3/2*w**4 + 7/4*w**2 - 1/4 - 1/4*w**3 + c*w = 0. What is w?
-1, -1/2, 1/3, 1
Factor -1/2*q + 0 - 1/2*q**2.
-q*(q + 1)/2
Factor 9*i + 27/2 + 3/2*i**2.
3*(i + 3)**2/2
Suppose 4/13 - 2/13*r**3 + 2/13*r - 4/13*r**2 = 0. What is r?
-2, -1, 1
Let x(f) = -4*f**3 - 4*f**2 + 5*f - 5. Let w(a) = 6*a**3 + 6*a**2 - 8*a + 8. Suppose z - 4 = -12. Let g(p) = z*x(p) - 5*w(p). Factor g(t).
2*t**2*(t + 1)
Let r(y) = y**4 - y**3 - y**2 + y. Let l(j) = 3*j**4 - 10*j**3 - 9*j**2 + 4*j. Let u(x) = -l(x) + 4*r(x). Factor u(t).
t**2*(t + 1)*(t + 5)
Let g = 206512 + -39031100/189. Let d = -32/27 - g. Suppose -18/7*j**3 + d + 18/7*j - 2*j**4 + 10/7*j**2 = 0. What is j?
-1, -2/7, 1
Let f(r) be the third derivative of 2/3*r**4 + 0 - 3*r**2 + 23/30*r**6 + 0*r - 4/3*r**5 - 2/15*r**7 + 0*r**3. Let f(s) = 0. What is s?
0, 2/7, 1, 2
Let a(b) be the third derivative of -b**7/210 - b**6/60 + b**5/20 + b**4/3 + 2*b**3/3 + 5*b**2. Factor a(o).
-(o - 2)*(o + 1)**2*(o + 2)
Let s(w) be the third derivative of 0*w**4 - 1/60*w**6 + 0 - 1/336*w**8 + 0*w + 1/70*w**7 - 4*w**2 + 0*w**3 + 0*w**5. Factor s(v).
-v**3*(v - 2)*(v - 1)
Suppose -4*q - 2 = -18. Let h = 6 - q. Suppose 2*l**2 + l**3 + 0*l**2 + l**4 - h*l**2 = 0. Calculate l.
-1, 0
Let q(s) be the second derivative of -5*s**7/14