4*m**4 + 60*m**3 - 6*m**2 - 70*m. Let p(x) = 4*x**4 - 20*x**3 + 2*x**2 + 23*x. Let y(n) = -6*o(n) - 20*p(n). Solve y(l) = 0.
-10, -1, 0, 1
Let m be (-9 - 70/(-8))*-8. Factor 3/5*t + 0 + 3/5*t**3 - 6/5*t**m.
3*t*(t - 1)**2/5
Let j(v) be the third derivative of v**8/84 - 6*v**7/35 + 7*v**6/10 - 19*v**5/15 + v**4 - v**2 - 10*v. Factor j(m).
4*m*(m - 6)*(m - 1)**3
Let h(j) be the second derivative of -169*j**4/15 - 26*j**3/3 - 5*j**2/2 + 207*j. Factor h(d).
-(26*d + 5)**2/5
Suppose -2*h = 5*x - 6, 9*x = 4*x + 3*h + 16. Let l = -14 - -15. Let t(g) = -g**3 + g**2. Let k(n) = -2*n**2 + 2*n. Let y(d) = l*k(d) + x*t(d). Factor y(f).
-2*f*(f - 1)*(f + 1)
Let i(g) be the first derivative of 4*g**3/3 + 4*g**2 + 251. Factor i(z).
4*z*(z + 2)
Suppose -360 = -2*r + 5*l, -74 = -2*r + 4*l + 282. Let p = r - 490/3. Suppose 2/3 - 160/3*v**4 + p*v - 40/3*v**3 + 128/3*v**5 + 50/3*v**2 = 0. Calculate v.
-1/4, 1
Let r(p) be the second derivative of 2/9*p**2 + 0 - 6*p + 1/18*p**3 - 1/108*p**4. Factor r(q).
-(q - 4)*(q + 1)/9
Let o(h) be the third derivative of 1/36*h**4 + 0 - 1/9*h**3 + 1/90*h**5 + 0*h + 13*h**2 - 1/180*h**6. Factor o(j).
-2*(j - 1)**2*(j + 1)/3
Let n = 2857 + -2852. Determine t, given that 4/5*t**4 + 8/5*t**3 - 4/5*t**2 + 0 - 6/5*t**n - 2/5*t = 0.
-1, -1/3, 0, 1
Let d = -123 + 121. Let u(r) = r**2 - 1. Let p(n) be the second derivative of n**4/2 - 2*n**3/3 - n**2/2 + n. Let m(b) = d*p(b) + 10*u(b). Factor m(y).
-2*(y - 2)**2
Let g(q) be the second derivative of q**8/672 - q**7/84 + q**6/30 - q**5/30 + q**2 - 8*q. Let m(d) be the first derivative of g(d). Solve m(n) = 0 for n.
0, 1, 2
Let f(j) = -j + 11. Let h be f(-5). Suppose 0*b = -4*b + h. Determine o, given that 6*o + 5*o + b*o**2 + 12 - 3*o - 8*o**2 = 0.
-1, 3
Factor 0*k + 18/19*k**3 + 8/19*k**2 + 10/19*k**4 + 0.
2*k**2*(k + 1)*(5*k + 4)/19
Let o(t) be the first derivative of -t**3/15 + 8*t**2/5 - 126. Factor o(r).
-r*(r - 16)/5
Let d(n) = -2*n - 1. Let s be d(-2). Let u = 163 - 161. Determine o, given that 0 - u*o**s - 2/3*o**2 + 0*o + 8/3*o**4 = 0.
-1/4, 0, 1
Let f(n) = 133*n - 796. Let h be f(6). Factor -12/7*s + 0 - 4*s**h - 16/7*s**3.
-4*s*(s + 1)*(4*s + 3)/7
Let v(m) be the third derivative of 1/140*m**7 - 1/40*m**5 - 1/80*m**6 + 1/224*m**8 + 0*m + 0*m**3 + 0*m**4 - 5*m**2 + 0. Factor v(o).
3*o**2*(o - 1)*(o + 1)**2/2
Suppose -7*p + 5*p + 16 = 0. Factor 0 - 9*d**3 + 9*d + 5*d**2 - 3 - p*d**2 + 6*d**4.
3*(d - 1)**2*(d + 1)*(2*d - 1)
Let c(k) = 34*k**2 + 64*k - 1031. Let l(n) = 5*n**2 - 1. Let z(b) = 5*c(b) - 35*l(b). Factor z(q).
-5*(q - 32)**2
Suppose 3 = 3*k + 7*s - 4*s, -2*s = -2*k + 14. Factor -5*b**k + 11*b**2 + 7*b**2 - 5*b + 5*b**3 - 20*b**2 + 7*b**2.
-5*b*(b - 1)**2*(b + 1)
Let s(v) be the third derivative of v**6/240 - v**5/240 - v**4/96 + 214*v**2. What is t in s(t) = 0?
-1/2, 0, 1
Let d(t) be the first derivative of -2*t**3/3 - 27*t**2 + 165. Suppose d(b) = 0. What is b?
-27, 0
Let q = 71/18 - 3487/900. Let p(s) be the second derivative of -q*s**5 + 1/20*s**4 + 0 - 1/210*s**7 + 0*s**3 + 0*s**2 - 5*s + 1/30*s**6. Factor p(u).
-u**2*(u - 3)*(u - 1)**2/5
Factor 2/5*c**2 + 24/5 - 26/5*c.
2*(c - 12)*(c - 1)/5
Let l(y) be the second derivative of -y**5/90 + 5*y**4/54 - y**3/9 - y**2 + 39*y. Factor l(d).
-2*(d - 3)**2*(d + 1)/9
Factor -13*t - 5 + 9*t + 6 - 98*t - 13*t**2 + 15.
-(t + 8)*(13*t - 2)
Let a(x) = x**2 - 2 - 32*x + 5 + 28*x. Let d(l) = l - 1. Let z(n) = -3*a(n) - 3*d(n). Factor z(m).
-3*(m - 2)*(m - 1)
Factor 16*n**2 - 31/7*n**3 - 108/7*n + 0 + 1/7*n**4.
n*(n - 27)*(n - 2)**2/7
Determine s, given that 33/5*s**4 + 3/5*s**5 + 243/5*s + 54*s**2 + 81/5 + 138/5*s**3 = 0.
-3, -1
Let i(r) = -5*r**3 + 10*r**2 - 7*r - 19. Let n(l) = -24*l**3 + 50*l**2 - 34*l - 94. Let g(f) = -28*i(f) + 6*n(f). Factor g(x).
-4*(x - 4)*(x - 2)*(x + 1)
Determine u so that 1/3*u**3 - 7/3*u**2 - 7*u + 9 = 0.
-3, 1, 9
Let m be ((-4)/(-5))/(36/690). Let i = m - 15. Suppose -4/3*o + 2*o**2 + i*o**4 + 5/3*o**3 - 8/3 = 0. Calculate o.
-2, 1
Let h(p) be the first derivative of -p**5/390 + 17*p**2/2 + 23. Let i(o) be the second derivative of h(o). Factor i(s).
-2*s**2/13
Let t(o) = -o**2 - 28*o - 12. Let a be t(-22). Let p = 1094/9 - a. Factor -p*v**3 - 2/9*v + 0 - 2/3*v**4 - 10/9*v**2.
-2*v*(v + 1)**2*(3*v + 1)/9
Let x(g) = -g**3 + g**2. Let s(q) = -12*q**3 - 152*q**2 + 1764*q. Let z(u) = s(u) - 16*x(u). What is l in z(l) = 0?
0, 21
Let o(h) be the third derivative of h**5/15 + 2*h**4 - 30*h**3 + 9*h**2. What is t in o(t) = 0?
-15, 3
Determine n so that -73 - 42*n - 72 + 51*n**2 - 3*n**3 + 49 = 0.
-1, 2, 16
Let d(f) be the third derivative of -f**5/20 - 7*f**4/4 - 13*f**3/2 + 2*f**2 - f. Suppose d(x) = 0. Calculate x.
-13, -1
Let h(u) be the third derivative of 0 - 6*u**2 + 0*u - 25/12*u**3 + 5/24*u**4 - 1/120*u**5. Let h(s) = 0. Calculate s.
5
Let v be (2/1)/2 + 1. Let p be 6/(-10) - (152/(-60))/v. Factor -1/3*m - 1/3*m**2 + p.
-(m - 1)*(m + 2)/3
Let d be (14/(-2) - -1)*6/(-8). Let m = 52 - 101/2. Suppose -m*q**4 + 0 + 3*q + 0*q**3 + d*q**2 = 0. Calculate q.
-1, 0, 2
Let y(j) be the second derivative of -11/27*j**3 - 1/108*j**4 - 121/18*j**2 + 0 + 11*j. Determine s so that y(s) = 0.
-11
Suppose 5*h + u - 5 = 0, -2*u - 8 = 3*h - 2*h. Factor 200*x - 200*x + h*x**3 - 2*x**2.
2*x**2*(x - 1)
Let w(d) = -d**2 - 13*d + 5. Let s(j) be the second derivative of j**2 - 2*j + j**3 - 2*j**3 + 3*j + 11*j. Let a(m) = 5*s(m) - 2*w(m). Factor a(b).
2*b*(b - 2)
Let a(h) be the first derivative of -h**5/15 + 2*h**4/3 - 2*h**3/3 - 20*h**2/3 - 25*h/3 - 256. Determine t so that a(t) = 0.
-1, 5
Suppose 6*t + 4*t = -17*t. Suppose -4/5*f**3 + 1/5*f + 2/5*f**4 - 2/5*f**2 + t + 3/5*f**5 = 0. Calculate f.
-1, 0, 1/3, 1
Let g(y) = -2*y**2 + 6*y**2 + y**3 - 5*y**2 + 1. Let w(m) = 20*m**3 - 40*m**2 - 15*m + 20. Let h(p) = -25*g(p) + w(p). Determine f so that h(f) = 0.
-1
Let c(i) be the second derivative of i**4/108 + i**3/54 + 8*i - 5. Determine z so that c(z) = 0.
-1, 0
Factor 0*s + 44/3*s**2 + 1/3*s**5 + 5*s**4 + 0 + 16*s**3.
s**2*(s + 2)**2*(s + 11)/3
Factor 6*r**2 - 9*r**2 + 24*r**2 - 5*r**3 + 0*r**3 - 60*r + 44*r**2.
-5*r*(r - 12)*(r - 1)
Let f(y) be the third derivative of 1/28*y**4 + 0*y + 4/21*y**3 + 31*y**2 + 1/420*y**5 + 0. Factor f(p).
(p + 2)*(p + 4)/7
Let m be (-1)/(-2 + 7) + 111/5. Let s be (((-42)/(-24))/7)/(m/16). Factor -s*c - 4/11*c**2 - 2/11*c**3 + 0.
-2*c*(c + 1)**2/11
Let j(s) be the third derivative of 0*s - 14*s**2 + 0 - 1/30*s**4 - 8/15*s**3 + 1/150*s**5. Suppose j(m) = 0. Calculate m.
-2, 4
Let w(r) = 17 - 22 - 5*r**3 + r**4 - 6*r**4 + 5*r. Let o(h) = 8*h**4 + 7*h**3 - 7*h + 7. Let i(u) = 5*o(u) + 7*w(u). Factor i(q).
5*q**4
Let d be (-44)/((-1760)/(-30))*(20/(-3))/2. Factor d*j**2 + 1/2*j - 1/2 + 3/2*j**3.
(j + 1)**2*(3*j - 1)/2
Suppose -12*j = -8*j - 28. Let h be (-4)/(-18)*(378/30)/j. Suppose h*z**2 + 2/5 + 4/5*z = 0. Calculate z.
-1
Factor 0 - 2*o - 1/3*o**3 - 5/3*o**2.
-o*(o + 2)*(o + 3)/3
Suppose -3*k**4 + 23 - 1 - 22 - 1323*k**2 - 126*k**3 = 0. Calculate k.
-21, 0
Let j(n) = n**5 + n**4 + 5*n**3 + 10*n**2 + 9*n - 16. Let w(g) = -g**4 - g**3 - 2*g + 2. Let m(v) = -3*j(v) - 15*w(v). Suppose m(d) = 0. What is d?
-1, 1, 2, 3
Factor 3/2*b**2 - b**3 + b - 1/4*b**4 - 5/4.
-(b - 1)**2*(b + 1)*(b + 5)/4
Suppose -34*u - 43*u = -308. Factor -8*h**3 - 16/3 - 16*h - 4/3*h**u - 52/3*h**2.
-4*(h + 1)**2*(h + 2)**2/3
Factor -7*g**3 - g**3 + 88*g**2 + 4*g**5 - 80*g**2 - 4*g**3.
4*g**2*(g - 1)**2*(g + 2)
Let i(k) be the third derivative of k**7/840 - 3*k**6/160 + k**5/16 - 7*k**4/96 + 91*k**2 + 1. Suppose i(o) = 0. What is o?
0, 1, 7
Let l = 234/1189 - 5/29. Let w = l - -121/82. Suppose 0 + 0*i + 0*i**2 - 3/2*i**4 + w*i**3 = 0. What is i?
0, 1
Let w(f) be the third derivative of -1/27*f**4 + 1/270*f**5 + 1/9*f**3 - 25*f**2 + 0 + 0*f. Find x, given that w(x) = 0.
1, 3
Let u(i) = -i + 7. Let h be u(4). Suppose -765*b = -583*b. Factor b + 4*z**h - 16/3*z + 4/3*z**4 + 0*z**2.
4*z*(z - 1)*(z + 2)**2/3
Let l(j) be the first derivative of 9*j**4/26 - 2*j**3/13 - 56*j**2/13 - 96*j/13 + 140. Factor l(z).
2*(z - 3)*(3*z + 4)**2/13
Let u(s) = s**5 + s**3 - s. Let c = 3 + 9. Let o(a) = 4*a**5 - 54*a**4 + 94*a**3 - 72*a**2 + 22*a. Let y(f) = c*u(f) + 2*o(f). Find j, given that y(j) = 0.
0, 2/5, 1, 2
Determine h so that 14*h - 3*h**2 +