). Factor k(i).
3*i*(i - 1)*(i + 5)
Let s = 126543/5 - 25523. Let p = -214 - s. Find m such that -2/5 + p*m**3 + 2/5*m**2 - 2/5*m = 0.
-1, 1
Let h(o) be the second derivative of 0 - 25/12*o**4 - 15*o + 1/4*o**5 - 15/4*o**2 - 115/24*o**3. Factor h(w).
5*(w - 6)*(2*w + 1)**2/4
Let w(v) be the second derivative of v**4/24 + 5*v**3/12 + 3*v**2/2 + 435*v. Factor w(n).
(n + 2)*(n + 3)/2
Suppose 1144*l = 1140*l + 8. Factor 1/2*h + 5/6*h**3 + 0 - 1/6*h**4 - 7/6*h**l.
-h*(h - 3)*(h - 1)**2/6
Let f(n) be the second derivative of n**6/105 + n**5/14 - n**4/7 - 32*n**3/21 + 32*n**2/7 + 2*n + 7. Factor f(q).
2*(q - 2)*(q - 1)*(q + 4)**2/7
Suppose -3*g = -5*g + 6. Let d = g - 1. Factor 2*b**3 + 6*b**d - b**3 + 6*b + 2 + 3*b**3 - 2*b**3.
2*(b + 1)**3
Determine r, given that 44/7*r**4 + 0 + 32/7*r + 108/7*r**3 + 100/7*r**2 + 4/7*r**5 = 0.
-8, -1, 0
Let j(l) be the second derivative of -l**4/12 + 4*l**3 + 26*l**2 + 36*l. Let c be j(26). Let -5/4*d**4 - 7/4*d**5 + 0 + 1/2*d**3 + c*d + 0*d**2 = 0. What is d?
-1, 0, 2/7
Let h be ((-3)/72)/((-61)/732). Factor 1/2*l**2 - 1/2*l**4 + 0 + h*l**5 - 1/2*l**3 + 0*l.
l**2*(l - 1)**2*(l + 1)/2
Let y(m) = 642*m + 7065. Let i be y(-11). Factor 78/5*o**4 - 12*o**i - 21/5*o**5 + 0*o + 0 - 24/5*o**2.
-3*o**2*(o - 2)**2*(7*o + 2)/5
Let f(j) be the first derivative of -2*j**3/27 + 5*j**2/3 - 52*j/9 + 194. Let f(t) = 0. What is t?
2, 13
Let y = 36 - 34. Determine l, given that 2*l**2 - 6*l + 17 + l**y - 17 = 0.
0, 2
Suppose o + 4*k + 13 = 0, -4*o + 14 = -5*k - 18. Factor 10*m**3 - 3*m**3 - 3*m + m**o - m - 4*m**5.
-4*m*(m - 1)**2*(m + 1)**2
Let q = -35 + 37. Suppose -5*a - 7*m - 5 = -2*m, 2*a - 2*m = 14. Factor 0*v**3 + 2*v**3 + 6*v**3 - 5*v**a - 3*v**q.
3*v**2*(v - 1)
Let v be 224/120 + 4/30. Factor -20*c**4 + 0*c**3 + 22*c**4 + v*c**5 + 4*c - 6*c**3 - 2*c**2 + 0*c**2.
2*c*(c - 1)**2*(c + 1)*(c + 2)
Let k(r) be the second derivative of -r**6/1440 - r**5/480 + r**4/16 - r**3/6 - 20*r. Let q(y) be the second derivative of k(y). Factor q(t).
-(t - 2)*(t + 3)/4
Let v(n) be the third derivative of -11*n**6/320 + 13*n**5/160 - n**4/32 - 35*n**2. Let v(q) = 0. What is q?
0, 2/11, 1
Let j = 4292/23485 + -2/2135. Determine y so that 6/11*y**3 + j*y**4 - 30/11*y + 36/11 - 14/11*y**2 = 0.
-3, 1, 2
Find z, given that 5 + 4*z**4 - 48*z**2 - 13 - 2 + 4 - 15*z**3 - 35*z = 0.
-1, -1/4, 6
Let s(c) be the first derivative of -1/5*c**5 - 1/4*c**4 + 2 + 2/3*c**3 + 0*c + 0*c**2. Factor s(m).
-m**2*(m - 1)*(m + 2)
Let f(s) = -s**2 + 7*s - 8. Let j be f(5). Factor -5*d**2 - 23*d**3 + 21*d**j + 19*d**3.
-4*d**2*(d - 4)
Factor 24*i**3 + 2 + 28*i**2 + 10*i + 4*i**4 - 2 - 39*i**5 + 37*i**5.
-2*i*(i - 5)*(i + 1)**3
Let i be (-27)/(-18)*-6 + 9. Factor -2/3 - 2/3*v**4 + 0*v**3 + i*v + 4/3*v**2.
-2*(v - 1)**2*(v + 1)**2/3
Let j(n) = 25*n**3 + 30*n**2 - n - 2. Let g be j(-1). Determine f, given that 34/13*f**g - 28/13*f**5 - 4/13*f**2 + 0 - 2/13*f**3 + 0*f = 0.
-2/7, 0, 1/2, 1
Suppose l = -5*f - 2, 5*f - 14 - 8 = -4*l. Factor -l*t**3 + t**3 + 7*t**3 - t**3.
-t**3
Let y(d) be the third derivative of d**6/160 + 21*d**5/80 + 39*d**4/32 + 19*d**3/8 - 98*d**2. Solve y(p) = 0.
-19, -1
Suppose 4*l = 3*j + 3 + 28, -18 = -2*l + 2*j. Solve -8*r**l + 28*r**5 + 20*r**3 - 94*r**3 - 10*r**3 + 16*r - 32*r**2 = 0 for r.
-1, 0, 2/7, 2
Let k(t) be the first derivative of 12 + t**3 - 3/2*t**2 + t - 1/4*t**4. Factor k(o).
-(o - 1)**3
Let b(w) be the second derivative of w**5/4 - 9*w**4/8 - w**3 - 25*w**2 + w + 12. Let u(z) be the first derivative of b(z). Determine q, given that u(q) = 0.
-1/5, 2
Let d(v) be the second derivative of 9*v**5/10 + 17*v**4/4 + 9*v**3/2 - 3*v**2 - 156*v. Factor d(h).
3*(h + 1)*(h + 2)*(6*h - 1)
Let t(d) be the first derivative of d**4/12 + d**3/6 - d**2 + 18*d + 5. Let s(w) be the first derivative of t(w). Determine k so that s(k) = 0.
-2, 1
Let f(o) be the third derivative of -o**8/336 + 2*o**7/35 - 29*o**6/120 + 3*o**5/10 + 278*o**2. What is q in f(q) = 0?
0, 1, 2, 9
Let t(k) be the third derivative of k**8/112 - 3*k**7/70 - k**6/10 + 4*k**5/5 - 8*k**3 + 6*k**2 + 3*k. Factor t(v).
3*(v - 2)**3*(v + 1)*(v + 2)
Let t = -75 + 50. Let r be t/(-12) - 5/15*1. Factor 0*b - 1/2*b**2 + 9/4*b**3 + 0 - r*b**4.
-b**2*(b - 1)*(7*b - 2)/4
Let q(h) be the third derivative of h**9/756 + h**8/420 - h**7/210 - h**6/90 - h**3/3 - 3*h**2. Let f(x) be the first derivative of q(x). Factor f(n).
4*n**2*(n - 1)*(n + 1)**2
Let i be (-5 - -10)*1155/1225. Factor -51/7*c**3 + 15/7*c**4 + 6/7 - i*c + 9*c**2.
3*(c - 1)**3*(5*c - 2)/7
Suppose 4*h - 3*l - 938 = 374, 0 = -3*h + 5*l + 995. Let w be 80/h - (-8)/52. Factor -2/5*q + 0 + w*q**3 + 0*q**2.
2*q*(q - 1)*(q + 1)/5
Let a = -108 + 122. Suppose 2*m = m - o, -4*o - a = -3*m. Determine f, given that 6/7*f - 3/7*f**m + 0 = 0.
0, 2
Let v = -2445 + 2445. Factor 0*t**2 + 2/7*t**4 + v*t + 2/7*t**3 + 0.
2*t**3*(t + 1)/7
What is s in 139*s - 100*s**2 - 4*s**3 - 29 + 166*s - 166 - 29 + 23*s = 0?
-28, 1, 2
Let m be 3*2/6 - 294/(-686). Factor 0 - 6/7*s**3 + 2/7*s**5 - 4/7*s - 2/7*s**4 + m*s**2.
2*s*(s - 1)**3*(s + 2)/7
Let c be -4*(-5 + 12/3). Let u be (-6)/c + 2 + 10/4. Factor -16/7 - 2/7*v**u - 12/7*v**2 - 24/7*v.
-2*(v + 2)**3/7
Let d(g) be the second derivative of 1/35*g**5 - 4/21*g**3 - 1/21*g**4 - 36*g + 0*g**2 + 0. Factor d(i).
4*i*(i - 2)*(i + 1)/7
Suppose -36 = -2*y - 54. Let t = 11 + y. Factor -4/9*a**t - 1/9 + 5/9*a.
-(a - 1)*(4*a - 1)/9
Suppose -82*n + 6 = -80*n. Factor -6*c**n - 4*c**5 + 16*c**4 - 18*c**3 + 16*c**2 - c - 3*c.
-4*c*(c - 1)**4
Factor -12996*c - 120012 + 60635 - 105239 - 3*c**3 - 342*c**2.
-3*(c + 38)**3
Let f(c) = 5*c**2 + 156*c - 55. Let x(y) = -3*y**2 - 78*y + 30. Let a(b) = -6*f(b) - 11*x(b). Factor a(m).
3*m*(m - 26)
Let a be (357/476)/((-5)/(-4)). Let r be 320/75 + 4/(-6). Factor -12/5*k**2 + r*k**3 + 3/5*k - 12/5*k**4 + 0 + a*k**5.
3*k*(k - 1)**4/5
Let r = -1165 - -2331/2. Factor 0 - r*h**3 - 1/3*h**2 - 1/6*h**4 + 0*h.
-h**2*(h + 1)*(h + 2)/6
Let a(l) = -45*l**2 + 74*l + 14. Let s(q) = -45*q**2 + 72*q + 12. Let u(x) = 4*a(x) - 3*s(x). Solve u(d) = 0 for d.
-2/9, 2
What is g in -4/3*g - 3*g**3 - 13/3*g**2 + 0 = 0?
-1, -4/9, 0
Let p(d) be the first derivative of 5 + 8/9*d - 5/9*d**2 + 2/27*d**3. Solve p(i) = 0 for i.
1, 4
Suppose -3*k + 6 = -2*r, -5*r + 38*k - 10 = 33*k. Determine x so that -2/7*x**3 + 0 + 0*x + 1/7*x**4 + r*x**2 = 0.
0, 2
Factor 1/3*s**2 - 16/3 + 2*s.
(s - 2)*(s + 8)/3
Let h be (-7)/((-66)/(9 - -2)). Factor 8/3*a + 2/3 + h*a**2.
(a + 2)*(7*a + 2)/6
Let c(z) be the first derivative of -z**4/8 + 7*z**3/4 - 9*z**2/2 - 24*z + 16. Let h(d) be the first derivative of c(d). Factor h(k).
-3*(k - 6)*(k - 1)/2
Let k = 94 - 92. Factor 175 + 20*t + k*t**2 + 131 - 256.
2*(t + 5)**2
Solve 0 + 440*j**3 + 43/2*j**4 + 0*j + 1/4*j**5 - 968*j**2 = 0.
-44, 0, 2
Let v = -53 - -94. Let 4*w + 22 + 21*w - v*w**2 + 8 + 36*w**2 = 0. Calculate w.
-1, 6
Factor -1/11*f**5 + 10/11*f**3 + 0*f**2 + 0*f - 3/11*f**4 + 0.
-f**3*(f - 2)*(f + 5)/11
Let s be 36 - -70 - 6/2. Let v = -100 + s. What is i in -2 - 3/2*i**2 - v*i - 1/4*i**3 = 0?
-2
Let c(v) = 9*v**2 + 3. Let l(h) = 17*h**2 + h + 6. Suppose 0 = 4*f + 29 + 11. Let d = -1 + f. Let w(q) = d*c(q) + 6*l(q). Find g, given that w(g) = 0.
-1
Suppose -4 + 0 = -y. Let d(v) be the first derivative of -1/3*v**6 + 0*v**2 - 2/5*v**5 + 0*v + 2/3*v**3 - 2 + 1/2*v**y. Suppose d(u) = 0. Calculate u.
-1, 0, 1
Let h(p) = 5*p**3 - 64*p**2 + 149*p - 66. Let y(m) = -55*m**3 + 705*m**2 - 1635*m + 725. Let c(k) = 65*h(k) + 6*y(k). Find u such that c(u) = 0.
1, 12
Let g be (1 + (-21)/5)*(-10 + (-935)/(-102)). Factor 4/3*n**4 + 0*n + 0 - 4*n**3 + g*n**2.
4*n**2*(n - 2)*(n - 1)/3
Let n = 1051 + -1048. What is w in -14/13*w**2 + 30/13*w + 2/13*w**n - 18/13 = 0?
1, 3
Let v(q) be the first derivative of -q**7/700 + q**6/200 + 11*q**3/3 - 11. Let y(d) be the third derivative of v(d). Factor y(k).
-3*k**2*(2*k - 3)/5
Let a = -183 - -188. Let d(o) be the first derivative of 5/9*o**3 + 0*o + 1/15*o**a + 1/3*o**2 - 2 + 1/3*o**4. Factor d(t).
t*(t + 1)**2*(t + 2)/3
Let t(r) be the third derivative of 0*r**3 + 0*r**4 + 11*r**2 + 0 - 1/20*r**6 - 3/20*r**5 - 1/210*r**7 + 0*r. Solve t(u) = 0.
-3, 0
Let 3/5*y**4 + 0 - 3/5*y**2 + 18/5*y + 3/5*y**5 - 21/5*y**3 = 0. What is y?
-3, -1, 0, 1, 2
Let m(k) be the 