3. Factor p(q).
-2*q**2*(q + 1)*(q + 2)/3
Let a be ((-319)/(-22) + -10)/6. Factor 3/2*r**3 - 3/2*r + 3/4*r**2 - a*r**4 + 0.
-3*r*(r - 2)*(r - 1)*(r + 1)/4
Let l be (-4)/14 - 48/(-21). Suppose -4*j + l*j = -4. Factor 0*i**3 + j*i**3 + 7 + 4*i - 7 + 6*i**2.
2*i*(i + 1)*(i + 2)
Factor -3/2*l**2 - 27/2 - 9*l.
-3*(l + 3)**2/2
Let h(c) = -135*c**3 - 190*c**2 + 430*c + 485. Let j(r) = -5*r**3 - 7*r**2 + 16*r + 18. Let g(s) = 2*h(s) - 55*j(s). Factor g(i).
5*(i - 2)*(i + 1)*(i + 2)
Let l(p) = -3*p**3 + p**3 + 32*p**2 + 4 + 3*p**3 - 21*p**2. Let d be l(-11). Determine f, given that -1 + d*f + 1 + 2*f**2 = 0.
-2, 0
Let q = 1209 + -838. Factor -2*u**3 + q - 3*u**2 - u**3 - 371 + 6*u.
-3*u*(u - 1)*(u + 2)
Factor 3*b**3 + 11025*b + 102130 + 26495 + 315*b**2 + 0*b**3.
3*(b + 35)**3
Let m(y) = -2*y**2 + 5*y + 1. Let p(o) = -56*o**2 + 88*o - 12. Let d(l) = 20*m(l) + p(l). Factor d(s).
-4*(s - 2)*(24*s + 1)
Let v(f) = -14 + 39 + 5*f - 4*f. Let s be v(-23). Let -4/7*g**4 + 2/7 - 6/7*g**3 + 2/7*g**s + 6/7*g = 0. What is g?
-1, -1/2, 1
Factor -687*i**2 + 4*i - i**3 - 20 + 1403*i**2 - 696*i**2 - 3*i.
-(i - 20)*(i - 1)*(i + 1)
Let q be (-60378)/(-12492) + (5/(-6)*-4)/2. Factor 3 - q*l + 1/2*l**2 + l**3.
(l - 2)*(l + 3)*(2*l - 1)/2
Let a(j) be the third derivative of j**5/240 + 13*j**4/32 - 5*j**3/3 - 23*j**2. Determine y, given that a(y) = 0.
-40, 1
Let y(z) be the second derivative of -z**7/1680 - z**6/240 - z**4/12 - 14*z**3/3 + 9*z - 2. Let t(n) be the third derivative of y(n). Factor t(x).
-3*x*(x + 2)/2
Suppose 3*k - 11 = -4*i, 6*i - 19 = i - 2*k. Factor -a**4 - 2*a - 2*a**2 + 2*a**3 + 0*a**2 - 2*a**4 + i*a**4.
2*a*(a - 1)*(a + 1)**2
Factor 44890/3 - 45560/3*t - 5/6*t**3 + 1345/6*t**2.
-5*(t - 134)**2*(t - 1)/6
Let s be (-2)/(10/(-8)*4/10). Determine n so that 3*n**3 - 7*n**2 + 6*n**3 + 2*n**s + 5*n**2 - 5*n**3 - 4*n = 0.
-2, -1, 0, 1
Let 26/11*x**2 + 0*x + 0 + 2/11*x**3 = 0. Calculate x.
-13, 0
Let j be 4*(7 - (1 + 2)). Let h be (j/(-20))/(1/(-5)). Determine m so that 61*m**3 - 75*m**h + 0*m**2 - m**3 - 12*m**2 = 0.
0, 2/5
Let l(k) = -k**3 + 3*k**2 + 19*k - 3. Let f be l(6). Let a(w) be the first derivative of 0*w**f + 3 + 0*w + 1/2*w**2 - 1/4*w**4. Factor a(c).
-c*(c - 1)*(c + 1)
Let z be (440/80)/((-22)/(-16)). Find y, given that -9/2*y**z + 10*y - 37/2*y**2 + 15*y**3 - 2 = 0.
2/3, 1
Let n be 141/6 - (-8)/12. Let b = 749/30 - n. Factor -4/5*x + 1/5*x**4 + b + 2/5*x**3 - 3/5*x**2.
(x - 1)**2*(x + 2)**2/5
Let -4/3*y**4 + 14*y**3 - 2/3*y**5 + 4/3*y**2 + 80 - 232/3*y = 0. Calculate y.
-5, -3, 2
Suppose -y + 17 = -2*t, y = -0*y + 3*t + 22. Suppose y*q - 3 = 6*q - 4*o, 5*q - 15 = o. Let -7/2*n**q + 2*n**2 + 2*n - 2*n**4 + 0 + 3/2*n**5 = 0. What is n?
-1, -2/3, 0, 1, 2
Determine t, given that -42*t - 120 + 197*t - 158*t**2 - 23*t - t**4 + 36*t**3 - t**3 + 112*t = 0.
1, 2, 30
Let r(q) be the third derivative of q**7/6300 - q**6/180 + q**5/12 - 5*q**4/8 + 14*q**2. Let c(x) be the second derivative of r(x). Solve c(f) = 0 for f.
5
Let -1/6*h - 1/6*h**3 + 0 + 1/3*h**2 = 0. What is h?
0, 1
Find u such that -11*u - 15*u + 111 + 8*u**2 - 135 = 0.
-3/4, 4
Suppose -12 = 29*o - 32*o. Suppose -o*t - 25 = -4*z - z, t - z + 5 = 0. Factor 1/3*r + 1/3*r**2 + t.
r*(r + 1)/3
Let d(t) = t + 1. Let r be d(-6). Let q = r + 7. Suppose -3*v**q + 5*v**2 - 4*v**2 = 0. Calculate v.
0
Factor -133*g - 62*g**2 - 2*g**3 + 4*g**3 - 63*g - 32*g**2.
2*g*(g - 49)*(g + 2)
Let w be ((-5)/(-4))/(1278/568). What is f in 2*f**4 + 4/9*f + 0*f**2 - 17/9*f**3 + 0 - w*f**5 = 0?
-2/5, 0, 1, 2
Let r(l) = -l**3 - l**2 + 2. Let a(d) = 69*d**3 - 923*d**2 + 452*d - 66. Let m(q) = -a(q) - 5*r(q). Factor m(z).
-4*(z - 14)*(4*z - 1)**2
Suppose -16*a = -38*a - 4840. Let t = -220 - a. Factor -3/8*j**3 + t*j - 15/8*j**2 + 0.
-3*j**2*(j + 5)/8
Let o(l) be the first derivative of -5*l**6/6 + 4*l**5 - 5*l**4 - 10*l**3/3 + 25*l**2/2 - 10*l - 1049. Factor o(r).
-5*(r - 2)*(r - 1)**3*(r + 1)
Let a(h) be the first derivative of -2*h**3/15 - 46*h**2/5 + 308. Factor a(g).
-2*g*(g + 46)/5
Factor 40/3*i**2 + 38/3 + 1/3*i**3 + 77/3*i.
(i + 1)**2*(i + 38)/3
Let k(c) be the second derivative of -c**4/12 - c**3 - 16*c. Let x be k(-6). Factor -1/3*r**3 + 0*r + x + 1/3*r**2.
-r**2*(r - 1)/3
Let 27/8*k - 27/8 - 3/8*k**3 + 3/8*k**2 = 0. Calculate k.
-3, 1, 3
Factor 5*i**2 + 123*i**2 + 272*i - 11*i**2 + 123 - 3*i**3 - 29*i.
-3*(i - 41)*(i + 1)**2
Let n be (0 - 3) + 2 - (297/36 + -10). Determine v so that 3/2*v**3 - 9/4*v**2 - 3*v + n*v**4 + 3 = 0.
-2, 1
Let y(b) be the third derivative of b**5/12 - 45*b**4/8 - 5*b**2. Factor y(l).
5*l*(l - 27)
Suppose 10*y - 5*y = -6*y. Let h(o) be the second derivative of 5*o - 49/60*o**5 - 2/9*o**3 - 7/9*o**4 + 0 + y*o**2. Factor h(c).
-c*(7*c + 2)**2/3
Let r be ((-10 + 10)*(7 + -6))/3. Factor r*l + 1/9*l**2 + 0.
l**2/9
Let w = -64 + 64. Let j(n) be the first derivative of w*n + 2/3*n**3 + 1/4*n**4 - 1/5*n**5 + 0*n**2 - 2. Suppose j(g) = 0. What is g?
-1, 0, 2
Let o(n) be the second derivative of -n**6/6 - 19*n**5 - 3785*n**4/6 - 6290*n**3/3 + 20535*n**2/2 + 541*n. Factor o(d).
-5*(d - 1)*(d + 3)*(d + 37)**2
Factor 0 + 1/5*m**4 - 1/5*m**2 - 2/5*m**3 + 2/5*m.
m*(m - 2)*(m - 1)*(m + 1)/5
Let p(o) be the first derivative of o**8/336 - o**7/28 + o**6/6 - 5*o**5/12 + 5*o**4/8 - 5*o**3/3 + 2. Let k(h) be the third derivative of p(h). Factor k(f).
5*(f - 3)*(f - 1)**3
Let 13*t**2 - 8*t**4 - t**2 + 155*t**3 - 109*t**3 = 0. What is t?
-1/4, 0, 6
Let r(f) = -f**2 + 8*f - 4. Suppose z - 8 + 1 = 0. Let o be r(z). Factor 0*c**2 + 1/3*c**o + 0 - 1/3*c.
c*(c - 1)*(c + 1)/3
Let z(q) = -82*q**2 + 83*q + 1. Let x(n) = -80*n**2 + 81*n + 2. Let i(s) = -2*x(s) + 3*z(s). Suppose i(g) = 0. Calculate g.
1/86, 1
Let t(f) be the second derivative of -125*f**7/42 - 55*f**6/6 - 21*f**5/2 - 17*f**4/3 - 4*f**3/3 + 26*f - 1. Let t(u) = 0. What is u?
-1, -2/5, 0
Let f(p) = -3 + 50*p**2 - 49*p**2 + p**4 - p**3 + 2. Let u(k) = 3*k**5 - 12*k**4 + 12*k**3 - 6*k**2 + 3. Let z(s) = 3*f(s) + u(s). Factor z(c).
3*c**2*(c - 1)**3
Suppose 3*z + 7*m = 4*m - 9, -5*m = 4*z + 18. Factor -1/4*l**4 + 3/4 + 3/2*l**z - 5/4*l - 1/4*l**5 - 1/2*l**2.
-(l - 1)**3*(l + 1)*(l + 3)/4
Let c(g) = 5*g**2 - 11*g + 8. Let s(a) = 51*a**2 - 111*a + 53 - 23 + 51. Let w(r) = -21*c(r) + 2*s(r). Solve w(b) = 0.
1, 2
Let p be (-2 - (-9)/5)/(-1). Let i = 1732/15 + -1729/15. Solve -i*y**2 + 0 + p*y = 0 for y.
0, 1
Let t = 1/24750 + 49493/173250. Factor -8/7 + t*f**2 + 0*f.
2*(f - 2)*(f + 2)/7
Let v(l) be the second derivative of -2*l**7/21 + 8*l**6/15 - l**5 + 2*l**4/3 + 29*l. Factor v(t).
-4*t**2*(t - 2)*(t - 1)**2
Suppose 5*y + 10 = 5*v, 3*y + 44*v - 2 = 43*v. Let h(s) be the first derivative of 4/9*s**3 + y*s**2 - 2 + 0*s + 0*s**4 - 4/15*s**5. Factor h(u).
-4*u**2*(u - 1)*(u + 1)/3
Factor -716 + 363 - 52*c + 409 - 4*c**2.
-4*(c - 1)*(c + 14)
Determine z so that -3*z**2 + 0 - 1/8*z**5 + 9/2*z + 3/4*z**4 - 5/8*z**3 = 0.
-2, 0, 2, 3
Let x be 22/5 + (-14)/35. Factor -x*h**2 - 3*h**2 - 3*h + 6*h**4 + 3*h**5 + h**2.
3*h*(h - 1)*(h + 1)**3
Let d be (-12)/20*(-10)/9. Factor -1/3*k**2 + k - d.
-(k - 2)*(k - 1)/3
Let h(p) be the first derivative of -4*p**3/15 + 112*p**2/5 - 3136*p/5 - 31. Factor h(z).
-4*(z - 28)**2/5
Let z(q) be the second derivative of -q**6/10 + 33*q**5/20 - 9*q**4/4 - 11*q**3/2 + 15*q**2 + 87*q. Factor z(f).
-3*(f - 10)*(f - 1)**2*(f + 1)
Let b(o) be the second derivative of 0 + 4/63*o**3 - 1/126*o**4 + 29*o + 0*o**2. Factor b(d).
-2*d*(d - 4)/21
Let u(n) be the third derivative of 1/60*n**5 + 31*n**2 + 0*n**3 - 5/24*n**4 + 0*n + 0. Let u(v) = 0. Calculate v.
0, 5
Find n such that n**2 + 24*n + 9 - 39 + 5 = 0.
-25, 1
Let n = 32 - 25. Let -2*t**2 + 20 - n*t - 40*t**3 + 25*t**4 + 22*t - 43*t**2 + 25*t = 0. What is t?
-1, -2/5, 1, 2
Let a(r) be the third derivative of 5/3*r**3 + 5/8*r**4 - 43*r**2 + 0 - 1/6*r**5 - 1/8*r**6 + 0*r. Factor a(o).
-5*(o - 1)*(o + 1)*(3*o + 2)
Let x(i) be the third derivative of -i**8/1512 - i**7/945 + i**6/108 - i**5/90 - 106*i**2. Factor x(s).
-2*s**2*(s - 1)**2*(s + 3)/9
Let w = -1234 + 1238. Let y(m) be the third derivative of -1/9*m**3 + 0 + 0*m - 5/72*m**w - 1/45*m**5 + 2*m**2 - 1/360*m**6. Let y(o) = 0. Calculate o.
-2, -1
Let s = -3/170 - -71/170. Let y(w) be the first derivative of -3 + 2/3*w - 1/3*w**4 + 4/9*w**3 - s*