x. Factor t(c).
3*(c - 9)*(c + 15)
Let l be (108/48)/((-60)/(-352)). Let w(d) be the first derivative of -d**3 - 6 - l*d**2 + 21/20*d**4 - 36/5*d. Let w(z) = 0. What is z?
-2, -2/7, 3
Let k be (-17144)/6429*(-26)/4. What is l in 69/2*l**2 - 27/2*l**3 + 2 + k*l = 0?
-2/9, 3
Suppose 47*a = -35*a - 5*a. Let v(t) be the third derivative of 1/5*t**3 + 1/150*t**5 + 1/15*t**4 + 0 + a*t + 14*t**2. Factor v(d).
2*(d + 1)*(d + 3)/5
Let x(p) = -63*p + 128. Let a be x(2). Let f(m) be the first derivative of 16 - 2/11*m + 3/22*m**a - 1/44*m**4 + 0*m**3. Suppose f(u) = 0. Calculate u.
-2, 1
Let t(c) be the third derivative of c**7/525 - c**6/150 - c**5/30 + c**4/10 - 5051*c**2 - 2*c. Let t(v) = 0. What is v?
-2, 0, 1, 3
Let s be 10/15 - (-2)/6. Suppose 3*f - 21 = -3*u, -4*u + 17 = s. Find o, given that -3 + 30*o + 0*o**2 + f*o**2 + 78 = 0.
-5
Let s be (-4 - -1)*168/(-126). Suppose -3 + 27 = 4*q. Suppose 0*r**3 - q*r - 8*r**2 - 4*r**3 - 2*r + s*r = 0. Calculate r.
-1, 0
Let i(p) be the first derivative of -3*p**5/20 + p**4 - p**3/2 - 9*p**2 + 171*p + 57. Let d(k) be the first derivative of i(k). Factor d(g).
-3*(g - 3)*(g - 2)*(g + 1)
Let y(b) = -b**3 + 10*b**2 - b + 13. Let q be y(10). Suppose q*u = 10*u + 4*u. Suppose 0*o**4 + 0*o + 0*o**2 - 2/5*o**3 + u + 2/5*o**5 = 0. Calculate o.
-1, 0, 1
Let v = -424 - -1158. Let q = 736 - v. Factor -2/3*f**q + 4/3*f + 16/3.
-2*(f - 4)*(f + 2)/3
Let c(d) be the second derivative of 15/4*d**4 + 0 + 48*d - 35*d**2 + 305/6*d**3. Factor c(w).
5*(w + 7)*(9*w - 2)
Let n(m) = 134*m - 1474. Let r be n(11). Let s(o) be the first derivative of 39/14*o**4 - 25 + r*o + 3/5*o**5 - 12/7*o**2 + 20/7*o**3. Solve s(y) = 0 for y.
-2, 0, 2/7
Let p be ((-6)/(-4) + 31/806*-13)/3. Factor -p*x**4 - 2/3 + 1/3*x - 1/3*x**3 + x**2.
-(x - 1)**2*(x + 1)*(x + 2)/3
Factor 40*g**3 + 14*g**5 - 3347*g**4 + 3301*g**4 + 3*g - 5*g**5 + 28*g**3 - 34*g**2.
g*(g - 3)*(g - 1)**2*(9*g - 1)
Let k = 4866 - 14596/3. Let p(l) be the first derivative of 0*l - 3 - 1/6*l**4 - k*l**2 - 2/3*l**3. Factor p(y).
-2*y*(y + 1)*(y + 2)/3
Let q(p) be the third derivative of 116*p**2 - p - 1/210*p**5 + 1/2*p**4 - 21*p**3 + 0. Factor q(r).
-2*(r - 21)**2/7
Let s be (-160)/13000*(-10)/48. Let k(u) be the third derivative of 0*u - s*u**5 + 0*u**3 + 0 + 16*u**2 + 0*u**4. Suppose k(w) = 0. Calculate w.
0
Let i(h) be the third derivative of -h**7/525 - 11*h**6/75 - 79*h**5/50 - 57*h**4/10 + 36*h**2 - h - 9. Solve i(s) = 0 for s.
-38, -3, 0
Let k(o) be the third derivative of o**8/112 - 8*o**7/35 - 9*o**6/20 + 4*o**5/5 + 17*o**4/8 - 11*o**2 - 2*o + 20. Solve k(c) = 0.
-1, 0, 1, 17
Let o(f) = -4 - 19 - 5 - 16*f**2 - 58*f - f**3 - 3 + 1. Let m be o(-11). Suppose 10/3*d**m - 10/3*d + 1/3*d**2 + 0 - 1/3*d**4 = 0. Calculate d.
-1, 0, 1, 10
Solve 8*q**3 - 80*q**2 + 6*q**3 - 38*q**3 + 13*q**3 + 10*q**3 = 0.
-80, 0
Find v, given that -14*v**5 + 18010/7*v**3 - 1016*v**4 + 12024/7*v**2 + 1800/7*v + 0 = 0.
-75, -2/7, 0, 3
Let z(l) = l**4 + l**3 - 3*l**2 + 3*l. Let k(q) = 3*q**4 - 45*q**3 + 40*q**2 + 112*q. Let a(c) = -k(c) + 4*z(c). Factor a(f).
f*(f - 2)*(f + 1)*(f + 50)
Let l(h) be the third derivative of h**5/390 + 9*h**4/52 + 2*h**3/3 - 437*h**2. Determine f so that l(f) = 0.
-26, -1
Let i(b) = -2*b**3 + 7*b**2 - 5*b + 5. Let f be i(6). Let q = f + 825/4. Factor -1/2*v**2 + 1/4*v**5 + v**4 - 1/2 + v**3 - q*v.
(v - 1)*(v + 1)**3*(v + 2)/4
Find o such that 400*o**2 - 72 + 4296*o - 9111*o + 4251*o - 68*o**3 = 0.
-2/17, 3
Suppose 0 + 384/5*j + 3/5*j**2 = 0. What is j?
-128, 0
Let k be (42/4)/(-7)*40/(-30). Suppose -47*q**3 + 43*q**2 - 19*q**2 + 21*q**k + 23*q**3 + 3*q**4 = 0. What is q?
0, 3, 5
Let p(h) be the second derivative of h**6/144 + 3*h**5/16 + 35*h**4/24 - 14*h**3/3 - h**2/2 + h + 1. Let x(a) be the second derivative of p(a). Factor x(y).
5*(y + 2)*(y + 7)/2
Let g(y) be the first derivative of -y**9/756 + y**8/140 - y**7/70 + y**6/90 + 7*y**3/3 + y + 41. Let m(t) be the third derivative of g(t). Solve m(f) = 0.
0, 1
Let a(v) be the first derivative of 1/48*v**4 + 8*v**2 - 1/8*v**3 + 9 + 1/240*v**5 + 0*v. Let j(f) be the second derivative of a(f). Solve j(h) = 0 for h.
-3, 1
Let c(g) be the third derivative of 1/42*g**7 - 2*g**2 + 125/3*g**4 - 33 + 0*g + 2/3*g**6 + 15/2*g**5 + 625/6*g**3. Factor c(q).
5*(q + 1)*(q + 5)**3
Suppose 1/5*n**2 + 3*n + 54/5 = 0. What is n?
-9, -6
Let t(y) = y + 47. Let z be t(-47). Suppose 5*m + 3 = 3*k + 2*m, 3*k + 3*m + 3 = z. What is q in 0 + 1/2*q**5 - 1/3*q**4 + k*q + 0*q**2 - 1/6*q**3 = 0?
-1/3, 0, 1
Suppose 644 = 31*j - 1247. Factor 65*c**2 + 432*c + 68*c**2 - j*c**2 + 3*c**3.
3*c*(c + 12)**2
Let l(b) = 5*b**2 - 5*b - 15. Let t = -451 - -446. Let u(o) = -2*o**2 + 3*o + 8. Let g(h) = t*u(h) - 3*l(h). Suppose g(r) = 0. What is r?
-1, 1
Let q(g) be the first derivative of 0*g - 3/22*g**4 - 4/55*g**5 + 1/33*g**6 + 0*g**2 + 0*g**3 - 35. Factor q(c).
2*c**3*(c - 3)*(c + 1)/11
Let o = 662512 - 662507. Suppose 5/3*w**2 + 0 - 5/3*w**4 + 0*w**3 + 5/6*w - 5/6*w**o = 0. Calculate w.
-1, 0, 1
Let v = -12 - -25. Let x = v - 11. What is j in -x*j**5 - 82 - 10*j**4 - 18*j**3 - 4*j - 14*j**2 + 82 = 0?
-2, -1, 0
Let s(q) = -7*q**2 - 161*q + 11. Let w be s(-23). Factor -w*d**2 - 2*d**4 + 24*d + 32*d - 87*d + 27*d - 8*d**3 + d**2.
-2*d*(d + 1)**2*(d + 2)
Factor -128/19*c + 2/19*c**2 + 480/19.
2*(c - 60)*(c - 4)/19
Let o(y) be the second derivative of -y**5/8 - 65*y**4/8 - 1675*y**3/12 + 1875*y**2/4 - 2*y - 5203. Factor o(l).
-5*(l - 1)*(l + 15)*(l + 25)/2
Suppose 20470*b - 10213*b - 10220*b = 0. Factor 30/11*l**2 - 72/11*l + b + 18/11*l**3.
6*l*(l + 3)*(3*l - 4)/11
Let y(c) be the third derivative of -5*c**8/784 + 11*c**7/245 + 2*c**6/7 + 37*c**5/70 + 3*c**4/8 - 3094*c**2. Determine n so that y(n) = 0.
-1, -3/5, 0, 7
Let j = 651413/4 + -1954063/12. Suppose 172/3*l + 16/3*l**2 - j = 0. What is l?
-11, 1/4
Suppose 161*v - 156*v + 300 = 0. Let w be ((-9)/15)/(1*18/v). Find k, given that -3/7*k**w + 0 + 6/7*k = 0.
0, 2
Let g(u) = -9253*u - 138792. Let i be g(-15). What is y in 4/3*y**4 - 22/3*y**2 - 8/3*y + 2/3*y**i + 8 = 0?
-2, -3/2, 1, 2
Let g(m) be the first derivative of m**6/2 - 66*m**5/5 - 36*m**4 - 2*m**3 + 141*m**2/2 + 72*m + 2178. Factor g(x).
3*(x - 24)*(x - 1)*(x + 1)**3
What is r in 0 + 185*r**2 + 0*r - 1/3*r**4 - 554/3*r**3 = 0?
-555, 0, 1
Factor -1/2*w**3 - 726*w - 5324 - 33*w**2.
-(w + 22)**3/2
Let x(j) = -12*j**4 - 288*j**3 + 2402*j**2 - 4512*j - 7210. Let d(z) = 8*z**4 + 144*z**3 - 1202*z**2 + 2256*z + 3606. Let m(r) = -5*d(r) - 3*x(r). Factor m(n).
-4*(n - 25)*(n - 6)**2*(n + 1)
Let j(n) be the first derivative of 2*n**3/27 - 5708*n**2/9 + 16290632*n/9 - 10160. Suppose j(c) = 0. What is c?
2854
Factor -11632*k**2 + 4290 + 11627*k**2 - 802*k + 467*k.
-5*(k - 11)*(k + 78)
Factor 64/5*d + 2/5*d**3 + 0 - 24/5*d**2.
2*d*(d - 8)*(d - 4)/5
Solve 423/5*y - 170 + 1/5*y**2 = 0.
-425, 2
Let g(l) be the first derivative of -115/12*l**3 - 23*l + 15/2*l**2 - 7/8*l**5 - 3 + 5*l**4. Let b(w) be the first derivative of g(w). Factor b(y).
-5*(y - 2)*(y - 1)*(7*y - 3)/2
Let b(k) be the first derivative of 3/10*k**5 + 53 - 21/4*k**2 + 9/2*k**3 + 3*k - 15/8*k**4. Factor b(l).
3*(l - 2)*(l - 1)**3/2
Let v(b) be the third derivative of b**5/15 - 499*b**4/3 + 498002*b**3/3 + 45*b**2 - 5*b. Suppose v(a) = 0. What is a?
499
Let q(n) be the second derivative of n**6/10 + 51*n**5/5 + 543*n**4/2 - 1190*n**3 + 3675*n**2/2 - 3278*n. Find t, given that q(t) = 0.
-35, 1
Solve 36*i**3 + 3580*i + 706*i**2 + 4084*i**2 + 598*i**2 + 596 = 0.
-149, -1/3
Let t(d) be the second derivative of 5*d**4/24 + 85*d**3/6 - 90*d**2 + 2354*d. Factor t(s).
5*(s - 2)*(s + 36)/2
Solve 173*d**3 + 848 + 119*d**3 + 322*d**2 - 1166*d**2 - 269*d - 64*d**3 + 41*d - 4*d**4 = 0.
-1, 1, 4, 53
Let z(g) be the second derivative of 16*g**7/105 - 584*g**6/75 + 841*g**5/50 - 29*g**4/30 - 209*g**3/15 - 7*g**2 + 279*g + 1. Suppose z(a) = 0. Calculate a.
-1/4, 1, 35
Let r(f) = -3*f - 54. Let o be r(-22). Factor -25*a**2 - 10*a + 57*a**2 - o - 30*a**2.
2*(a - 6)*(a + 1)
Suppose -3*c - 5*d + 339 = 0, 2*c + 3*d + 113 = 3*c. Suppose -119*p = -c*p. Factor 3 - 4*a - 4 - a**2 + p - 3.
-(a + 2)**2
Let d(m) be the third derivative of -1/30*m**5 + 0*m - 4 - 3/4*m**4 - 14/3*m**3 - 18*m**2. Solve d(z) = 0.
-7, -2
Let g = -3880 + 388