 Factor s(m).
-5*(m - 4)*(m + 2)
Let k(m) be the first derivative of 3*m**5/10 + 9*m**4/2 - 315*m**3/2 - 6075*m**2/2 - 8161. Determine a so that k(a) = 0.
-15, 0, 18
Let u(a) be the second derivative of 0 + 13*a - 5/9*a**3 - 1/90*a**5 - 1/6*a**4 + 25/9*a**2. Factor u(z).
-2*(z - 1)*(z + 5)**2/9
Let c(u) be the second derivative of -u**7/210 - 3*u**6/80 + u**5/20 + 5*u**4/48 + 17*u**2/2 + 2*u - 48. Let o(i) be the first derivative of c(i). Factor o(f).
-f*(f - 1)*(f + 5)*(2*f + 1)/2
Suppose -s + 2*b + 17 = 5, -3*b - 16 = -s. Let g be 2/(1*2/28). Determine k so that -25*k**s - 4 + g*k + 3*k**2 - 72*k**2 + 70*k**3 + 0*k**2 = 0.
2/5, 1
Let m(t) = t**3 - 73*t**2 - 116*t + 3108. Let l be m(74). Factor 0*k**2 + 0 - 2/15*k**5 + 0*k**4 + 2/15*k**3 + l*k.
-2*k**3*(k - 1)*(k + 1)/15
Let v(s) = 11*s**2 - 1165*s + 20246. Let d be v(84). What is i in -1/2*i**3 + 27/2*i**d + 25/2 - 51/2*i = 0?
1, 25
Let h = -136 - -97. Let o = h + 52. Suppose -52*n + 15*n**2 - 15 - o*n - 13*n + 38*n = 0. What is n?
-1/3, 3
Factor -106722/5 - 1/10*r**2 - 462/5*r.
-(r + 462)**2/10
Let 0*f**2 + 0*f + 189/4*f**3 + 1/4*f**4 + 0 = 0. What is f?
-189, 0
Suppose -459*h + 479*h + 605*h - 3579 = -568*h. Let -100/7*u**2 + 0 - u**h - 4*u = 0. Calculate u.
-14, -2/7, 0
Let u(t) = -7*t**2. Let x(q) = 38*q**2 + 5496*q - 1887876. Let g(k) = -6*u(k) - x(k). Solve g(z) = 0.
687
Suppose 2*r**2 - 37/4*r + 1/4*r**3 - 11 = 0. What is r?
-11, -1, 4
Let x(p) be the second derivative of -p**4/9 + 44*p**3/9 - 242*p**2/3 - 50*p - 6. Factor x(z).
-4*(z - 11)**2/3
Let i(q) = -7*q**2 - 1014*q - 39. Let d(s) = s**2 + 169*s + 6. Let w(n) = 39*d(n) + 6*i(n). Let w(t) = 0. Calculate t.
0, 169
Suppose -u = -4*v + 25, -3*v + 16*v = u + 88. Find h such that -24*h + 10/3*h**u - 4*h**4 + 40/3*h**2 + 2/3*h**5 + 32/3 = 0.
-2, 1, 2, 4
Let p(y) be the first derivative of -y**7/441 + y**6/315 + y**5/210 - y**4/126 + 30*y + 77. Let i(q) be the first derivative of p(q). Factor i(c).
-2*c**2*(c - 1)**2*(c + 1)/21
Factor 40*o + 1326*o**2 - 651*o**2 - 16*o**4 - 4*o**3 - 623*o**2.
-4*o*(o - 2)*(o + 1)*(4*o + 5)
Let g be (4/(-6))/((15/(-9))/(0 + 1)). Let c(h) be the second derivative of 0 + 1/15*h**4 - 1/5*h**3 - g*h**2 - 4*h. Factor c(w).
2*(w - 2)*(2*w + 1)/5
Let q(l) be the first derivative of l**7/1155 - l**6/330 - 32*l**2 + 62. Let m(z) be the second derivative of q(z). Solve m(t) = 0.
0, 2
Let f(h) = 3*h**2 - 20*h + 3. Let s be f(0). Let q = -3 - -5. Factor -2159*m + 5*m**4 - 119*m**3 + 3125 + 19*m**s + 750*m**q - 341*m.
5*(m - 5)**4
Let t(n) be the third derivative of -n**6/60 - 58*n**5/5 - 10207*n**4/4 - 59858*n**3/3 + 192*n**2. Let t(v) = 0. What is v?
-173, -2
Let a be ((-5)/1 + 208/78)*(-4)/14. Let s(x) be the third derivative of -a*x**3 - 1/6*x**4 + 0 - 1/60*x**5 + 0*x - 19*x**2. Factor s(u).
-(u + 2)**2
Let b(h) = h**3 - 342*h**2 + 9637*h + 124. Let o be b(31). Factor -3/7*q**4 + 0*q - 36/7*q**2 + o - 39/7*q**3.
-3*q**2*(q + 1)*(q + 12)/7
Let b be (-277)/4 - (-284340)/4062. Find f such that 3*f + b*f**3 + 0 + 3*f**2 = 0.
-2, 0
Let m(u) = -3*u**2 + 386*u - 730. Let h(y) = -30*y**2 + 3867*y - 7299. Let f(g) = 2*h(g) - 21*m(g). Solve f(w) = 0.
2, 122
Let o(h) = 9*h + 31. Let k(t) = 14*t + 46. Let b(f) = 5*k(f) - 8*o(f). Let c be b(-9). What is j in 22*j**2 + 4 - 6*j**4 - 8*j**3 + 0*j**4 + 32*j + c + 4 = 0?
-2, -1, -1/3, 2
Factor -3*n**2 + 236*n + 233*n + 198 - 454*n.
-3*(n - 11)*(n + 6)
Let l = -5/65174 + 195547/325870. Factor -3/5*k**4 + 3/5*k**3 - 3/5*k + 0 + l*k**2.
-3*k*(k - 1)**2*(k + 1)/5
Let q(f) be the third derivative of -f**8/48 - 4*f**7/35 - f**6/4 - 4*f**5/15 - f**4/8 - 481*f**2 + 2. Factor q(r).
-r*(r + 1)**3*(7*r + 3)
Let s(r) be the first derivative of -r**5 - 60*r**4 + 515*r**3/3 + 375*r**2 + 3394. Solve s(k) = 0.
-50, -1, 0, 3
Suppose 8*w = -w. Suppose -7*y + 0*y + 84 = w. Find f such that 10*f - f**2 + y*f + 28 - 3*f**2 + 2*f = 0.
-1, 7
Let f be (-7 - -9)/((14/(-21))/1). Let h be (-15)/(-70)*-7 - 7/f. Let -2/3*a**3 + h*a - 1/6*a**5 + a**2 - a**4 + 0 = 0. What is a?
-5, -1, 0, 1
Factor 0 + 2*t - 2/9*t**4 + 2*t**2 - 2/9*t**3.
-2*t*(t - 3)*(t + 1)*(t + 3)/9
Suppose q - k = 13, 3*k = q - 0*k - 9. Suppose 0 = a - 3*c + q, 2*c - 5*c + 15 = -4*a. Let -6*y - 31*y**2 - 28*y**3 - 5*y**2 + a*y - 2*y = 0. What is y?
-1, -2/7, 0
Let w be 10/(-80) - (-66)/16. Factor -w*t + 6*t**2 + 40 - 40 - 2*t**2.
4*t*(t - 1)
Let -159*p**2 + 9*p**2 - 120*p + 260 - 6*p**3 + p**3 + 15*p**2 = 0. Calculate p.
-26, -2, 1
Let v(n) be the second derivative of -n**6/60 - 3*n**5/5 - 83*n**4/24 - 5*n**3 - 80*n - 7. Factor v(t).
-t*(t + 1)*(t + 3)*(t + 20)/2
Factor 2/3*z**3 + 341138/3 + 342790/3*z + 1654/3*z**2.
2*(z + 1)*(z + 413)**2/3
Let o(x) = -9*x**2 + 32*x + 67. Let c be o(5). Let p(r) be the first derivative of -4/5*r**c + 9 + 2/15*r**3 - 2*r. Factor p(y).
2*(y - 5)*(y + 1)/5
Solve -24*h + 0 + 1/2*h**2 = 0 for h.
0, 48
Let c = -332 + 367. Suppose 90 = c*t + 20. Factor 2 + t*x + 1/2*x**2.
(x + 2)**2/2
Determine k so that -20*k**3 - k**5 + 794967*k**2 - 15*k**4 - 794904*k**2 - 27*k**3 = 0.
-9, -7, 0, 1
Let g(i) be the third derivative of 1/360*i**6 + 1/20*i**5 + 1/3*i**4 - 34*i**2 + 0*i - 13/6*i**3 + 0. Let s(a) be the first derivative of g(a). Factor s(q).
(q + 2)*(q + 4)
Let p(n) be the second derivative of n**5/40 - n**4/12 - 2*n**3/3 - 2706*n. Factor p(v).
v*(v - 4)*(v + 2)/2
Let v(u) be the second derivative of -16/3*u**3 - 14*u**2 + 2*u + 5 - 1/3*u**4. Factor v(p).
-4*(p + 1)*(p + 7)
Let y(o) be the third derivative of -5*o**8/84 - 43*o**7/42 - 11*o**6/8 + 247*o**5/12 - 1015*o**4/24 + 30*o**3 - 38*o**2 + 5. Determine s so that y(s) = 0.
-9, -4, 1/4, 1
Let o(g) be the third derivative of g**7/945 + g**6/135 - g**5/90 - g**4/6 - 3*g**2 - 20*g + 8. Factor o(b).
2*b*(b - 2)*(b + 3)**2/9
Let b(j) be the first derivative of 3*j**4/28 - 198*j**3/7 - 600*j**2/7 + 1913. Factor b(p).
3*p*(p - 200)*(p + 2)/7
Let a(i) = -9 + 13 + i**2 - i - 7*i. Let h be a(8). Factor 5*x - 5*x**3 - 9 + 5*x**2 + 8 + 0 - h.
-5*(x - 1)**2*(x + 1)
Factor 129/2*d - 3/2*d**2 + 2277.
-3*(d - 66)*(d + 23)/2
Let m(k) be the third derivative of k**5/100 + 17*k**4/8 - 132*k**3/5 - 147*k**2 + 2*k - 2. Solve m(j) = 0.
-88, 3
Let q(c) be the third derivative of 0*c**3 - 1/80*c**5 + 0*c + 0*c**4 + 28*c**2 + 0. Factor q(p).
-3*p**2/4
Suppose -f + 4*v + 15 = v, -2*v - 5 = f. Let n be ((-28)/(-12))/(1/f). Find h, given that -7*h - 16*h**3 - 15*h + 24*h**2 + 6*h + 4 - 3*h**4 + n*h**4 = 0.
1
Let y = 719/2 - 357. Let x(o) be the third derivative of -2*o**2 + 0 - y*o**3 + 0*o - 5/12*o**5 + 1/24*o**6 + 35/24*o**4. Factor x(s).
5*(s - 3)*(s - 1)**2
Let 69/4*y**2 + 435/8*y + 147/4 - 3/8*y**3 = 0. What is y?
-2, -1, 49
Let w = 31 - 25. Suppose 2 + 0 = v. Solve -2 - 2*x - w*x**3 + 4*x + 4*x**3 + 2*x**v = 0 for x.
-1, 1
Let d be 78/507 - 2246644/234. Let b = -9590 - d. Factor 104/9*s + 16/9 - b*s**3 + 140/9*s**2.
-2*(s - 2)*(7*s + 2)**2/9
Let f = 245/443 - -151/1329. Factor -8*i + f*i**3 + 0 - 22/3*i**2.
2*i*(i - 12)*(i + 1)/3
Let u(v) be the first derivative of v**3/3 - 905*v**2/4 - 453*v/2 - 6211. Determine d, given that u(d) = 0.
-1/2, 453
Let k(p) be the first derivative of 3*p**5/25 + 3*p**4/5 - 222*p**3/5 + 1722*p**2/5 - 2793*p/5 - 3234. Solve k(s) = 0.
-19, 1, 7
Let p = -16833 + 16836. Let i(m) be the third derivative of 1/8*m**4 + 5/12*m**p + 2*m**2 + 1/120*m**5 + 0*m + 0. Factor i(c).
(c + 1)*(c + 5)/2
Solve 1/11*m**3 + 2*m**2 + 72/11 + 76/11*m = 0 for m.
-18, -2
Determine d, given that -1480*d + 4*d**3 + 569 - 342 + 484*d**2 + 765 = 0.
-124, 1, 2
Let p(s) be the third derivative of -s**6/180 + 22*s**5/45 + 47*s**4/36 - 10*s**3 - 28*s**2 - 13*s. What is r in p(r) = 0?
-2, 1, 45
Let y(b) be the first derivative of 3*b**2 - 1/2*b**3 + 15 - 1/4*b**4 - 14*b. Let q(w) be the first derivative of y(w). Factor q(v).
-3*(v - 1)*(v + 2)
Let a = 2399/4658 - 35/2329. Factor -11/2 - a*z**3 + 1/2*z + 11/2*z**2.
-(z - 11)*(z - 1)*(z + 1)/2
Let x(j) = j**2 + 29*j + 165. Let s be x(-6). Suppose -12*t = -3*t - s. Factor 3*d**2 + 3/4*d**5 + 0 - 9/4*d**3 - 3/2*d**4 + t*d.
3*d*(d - 2)**2*(d + 1)**2/4
Let v(n) be the second derivative of 51*n**5/80 + n**4/24 - 153*n**3/2 - 9*n**2 + 22*n - 95. Factor v(c).
(c - 6)*(c + 6)*(51*c + 2)/4
Let y(h) = -h**2 - 17*h - 58. Let b = -157 - -150. Let i