Let w(l) = 15*l**4 + 1905*l**3 + 3025*l**2 - 14890*l + 110. Let c(j) = j**4 + 136*j**3 + 216*j**2 - 1064*j + 8. Let g(d) = -55*c(d) + 4*w(d). Factor g(s).
5*s*(s - 2)*(s + 4)*(s + 26)
Let w be 5/((-25)/178)*5/(-2). Let q = 95 - w. Factor -3*t**4 + 42*t**2 - 2*t - 50*t**2 + 5*t**3 + q*t + 2*t**4.
-t*(t - 2)**2*(t - 1)
Find f such that -3246*f**3 + 0 - 21/2*f**5 - 2400*f + 9360*f**2 - 396*f**4 = 0.
-20, 0, 2/7, 2
Let t(k) be the second derivative of 91*k - 2/3*k**3 - k**4 + 0 + 1/5*k**5 + 6*k**2. Suppose t(h) = 0. What is h?
-1, 1, 3
Let q(i) be the first derivative of i**5/100 + i**4/6 + 3*i**3/10 - 7*i - 17. Let d(b) be the first derivative of q(b). Determine h so that d(h) = 0.
-9, -1, 0
Let c(v) be the first derivative of -3*v**4/2 + 25*v**3/3 + 13*v**2 - 5*v + 2503. Factor c(l).
-(l - 5)*(l + 1)*(6*l - 1)
Let o be (14/(-5))/7 + (-52)/(-5). Suppose -4*w + 6 + o = 0. Factor 6*u**w + 4*u - 4 + 0*u**4 + 4*u**4 - 2*u**4 - 20*u**3 + 12*u**2.
4*(u - 1)**3*(2*u + 1)
Let s(g) be the first derivative of 1/280*g**6 - 2/21*g**4 + 8 + 0*g + 1/84*g**5 - 2/7*g**3 + 5*g**2. Let z(m) be the second derivative of s(m). Factor z(a).
(a - 2)*(a + 3)*(3*a + 2)/7
Let s(m) be the third derivative of -m**5/150 - 6*m**4/5 - 432*m**3/5 - 599*m**2. Let s(l) = 0. Calculate l.
-36
Solve 8640*v - 1/4*v**4 + 648*v**2 + 12*v**3 + 36288 = 0.
-12, 84
Let o(h) be the third derivative of 70 - 1/8*h**4 - 1/40*h**6 - 1/8*h**3 - 1/280*h**7 - 3/40*h**5 + 0*h + h**2. Find b such that o(b) = 0.
-1
Let r = 287 - 252. Factor -9*g**3 - r*g**4 - g + 39*g**4 + 4*g - 10*g**2.
g*(g - 3)*(g + 1)*(4*g - 1)
Factor 0 + 82*d**2 + 114*d + 2/3*d**4 + 50/3*d**3.
2*d*(d + 3)**2*(d + 19)/3
Let c(t) be the third derivative of t**6/120 - 637*t**5/180 - 89*t**4/6 - 214*t**3/9 - 468*t**2 - 2*t. Factor c(s).
(s - 214)*(s + 1)*(3*s + 2)/3
Let x(q) be the third derivative of q**7/630 + 19*q**6/360 + 13*q**5/180 - 29*q**4/24 + 3*q**3 - 2*q**2 - 2*q - 1845. Factor x(s).
(s - 1)**2*(s + 3)*(s + 18)/3
Suppose -44*u + 50*u = -35*u + 82. Find t such that -34*t**u - 15*t**3 - 17*t - 5/2 + 9/2*t**4 = 0.
-1, -1/3, 5
Let t(w) = -85*w**2 + 265*w - 180. Let j(c) = 7*c**2 - 22*c + 15. Let s = -63 + 38. Let x(h) = s*j(h) - 2*t(h). Factor x(v).
-5*(v - 3)*(v - 1)
Suppose 6794 = w - 4*t, -5*w + 23178 + 10744 = 4*t. Find l, given that 7182*l + 76*l**2 - w*l + 4*l**3 + l**3 + 324 - l**3 = 0.
-9, -1
Let t(n) = -27*n + 14. Let s be t(4). Let k = 98 + s. Factor 2*a**5 + 21 + 10*a**4 + 0*a + k*a + 18*a**3 - 21 + 14*a**2.
2*a*(a + 1)**3*(a + 2)
Let d(n) = n**3 + 262*n**2 - 37*n - 9690. Let a be d(-262). Solve -2/5*c**a + 72*c - 236/5*c**2 + 8*c**3 - 162/5 = 0.
1, 9
Suppose 4*s + q = -2, 0*s - 4*s = 2*q + 4. Let o be 301/129 + -2 + s + 1. Factor 2/3*j**3 + 0 - o*j**2 + 1/3*j**4 - 8/3*j.
j*(j - 2)*(j + 2)**2/3
Let b be 5/(55/24) - (-60)/(-330). Solve -19*i**3 + 57 + 15 + 13*i**4 - 3*i**4 + 12*i - i**5 - 82*i**b + 8*i**3 = 0.
-2, -1, 1, 6
Let h(p) be the first derivative of -5/4*p**2 + p + 1/2*p**3 - 1/10*p**5 + 104 + 1/8*p**4. Find y, given that h(y) = 0.
-2, 1
Let p(u) be the third derivative of u**8/1008 - 131*u**7/630 + 4223*u**6/360 + 4487*u**5/180 - 176*u**4/3 - 242*u**3 - 243*u**2 - 2. Let p(c) = 0. What is c?
-1, 1, 66
Let x(w) be the first derivative of -w**4/4 + 917*w**3 - 2522667*w**2/2 + 771095213*w - 5406. Find c such that x(c) = 0.
917
Let n(s) be the second derivative of 1/56*s**7 - 27/40*s**6 - 505/16*s**4 + 7 + 657/80*s**5 + 57*s**3 + s - 54*s**2. Factor n(d).
3*(d - 12)**2*(d - 1)**3/4
Factor -1244/11 + 626/11*n - 2/11*n**2.
-2*(n - 311)*(n - 2)/11
Let d be ((36/14)/(-3))/(17/(-119)). Suppose 0*o = 3*o - 6. Factor 2*g**o - d + 2*g**3 + 4*g + 20*g + 22 + 10*g**2.
2*(g + 2)**3
Let j be (1 - (7 + -3)) + 0. Let b be 4*((-294)/28)/(1*j). Let -9*p**3 - b - 196*p**4 + 181*p**4 - p - 10 + 66*p**2 + 37*p = 0. Calculate p.
-2, -1, 2/5, 2
Let v = 18605 - 18603. Factor 77/4*r**v - 49/4*r**3 + 1 - 8*r.
-(r - 1)*(7*r - 2)**2/4
Let g(l) be the third derivative of -l**8/84 - 24*l**7/35 - 329*l**6/30 + 1078*l**5/15 + 3430*l**4 + 38416*l**3/3 - 1625*l**2. Factor g(q).
-4*(q - 7)*(q + 1)*(q + 14)**3
Let n be 162/90*(3 + 142). Let y = n - 259. Solve 1/4*c**y + 0 + 1/2*c = 0 for c.
-2, 0
Let l = 347 + -92. Let b = l + -255. Factor 0*f + b + 4/3*f**2 + 1/3*f**4 - 4/3*f**3.
f**2*(f - 2)**2/3
Let x be 5/4*15*(-440)/(-4125). Suppose -21/4*z - 1/4*z**x - 5 = 0. Calculate z.
-20, -1
Let p = -3626036/13 + 278926. Factor p*n**2 + 2/13 + 4/13*n.
2*(n + 1)**2/13
Let w be 492/(-3567) - 244/(-928). Factor -13/2*n - 169/2 - w*n**2.
-(n + 26)**2/8
Factor -2/11*r**2 - 50/11*r + 48.
-2*(r - 8)*(r + 33)/11
Let l(f) be the first derivative of f**4/42 - 10*f**3/7 + 225*f**2/7 - 29*f - 39. Let z(s) be the first derivative of l(s). Determine h, given that z(h) = 0.
15
Suppose 0 = -2*z - 6*z + 400. Let a = z - 47. Factor 6*o**3 - 20*o**3 - 4*o**2 + 6*o**a + 4*o**3.
-4*o**2*(o + 1)
Let f(v) be the first derivative of v**3/5 + 39*v**2/2 - 612*v/5 + 1498. Factor f(t).
3*(t - 3)*(t + 68)/5
Factor -1984/13*v - 2/13*v**2 - 3960/13.
-2*(v + 2)*(v + 990)/13
Suppose 0 = -5*r - 4*j + 892, j = 3*r - 595 + 53. Suppose -h**4 - 60*h**3 - 4*h**4 - r*h**2 + 0*h**3 = 0. What is h?
-6, 0
Factor 219*d**2 - 70*d**4 - 2387*d + 67*d**4 + 2498*d + 105*d**3.
-3*d*(d - 37)*(d + 1)**2
Let c(j) be the second derivative of j**5/10 + 19*j**4/3 - 105*j**3 + 1847*j. Determine h so that c(h) = 0.
-45, 0, 7
Let x(v) be the second derivative of 3*v - 32/3*v**3 - 71/3*v**4 + 9/10*v**5 + 26 + 0*v**2. Factor x(k).
2*k*(k - 16)*(9*k + 2)
Let 3/2*k**4 + 13975/2*k + 3017/2*k**2 + 173/2*k**3 - 2500 = 0. Calculate k.
-25, -8, 1/3
Suppose 4*n + c - 22 = 2*c, 4*c = 2*n - 4. Let r(h) = -h**2 + 5*h + 8. Let f be r(n). Solve j**3 + j**2 - 7*j + f*j**2 + 10*j + 1 = 0 for j.
-1
Let d be (-105)/10*(-4)/6. Suppose 9*n - 5 = 13. Suppose -r**4 - 3*r + 8 - 12*r**3 - 8 - d*r**n + 7*r**3 = 0. Calculate r.
-3, -1, 0
Let w(f) be the third derivative of -f**8/224 + 3*f**7/28 - 33*f**6/40 + 29*f**5/10 - 9*f**4/2 - 9*f**2 - 9*f - 19. Factor w(p).
-3*p*(p - 9)*(p - 2)**3/2
Let a(p) be the third derivative of -p**5/40 + 577*p**4/8 + 3*p**2 - 77. Factor a(v).
-3*v*(v - 1154)/2
Let c(q) be the second derivative of -q**5/10 + 16*q**4/3 - 31*q**3/3 - 7092*q. Factor c(n).
-2*n*(n - 31)*(n - 1)
Let t = -7684 - -7684. Let f(g) be the third derivative of -15*g**2 + t*g + 0 - 1/15*g**5 - 8/3*g**3 - 2/3*g**4. Factor f(i).
-4*(i + 2)**2
Let g = -87 + 105. Suppose -n = -4*b + g, 3*b = 8*b - 2*n - 21. Suppose -8*j**3 - 4*j**2 - b*j**4 + j**4 - 4*j**2 + 2*j**4 = 0. Calculate j.
-2, 0
Suppose 0 = 3*z + 3*p + 54, -z = 3*z + 5*p + 77. Let w = 7 - z. Suppose 25*r**2 + 23*r**3 - w*r - 14*r**3 - 14*r**3 = 0. Calculate r.
0, 1, 4
Let m(s) be the second derivative of s**6/6 - s**5 - 55*s**4/12 + 55*s**3 - 180*s**2 + 9*s + 1. Determine w so that m(w) = 0.
-4, 2, 3
Let b(d) be the second derivative of 116/27*d**3 - 29 + 1/45*d**5 + 3*d + 0*d**2 - 59/27*d**4. Factor b(h).
4*h*(h - 58)*(h - 1)/9
Let k be 70/(-20)*5/35*-6. Factor k*n**2 + 4*n + 35*n + 9*n.
3*n*(n + 16)
Let s(c) be the second derivative of c**6/240 - c**5/10 + 79*c**4/96 - 13*c**3/4 + 27*c**2/4 - 565*c. Suppose s(w) = 0. Calculate w.
2, 3, 9
Let k be (-4)/18*(-49 - 1080/(-27)). Find v, given that 2/9*v**3 - 110/9*v - 52/9*v**k - 56/9 = 0.
-1, 28
Let n(d) = d**2 + 4*d - 1. Let u(c) = 3*c**2 + 64*c - 580. Let m(l) = 8*n(l) - 2*u(l). Determine b, given that m(b) = 0.
24
Let d = -607 + 616. Let o(y) = y**2 - 6*y - 2. Let v be o(7). Suppose 6*i**3 - 3*i**3 - v*i**2 - i**2 - d*i = 0. What is i?
-1, 0, 3
Factor 48 - 2/9*m**2 - 100/9*m.
-2*(m - 4)*(m + 54)/9
Let g be (19 + -16)/(6/68). Let f be (g/51)/(4/18). Factor -28*v**2 - 4*v**4 + 14*v**3 + 11*v + 6*v**f + v.
-4*v*(v - 3)*(v - 1)**2
Let i(v) be the second derivative of v**5/12 + 115*v**4/4 + 7935*v**3/2 - 107*v**2 + 143*v. Let f(b) be the first derivative of i(b). Factor f(z).
5*(z + 69)**2
Let a be -18*(-65)/2300 + (-2)/8. Let b = a + -1/115. Factor -3/2*q - 9/4 - b*q**2.
-(q + 3)**2/4
Suppose 741*m + 360 = 744*m. Solve -14 - 6 + m*g**2 + 12*g**5 + 38*g**4 - 10*g**4 - 136*g**3 - 4*g = 0.
-5, -1/3, 1
Let h be ((-55)/(-9))/((-86)/(-528) - 82/656). Factor -10/3*l**2 + h*l - 64.
-2*(l - 48)*(5*l - 2)/3
Suppose 5*t + 4*b - 62 = -0