16). Find m, given that b - 2/7*m**3 - 2*m**2 - 24/7*m = 0.
-4, -3, 0
Let o(b) be the first derivative of 0*b + 180 + 45*b**2 + 5/4*b**4 - 15*b**3. Find x, given that o(x) = 0.
0, 3, 6
Let g be (-225)/105 + (-5742)/(-1386). Factor -6/7*s**g - 234/7 - 240/7*s.
-6*(s + 1)*(s + 39)/7
Let r(f) be the first derivative of -4*f**3/21 - 942*f**2/7 - 1880*f/7 - 2777. Suppose r(c) = 0. Calculate c.
-470, -1
Let i = 66 - 60. Factor -3042 + 15*t**2 - 41*t - 11*t**2 - i*t**2 - 115*t.
-2*(t + 39)**2
Let h(c) be the second derivative of -5*c**7/42 - 11*c**6/6 - 43*c**5/4 - 365*c**4/12 - 140*c**3/3 - 40*c**2 - 2*c - 28. Factor h(m).
-5*(m + 1)**3*(m + 4)**2
Factor 106010*w**2 + 440*w - 105782*w**2 + 6*w**3 - 2*w**3.
4*w*(w + 2)*(w + 55)
Let i = -81/67 - -877/670. Let t(y) be the first derivative of -11 - 1/5*y**2 - 2/5*y + 2/15*y**3 + i*y**4. Determine s, given that t(s) = 0.
-1, 1
Let h(s) be the first derivative of s**4/2 + 64*s**3/3 + 135*s**2 - 1525. What is a in h(a) = 0?
-27, -5, 0
Suppose 2 = 112*i - 111*i. Find p such that -2*p**i + 20*p + 4*p + 5*p**2 + 48 = 0.
-4
Let s(p) be the first derivative of p**3/18 + 71*p**2/4 + 106*p/3 + 1580. Let s(g) = 0. What is g?
-212, -1
Let g = -16 + 20. Suppose -333 = -5*z - 4*v, -g*z - v + 270 = v. Factor -36*n**5 + z*n**5 - 29*n**5 - 4*n**3.
4*n**3*(n - 1)*(n + 1)
Let p(g) be the second derivative of -36*g**2 - 1/5*g**5 + 0 - 63*g - 20/3*g**4 - 74/3*g**3. Suppose p(s) = 0. Calculate s.
-18, -1
Solve -55/2*l + 135 + 5/6*l**2 = 0.
6, 27
Let n(o) be the second derivative of -o**5/70 + 2*o**4/21 - 4*o**3/21 + 2*o + 265. Factor n(t).
-2*t*(t - 2)**2/7
Let s(u) be the second derivative of 0*u**2 + 2/45*u**6 - 4/9*u**4 - 1/126*u**7 + 8/9*u**3 + 61*u + 0 + 0*u**5. Suppose s(w) = 0. What is w?
-2, 0, 2
Let t(r) be the second derivative of 7/4*r**4 - 1/20*r**5 + 0 + 0*r**2 + 267*r + 0*r**3. Factor t(q).
-q**2*(q - 21)
Let p be (36 - 31)*(-18)/(-15). Suppose 171*c - 168*c = p. Factor -3/4*n**c + 3/2*n - 3/4.
-3*(n - 1)**2/4
Factor -3/5*b**4 - 72/5*b - 102/5*b**2 - 33/5*b**3 + 0.
-3*b*(b + 1)*(b + 4)*(b + 6)/5
Let f(x) be the second derivative of x**5/60 + x**4/2 + 9*x**3/2 + 18*x**2 - 90*x. Factor f(z).
(z + 3)**2*(z + 12)/3
Let j(y) be the third derivative of -y**8/168 - 38*y**7/105 + 38*y**6/5 - 113*y**5/3 + 1049*y**4/12 - 112*y**3 - y**2 + 67*y - 6. Factor j(s).
-2*(s - 7)*(s - 1)**3*(s + 48)
Let g be (2/7)/((-2)/(-98)). Factor -231*t - 226*t + 3*t**2 - t**2 + 441*t + g.
2*(t - 7)*(t - 1)
Let a be ((3 + 0 - 6) + 1)*-7. Suppose 3*g + g - q = 14, -5*g + 3*q + a = 0. Factor 3*p + 147*p**3 + g - 441*p**2 + 32 - 15*p.
3*(p - 3)*(7*p - 2)*(7*p + 2)
Let a(l) be the second derivative of 0 - 67*l - 1/27*l**4 + 136/27*l**3 - 2312/9*l**2. Find g, given that a(g) = 0.
34
Let t(k) be the third derivative of -k**6/60 + k**4/8 + k**3/2 - 376*k**2. Let d be t(-1). Factor -18/11*z**3 - 6/11*z**4 + 0*z + 0 - 12/11*z**d.
-6*z**2*(z + 1)*(z + 2)/11
Let s(i) be the first derivative of i**3/21 - 69*i**2/14 - 292*i/7 + 298. Solve s(b) = 0 for b.
-4, 73
Let h(q) be the third derivative of -q**7/1260 + 2*q**6/45 + 5*q**4/8 - q**3/6 - 56*q**2. Let z(d) be the second derivative of h(d). Factor z(p).
-2*p*(p - 16)
Determine m so that 59628/5*m**3 - 122694/5 + 3/5*m**5 + 123546/5*m**2 - 852/5*m**4 - 59631/5*m = 0.
-2, -1, 1, 143
Determine q so that 69*q**2 - 69*q**2 + 3 - 705*q**4 - 3 + 5*q**5 = 0.
0, 141
Suppose 117 = 4*c - 3*r - 2777, -4*c + 2906 = 3*r. Let -27 + 2*h + 724*h**2 + 3*h + h - c*h**2 + 6*h = 0. Calculate h.
3, 9
Let s be (12/9 + -2)/((-10)/165). Suppose -2*w + 0*w + 5*g = -11, -g = -4*w + 13. Factor -30*u + 12*u + s*u + w*u**2 + 4*u.
3*u*(u - 1)
Factor 39*a**2 - 14*a**2 + 163*a - 118*a - 8*a**2 - 18*a**2.
-a*(a - 45)
Let x be -6 + 10/(-3 - (6 - 10)). Solve 10*a**2 - 24*a**4 + x*a + 7*a**2 - 4*a - 31*a**2 - 50*a**3 = 0.
-7/4, -1/3, 0
Let d(k) = -k**2 + 14*k + 255. Let q be d(24). Let m(s) be the first derivative of 1/12*s**3 + 1/4*s**2 + 1/4*s + q. Determine b so that m(b) = 0.
-1
Let d = 433 - 27278/63. Let z(w) be the first derivative of 0*w**3 + 0*w**5 + d*w**6 - 1/21*w**4 - 18 + 1/21*w**2 + 0*w. Factor z(u).
2*u*(u - 1)**2*(u + 1)**2/21
Let l(v) = -12*v**2 + 1185*v - 28821. Let r(g) = 3*g**2 - 296*g + 7205. Let a(w) = w**2 + 4*w - 34. Let c be a(4). Let q(u) = c*l(u) - 9*r(u). Factor q(k).
-3*(k - 49)**2
Let l(x) = -5*x**2 - 11*x + 20. Let k(h) = 2*h**2 + h + 1. Let n(c) = k(c) + l(c). Let b(y) = y**2 + 3*y - 7. Let v(w) = -8*b(w) - 3*n(w). Factor v(m).
(m - 1)*(m + 7)
Let n = -44125/176 + 4023/16. Factor 6/11*c**2 - 2/11*c**3 + n*c + 0.
-2*c*(c - 4)*(c + 1)/11
Let w(k) = -181*k**2 - 177*k + 7. Let a(c) = 904*c**2 + 884*c - 36. Let f(p) = -3*a(p) - 16*w(p). Factor f(l).
4*(l + 1)*(46*l - 1)
Let b(v) be the second derivative of v**9/19656 - v**7/5460 - 2*v**3/3 + v**2/2 + 78*v. Let t(c) be the second derivative of b(c). Factor t(h).
2*h**3*(h - 1)*(h + 1)/13
Let l(o) be the second derivative of 5329*o**4/9 - 584*o**3/3 + 24*o**2 + 7*o + 1. Factor l(n).
4*(73*n - 6)**2/3
Suppose -r + 2*q - 198 = 4*q, 0 = -2*r - 3*q - 394. Let n = r - -384. Factor -6*w**2 - w**4 - 11*w**4 + 175*w**3 - n*w**3 - 3*w**5.
-3*w**2*(w + 1)**2*(w + 2)
Let c(k) be the first derivative of k**5 + 35*k**4/4 - 70*k**3/3 - 120*k**2 - 178. Factor c(n).
5*n*(n - 3)*(n + 2)*(n + 8)
Let v(i) be the first derivative of i**4/14 - 370*i**3/7 + 77283*i**2/7 - 153458*i/7 - 1625. What is p in v(p) = 0?
1, 277
Factor 45/4 + 7/2*i + 1/4*i**2.
(i + 5)*(i + 9)/4
Suppose 9*u + 6263 = 881. Let i = 266 - u. Let -324*j + 72*j**2 + 246*j - 4*j**3 - 354*j + i = 0. Calculate j.
6
Let h = 144417 - 144413. Factor -17/4*j**2 - 23/8*j - 3/4 - 3*j**3 - j**h - 1/8*j**5.
-(j + 1)**3*(j + 2)*(j + 3)/8
What is f in -2/9*f**5 + 0 - 32/9*f - 20/9*f**4 - 22/3*f**3 - 80/9*f**2 = 0?
-4, -1, 0
Let a(t) be the first derivative of -t**4 - 64*t**3 - 834*t**2 - 1480*t - 4283. Factor a(b).
-4*(b + 1)*(b + 10)*(b + 37)
Suppose -960 + 26*d + 47*d**2 - 26*d**2 - 10*d**2 - 286*d - 16*d**2 = 0. Calculate d.
-48, -4
Factor -430*i**2 + 5*i**3 - 7025*i - 3075*i**2 + 198395 - 403566 + 201656.
5*(i - 703)*(i + 1)**2
Suppose 37 - 35 = 3*l + 2*i, -l + 5*i + 12 = 0. Suppose -b + 3*b - 5*c = 0, 2*c + 12 = 2*b. Solve 5*t + 5/2 - b*t**l + 15/2*t**4 - 5*t**3 = 0.
-1, -1/3, 1
Determine o so that 1132*o**3 - 1134*o - 390439 + 2455*o**2 + 90*o**4 + 101*o**2 + 387793 + 2*o**5 = 0.
-21, -3, -1, 1
Let m(o) be the first derivative of -162*o**5/5 + 855*o**4/2 - 4076*o**3/3 - 1036*o**2 - 240*o - 305. Suppose m(u) = 0. What is u?
-2/9, 5, 6
Let n(v) be the first derivative of v**3 - 14*v**2 - 55*v + 1015. Suppose n(a) = 0. What is a?
-5/3, 11
Let f be 1640/2870*(-21)/(-28). What is u in 15/7*u - 15/7*u**3 + 0 - 3/7*u**4 + f*u**2 = 0?
-5, -1, 0, 1
Let t(l) = -19*l**2 + 47*l + 33. Let g(q) = -17*q + 7*q**2 - 11 + 3*q + q - 3*q. Let b(w) = -11*g(w) - 4*t(w). Factor b(n).
-(n + 1)*(n + 11)
Factor 638 + 490 + 289*x - 6423*x**2 + 75*x + 6419*x**2.
-4*(x - 94)*(x + 3)
Let u(i) be the first derivative of 4/3*i**3 + 0*i**2 - 1/270*i**5 + 0*i + 0*i**4 - 1/1620*i**6 + 7. Let n(b) be the third derivative of u(b). Factor n(j).
-2*j*(j + 2)/9
Let x be (-270)/32*(-26)/65. Factor x*l**2 + 39/2 - 3/8*l**3 + 18*l.
-3*(l - 13)*(l + 2)**2/8
Suppose y + 0*y + 221 = 5*v, 2*v + 1213 = -5*y. Let f = 244 + y. What is a in 1/5*a**f + 9/5*a + 6/5*a**2 + 4/5 = 0?
-4, -1
Suppose 0 = -4*g + 16, 0 = 2*k + 5*g - 3*g - 14. Let 3*q**k + 311*q**2 + 34 - 273*q**2 - q**3 - 4*q**3 - 70*q = 0. What is q?
1, 17
Suppose -2*b + 4*y + 26 = 0, 2*b - y = 3 + 8. Let h = 1262 - 1258. Determine z, given that -z**5 - b*z + z - 30*z**4 - 9*z**3 - 7*z**2 + 25*z**h = 0.
-2, -1, 0
Suppose 3/4*g**5 - 9/2*g**3 - 51/2*g**2 + 159/4*g + 21/4*g**4 - 63/4 = 0. What is g?
-7, -3, 1
Let y(w) be the second derivative of -w**6/60 + w**5/8 - w**4/6 - 27*w + 1. Factor y(a).
-a**2*(a - 4)*(a - 1)/2
Suppose 84*g - 2960 = 94*g. Let y = -294 - g. Solve y*z**3 - 5/2*z + 1/2*z**5 - z**2 - 1 + 2*z**4 = 0 for z.
-2, -1, 1
Factor 1325*o - 9426*o**2 + 9430*o**2 + 1 - 781*o - 1.
4*o*(o + 136)
Suppose -53*c - 186910 = -187069. Determine v, given that -8*v**2 + 0 + 14/5*v**5 - 12*v**4 + 24/5*v - 138/5*v**c = 0.
-1, 0, 2/7, 6
Let l(t) be the third derivative of -t**5/240 - 67*t**4/16 + 403*t**3/24 - 2508*