8. Let a = 665/2628 - u. Factor 1/4 - 1/4*q**2 + 1/4*q**3 - a*q.
(q - 1)**2*(q + 1)/4
Let h be ((-40)/60)/((-4)/12). Factor 28*l - 64 - 315*l**2 - 8 + 319*l**h.
4*(l - 2)*(l + 9)
Let w(a) be the first derivative of 0*a + 3/2*a**5 + 45/4*a**2 + 35/2*a**3 - 2 - 85/8*a**4. Determine m so that w(m) = 0.
-1/3, 0, 3
Suppose 5*o - 729 = -4*o. Suppose -9*r + 8*r = -o. Factor 4*l**3 - 5*l**3 + 0*l + r - 63*l - 17*l**2.
-(l - 1)*(l + 9)**2
Let g(s) = -2*s**3 + 114*s**2 - 1728*s - 6140. Let y(u) = -2*u**3 + 112*u**2 - 1744*u - 6139. Let h(m) = -5*g(m) + 4*y(m). Factor h(j).
2*(j - 32)**2*(j + 3)
Let u = 82348387/508 - 162103. Let f = u - -16/127. Factor f*j**3 - j**2 + j + 0.
j*(j - 2)**2/4
Let x = -960 - -964. Let d(f) be the first derivative of f + 1/4*f**2 - 1/3*f**3 + 16 - 1/8*f**x. Find g, given that d(g) = 0.
-2, -1, 1
Suppose 257*x - 216*x + 241*x - 2816 = -422*x. Find l, given that -2/7*l**x + 4 + 2*l**3 + 6/7*l**2 - 46/7*l = 0.
-2, 1, 7
Suppose -5*q + 4*g = -134, -2*q - 2*g - 32 = -100. Suppose 4*h - q - 18 = 0. Suppose -15*y**2 + 17*y + 19*y - h*y - 12 + 3*y**3 = 0. Calculate y.
1, 2
Let a(x) be the first derivative of -40/3*x**2 - 55/12*x**4 - 320/3*x + 1/3*x**5 + 20*x**3 + 25. Factor a(m).
5*(m - 4)**3*(m + 1)/3
Find d, given that 6144/11*d - 192/11*d**2 - 65536/11 + 2/11*d**3 = 0.
32
Let n(a) be the first derivative of a**7/42 - a**6/6 + a**5/5 - 63*a + 45. Let c(m) be the first derivative of n(m). Factor c(d).
d**3*(d - 4)*(d - 1)
Let y(l) be the third derivative of -l**5/30 + 80*l**4 - 76800*l**3 + 39*l**2 + 16. Let y(k) = 0. Calculate k.
480
Solve 156/17*k + 454/17*k**2 + 2/17*k**5 - 150/17*k**4 - 304/17 - 158/17*k**3 = 0.
-2, -1, 1, 76
Let t be (-6 + 10)*11/4. Let x(f) be the second derivative of t*f + 0*f**3 + 0*f**2 + 1/25*f**5 + 0*f**4 + 0. Let x(b) = 0. Calculate b.
0
Suppose 0 = -674*y + 763*y - 267. Solve 0 + 0*x**2 - 1/8*x**y + 1/2*x = 0 for x.
-2, 0, 2
Determine s so that -3 - 12*s**2 + 770*s**3 - 4*s**5 + 3 - 798*s**3 - 20*s**4 = 0.
-3, -1, 0
What is i in 3/5*i**3 + 6 - 39/5*i + 6/5*i**2 = 0?
-5, 1, 2
Let p(c) be the third derivative of 1/140*c**5 - 1/168*c**4 - 2 + 0*c - 12*c**2 - 1/21*c**3. What is z in p(z) = 0?
-2/3, 1
Let g(r) be the second derivative of 0 + 1/54*r**4 - 20/9*r**2 + 89*r + 8/27*r**3. Find j, given that g(j) = 0.
-10, 2
Let h be -1*10/12*162/(-20). Factor 75/4 + 45/4*l - h*l**2 + 3/4*l**3.
3*(l - 5)**2*(l + 1)/4
Let v be (-6)/(-14)*(58 - 51). Factor 11*b**3 - 2*b**3 - 10*b**v + 9*b**3 - 4*b**4 - 4*b**2.
-4*b**2*(b - 1)**2
Let w(k) = 11 - 12*k**3 - 5*k**3 - 7*k**3 + 5*k**2 - 5*k + 25*k**3. Let s be w(-6). Factor -10 + s*y**3 + 20 - 35*y + 20.
5*(y - 2)*(y - 1)*(y + 3)
Let f be 236/944*6/33. Let c(k) be the third derivative of 21*k**2 + 0*k - f*k**3 + 1/660*k**5 - 1/132*k**4 + 0. Suppose c(l) = 0. Calculate l.
-1, 3
Let o(q) = 25*q**2 - 17*q + 12. Let w be (1 - 1/(-2))/(2/12). Let a(y) = 49*y**2 - 35*y + 22. Let c(s) = w*o(s) - 5*a(s). Solve c(t) = 0 for t.
1/10, 1
Factor -30*b**2 - 151*b - 29*b**2 - 1104 + 55*b**2 - 141*b.
-4*(b + 4)*(b + 69)
Let q be (90/28 + -3)*(23 + -19). Let o(c) be the first derivative of -2/35*c**5 + 4/7*c**2 + q*c - 2/7*c**4 + 24 - 4/21*c**3. Suppose o(n) = 0. What is n?
-3, -1, 1
Let h = -2235 + 484997/217. Let l = h + 60/217. Find y such that -2/21*y - 2/7*y**2 - l*y**3 - 2/21*y**4 + 0 = 0.
-1, 0
Determine d so that -150*d**5 + 243*d + 163487*d**2 + 57*d - 164437*d**2 + 235*d**4 + 40 + 525*d**3 = 0.
-2, -1/10, 2/3, 1, 2
Determine h so that -27/8*h**2 + 0 - 27/4*h + 3/4*h**3 + 3/8*h**4 = 0.
-3, -2, 0, 3
Let k be (380/104 + -4)/((-12)/16). Let a be (712/(-5785))/((8/(-10))/2). Factor a*z**3 + k*z**2 + 0*z - 2/13.
2*(z + 1)**2*(2*z - 1)/13
Suppose 2*v + 33*f = 37*f + 48, 60 = 3*v - 2*f. Let m be 3 - 58/v - 8/(-36). Factor -1/4*t**4 + m + t**2 - 1/4*t**3 + t.
-t*(t - 2)*(t + 1)*(t + 2)/4
Suppose 137*a - 1050*a + 2739 = 0. Factor 2/3 + 1/3*s**a + 4/3*s**2 + 5/3*s.
(s + 1)**2*(s + 2)/3
Let r(b) be the third derivative of -b**7/42 + 29*b**6/12 + 31*b**5 + 475*b**4/3 + 1280*b**3/3 - 3454*b**2. Factor r(z).
-5*(z - 64)*(z + 2)**3
Let u(i) be the first derivative of -3*i**4/4 - 641*i**3 - 307197*i**2/2 + 309123*i + 1316. Let u(g) = 0. Calculate g.
-321, 1
Let u = 699/1490 - 55/149. Let k(m) be the second derivative of -u*m**5 + 0 + 7/3*m**4 + 0*m**2 - 49/3*m**3 - 22*m. Let k(d) = 0. What is d?
0, 7
Let j(h) be the third derivative of h**7/630 + h**6/18 - 43*h**5/180 + 11*h**4/36 + 2*h**2 + 2013*h - 1. What is y in j(y) = 0?
-22, 0, 1
Let k = 2 - -1. Suppose 60*a + 22*a = 12*a + 44520. Let 2*r**2 + 633*r**k - a*r**3 - 5*r**2 = 0. What is r?
-1, 0
Find y such that -587 - 107*y - 258*y + 5*y**2 - 428 - 125 = 0.
-3, 76
Factor 211*r**2 + 207*r**2 + 38 + 174 - 420*r**2 + 210*r.
-2*(r - 106)*(r + 1)
Let u(d) be the third derivative of -5*d + 1/44*d**4 + 0 + 1/330*d**5 + 8*d**2 + 0*d**3. Let u(h) = 0. What is h?
-3, 0
Let r(k) be the first derivative of -5/2*k**2 - 5/3*k**3 + 54 + 0*k. Factor r(v).
-5*v*(v + 1)
Let w(l) be the third derivative of -3*l**8/4 + 304*l**7/21 - 1156*l**6/15 + 32*l**5/5 + 24*l**4 - 3*l**2 + 112. Find m such that w(m) = 0.
-2/9, 0, 2/7, 6
Let i(c) = 31*c**2 - 709*c + 6458. Let m(g) = -6*g**2 + 142*g - 1292. Suppose -31*k + 1 = 342. Let t(q) = k*m(q) - 2*i(q). Let t(v) = 0. What is v?
18
Let q(r) be the second derivative of 7*r**5/270 - r**4/36 - 4*r**3/27 - 14*r**2 - 188*r. Let p(j) be the first derivative of q(j). Factor p(n).
2*(n - 1)*(7*n + 4)/9
Let l(x) = x**4 + x**3 - x + 1. Let c = 104 - 109. Let o(f) = -15*f**5 - 55*f**4 - 55*f**3 + 30*f + 5. Let b(h) = c*l(h) - o(h). Solve b(t) = 0.
-1, 2/3
Suppose 5*j + 2*r = 0, r + 28857 - 28852 = 0. Factor 12/5*f - 3/5*f**j + 0.
-3*f*(f - 4)/5
Let 1255 + 772 - 65*i - 5*i**2 + 73 = 0. What is i?
-28, 15
Suppose 9*n + 12 = 5*n. Let h be 11/((1 - n)/4). Factor -2*a**3 + 6 - 8*a**3 + h*a - 6*a**2 - 3*a + 2*a**3.
-2*(a - 1)*(a + 1)*(4*a + 3)
Factor 1/5*r**3 - 1008/5*r**2 + 338688/5*r - 37933056/5.
(r - 336)**3/5
Factor 1/3*y**2 + 0 - 290/3*y.
y*(y - 290)/3
Let d(u) = -11*u**2 + 68*u + 1060. Let i(f) = -61*f**2 + 340*f + 5302. Let p(w) = -11*d(w) + 2*i(w). Factor p(j).
-(j + 24)*(j + 44)
Let w = -2636 + 2639. Let f = 34 - 32. Solve 2 - 4/3*s**f - 8/3*s**w + 8/3*s - 2/3*s**4 = 0 for s.
-3, -1, 1
Let u = -839 + 836. Let l be 4/u*(-16 + 29/2). Factor -1/5*n**3 + 0*n + 0 - 1/5*n**l.
-n**2*(n + 1)/5
Let y(j) be the first derivative of 4*j**5/5 + 52*j**4 + 1048*j**3 + 8856*j**2 + 30132*j + 1055. Determine r so that y(r) = 0.
-31, -9, -3
Let i(r) be the third derivative of -r**7/735 - r**6/35 - 41*r**5/210 - 3*r**4/14 + 24*r**3/7 - 112*r**2 - 2. Suppose i(d) = 0. What is d?
-6, -4, -3, 1
Let y(k) be the first derivative of 1/12*k**4 + 1089/2*k**2 - 30 - 11979*k - 11*k**3. Solve y(r) = 0 for r.
33
Factor 34*s + 2*s**2 + 73952 + 78*s - 73952.
2*s*(s + 56)
Suppose 4*h = 4*f + 44, -636*f + 632*f = 5*h - 1. Factor 1/5*x**4 + h + 46/5*x**2 - 12*x - 12/5*x**3.
(x - 5)**2*(x - 1)**2/5
Let b be 60/99*798/1330. Factor 0*y - 2/11*y**4 - b*y**3 + 0 + 6/11*y**2.
-2*y**2*(y - 1)*(y + 3)/11
Solve -1/7*c**3 - 82/7*c**2 - 157/7*c + 240/7 = 0.
-80, -3, 1
Solve -5/4*p**4 - 27/2*p**2 + 0 - 137/4*p**3 + 0*p = 0.
-27, -2/5, 0
Let i(g) be the first derivative of 0*g + 2 + 243/4*g**4 + 0*g**2 - 243*g**3 - 27/5*g**5 + 1/6*g**6. Factor i(a).
a**2*(a - 9)**3
Let r(o) be the second derivative of -2/3*o**3 - 13/84*o**4 - 2/7*o**2 + 5 - o. Factor r(b).
-(b + 2)*(13*b + 2)/7
Suppose 157*g = 156*g + 4. Let t be (-1 + g)*(-88)/(-66). What is s in 4/9*s**t + 22/9*s + 22/9*s**5 + 4/9 - 44/9*s**3 - 8/9*s**2 = 0?
-1, -2/11, 1
Let z(g) be the third derivative of g**5/120 - 153*g**4/16 - 115*g**3/3 - 3617*g**2. Let z(c) = 0. What is c?
-1, 460
Let g = 4629052685/712 - 6501480. Let a = -12/89 - g. Solve 9/8*n**3 + 1/2*n**5 - 1/8*n + 0 + 1/8*n**2 + a*n**4 = 0.
-1, 0, 1/4
Let j = -331049/75 - -4414. Let z(w) be the second derivative of 4/25*w**5 - j*w**6 + 0 - 11/15*w**4 - 12*w - 9/5*w**2 + 8/5*w**3. Let z(u) = 0. What is u?
1, 3
Let f = -6776657/2 - -3388329. Let i = -3 - -4. Factor -1/2*j**2 + i + f*j.
-(j - 2)*(j + 1)/2
Let p(w) be the second derivative of -30/17*w**2 + 6*w + 1/102*w**4 - 29/51*w**3 + 5. Let p(d) = 0. Calculate d.
-1, 30
Let v be (-28*45/1575)/(0 + -2). Factor