 33. Let f be g(-3). Factor -10*m**2 + f*m + 10 - 3*m**3 - 2*m**3 - 85*m.
-5*(m - 1)*(m + 1)*(m + 2)
Let l(a) be the first derivative of 63654*a**5/5 - 11227*a**4/2 + 418*a**3/3 - a**2 + 6140. Suppose l(y) = 0. What is y?
0, 1/103, 1/3
Let q(m) be the first derivative of -m**3/6 - 137*m**2/8 - 17*m - 820. Let q(p) = 0. Calculate p.
-68, -1/2
Let y(d) = -2*d**3 + d**2 + 17*d + 20. Let p be y(-5). Factor -p*i + 18*i - 12*i**4 - 272 + 36*i**3 + 96*i**2 - 3*i**5 + 272.
-3*i*(i - 2)**2*(i + 4)**2
Let h(u) be the first derivative of -u**5/5 + 80*u**4 + 643*u**3/3 + 161*u**2 + 5381. Factor h(w).
-w*(w - 322)*(w + 1)**2
Let c(g) be the third derivative of g**7/1365 + 7*g**6/260 + g**5/10 + 19*g**4/156 + 9*g**2 + 13*g + 3. Factor c(y).
2*y*(y + 1)**2*(y + 19)/13
Let n(g) be the second derivative of g**4/60 - 3*g**3/10 - 11*g**2/5 - 31*g - 15. Factor n(p).
(p - 11)*(p + 2)/5
Let h(d) = -3*d**2 + 37*d - 10. Let i be h(12). Suppose 0*y**4 - 71*y**i - 31*y**3 + 31*y**2 - 5*y**4 + y**3 = 0. Calculate y.
-4, -2, 0
Let g be 56/(-10)*(0 + -115). Suppose 25*n - 29*n + g = 0. Factor 155*k - 3 + 3 - n*k - 11*k**2.
-k*(11*k + 6)
Suppose -2*l - 5*g - 4009 = -0*g, -2*g + 10 = 0. Let s = l - -10101/5. Solve -56/5*b + 348/5*b**2 + 206/5*b**3 - 182/5*b**4 - s = 0.
-1, -2/13, 2/7, 2
Let s(g) be the third derivative of g**8/672 + 17*g**7/420 + 23*g**6/60 + 4*g**5/3 - 25*g**2 - 114. Solve s(x) = 0.
-8, -5, -4, 0
Let j(s) be the third derivative of s**7/70 + s**6/20 - s**5 + 3*s**4 + 14*s**2 + 10*s. Factor j(m).
3*m*(m - 2)**2*(m + 6)
Factor -297 - 1/3*j**3 + 39*j + 7/3*j**2.
-(j - 9)**2*(j + 11)/3
Let v be 1/(-10) - 131/(-1310). Let r(i) be the first derivative of v*i + i**3 - 1/2*i**2 - 15. Factor r(z).
z*(3*z - 1)
Let b(n) = -2*n + 36. Let l be b(20). Let t be (45/225)/((-3)/(-65)) + l. Factor -2/3*o**2 + t*o**5 + 1/3*o**4 - 2/3*o**3 + 1/3 + 1/3*o.
(o - 1)**2*(o + 1)**3/3
Let p = -9216289/7 + 1324773. Determine x so that 527280/7*x**3 + 2808000/7*x - p*x**4 - 1620000/7 - 1825200/7*x**2 = 0.
30/13
Let k be (-325)/52 + 6 - 74/(-8). Let w(n) be the third derivative of 0*n**6 + 0 + 0*n**5 + 0*n**4 + 0*n**3 - 1/42*n**7 + k*n**2 + 0*n. Solve w(r) = 0 for r.
0
Suppose 5*q + f = -1, 5 = -3*q - 3*f + 2. Let i = 4796 + -33566/7. Solve -8/7 + i*p**2 - 2/7*p**3 + q*p = 0.
-1, 2
Let w(d) = 70*d**2 + 228*d - 117. Let j(x) = 11*x**2 + x + 1. Let t(u) = 35*j(u) - 5*w(u). Find l, given that t(l) = 0.
4/7, 31
Let w(v) be the third derivative of -v**5/100 - 7*v**4/8 + 75*v**3 + 4*v**2 - v + 123. Suppose w(c) = 0. What is c?
-50, 15
Suppose 2*r = -348 - 352. Let z = r - -354. Solve -8/5 - 44/5*d - 12/5*d**z - 76/5*d**2 - 52/5*d**3 = 0.
-2, -1, -1/3
Let l be (12/(-18))/((-4)/18) - 0. Suppose -2*s = s - 2*v - 6, 0 = l*s - v - 6. Find z, given that -3 + 3*z**2 + 6 - 1 - 5*z**s = 0.
-1, 1
Let l(r) be the first derivative of 2*r**5/15 - 92*r**4/3 + 730*r**3/9 - 182*r**2/3 - 1983. Factor l(z).
2*z*(z - 182)*(z - 1)**2/3
Let o(y) be the third derivative of -y**8/168 + 8*y**7/105 + y**6/3 + y**5/15 - 19*y**4/12 - 10*y**3/3 - 4663*y**2. Suppose o(g) = 0. What is g?
-1, 1, 10
Factor 18*w + 11*w**5 - 2*w**5 - 6*w**5 + 4*w**4 - 9*w**3 - 21*w**2 + 7*w**4 - 2*w**4.
3*w*(w - 1)**2*(w + 2)*(w + 3)
Factor 45*h**4 + 29*h**2 + 27*h**3 + 72*h - h**5 - 38*h**4 - 62*h.
-h*(h - 10)*(h + 1)**3
Suppose 0 = -8*y + 1 + 15. Let o be (-5)/(-9 + 4) + y. Factor 5*w**3 + 3*w**4 - 2*w**o + 0*w**4.
3*w**3*(w + 1)
Let u(y) be the second derivative of y**5/20 + 37*y**4/12 - 83*y**3/2 + 387*y**2/2 - 722*y. Factor u(v).
(v - 3)**2*(v + 43)
Let b(z) = 49*z**4 + 272*z**3 + 15*z**2 - 283*z - 42. Let h(u) = 2*u**4 + 2*u**2 - u - 2. Let m(q) = -2*b(q) + 22*h(q). Let m(f) = 0. What is f?
-10, -1, -2/27, 1
Let s(f) be the second derivative of -f**5/4 - 335*f**4/6 - 10150*f**3/3 + 73500*f**2 - 14*f - 608. Factor s(n).
-5*(n - 6)*(n + 70)**2
Suppose -2*k = 2*h + 2*k - 28, 0 = 3*k - 3. Factor 7*g + g - 15*g**3 + h*g**3 - 5*g.
-3*g*(g - 1)*(g + 1)
Let y(z) be the second derivative of -215*z**4/24 - 5*z**3/2 - 2*z + 1334. Let y(n) = 0. What is n?
-6/43, 0
Factor 0 + 25/4*g**2 - 135*g.
5*g*(5*g - 108)/4
Let w(m) be the first derivative of -3*m**4/34 + 26*m**3/51 - 16*m**2/17 + 8*m/17 - 749. Factor w(s).
-2*(s - 2)**2*(3*s - 1)/17
Find t such that -2388/7*t + 0 + 4/7*t**2 = 0.
0, 597
Let s(q) be the third derivative of -3*q**5/20 - 65*q**4/8 + 11*q**3 - 21*q**2 + 9*q. Find z, given that s(z) = 0.
-22, 1/3
Let u(x) be the first derivative of x**5/15 + x**4 - 31*x**3/9 - 7*x**2 - 10. Let u(j) = 0. What is j?
-14, -1, 0, 3
Suppose 1692*z - 1044*z**2 + 1772*z - 3384*z - 176*z**3 + 48 = 0. What is z?
-6, -2/11, 1/4
Let 2/3*g**2 - 32/15*g - 6 = 0. What is g?
-9/5, 5
Suppose -5*a + 8 = -2. Suppose a*s = -2*s + 8. Let -3*r**2 - 5 - r**s + 5 = 0. Calculate r.
0
Suppose -2*k - 14 = -2*m, 603 = 4*m + k + 595. Determine f, given that 3/4*f**3 + 3 - m*f - 3/4*f**2 = 0.
-2, 1, 2
Let y(x) = -x**3 - 15*x**2 + 18*x + 37. Let g be y(-16). Solve -85*h - 75*h**3 + 1345*h**2 - 2416*h**2 + 1226*h**2 + g = 0 for h.
1/15, 1
Let o(x) = 70379*x + 633414. Let r be o(-9). Solve -1120*q**2 + 1280*q + 5/4*q**5 + 0 + 165*q**r + 35*q**4 = 0.
-16, 0, 2
Factor 404*j**3 + 407636*j - 1018081/5 - 1022118/5*j**2 - 1/5*j**4.
-(j - 1009)**2*(j - 1)**2/5
Factor 0*h**5 - 4088*h**3 + 4*h**5 - 4108*h - 3464*h**4 - 3963*h**4 + 6152*h**2 - 4033*h**4 + 12472*h**4 + 1028.
4*(h - 1)**4*(h + 257)
Let h(m) be the second derivative of -7*m**2 + m - 63 + 1/6*m**4 - 2*m**3. Factor h(s).
2*(s - 7)*(s + 1)
Let k(c) = -c - 5. Suppose 3*m - 2*m = -8. Let y be k(m). Factor y*b**2 + 2*b**3 - 3*b**3 + 2*b + 2*b**3 + 1 + b.
(b + 1)**3
Factor -440*p - 9036*p - 7521*p**2 + 571 + 25*p**3 + 1325 + 19351*p**2.
(p + 474)*(5*p - 2)**2
Find a such that 8/7*a**2 + 16610/7*a + 4152/7 = 0.
-2076, -1/4
Let r(x) be the third derivative of x**5/270 - 679*x**4/36 + 2036*x**3/27 - 11*x**2 + 32*x + 3. Factor r(i).
2*(i - 2036)*(i - 1)/9
Let i = 784 - 776. Suppose i = -2*l + 12. Let -3/2*f - 1/2*f**3 + 1/2 + 3/2*f**l = 0. What is f?
1
Suppose -5*r = -25, -4*o - 2*r + 1245 = -r. Let i = 310 - o. Factor 0 - 2/15*q**2 + i*q + 2/15*q**3.
2*q**2*(q - 1)/15
Let -248/3 - 2/15*l**2 + 208/5*l = 0. Calculate l.
2, 310
Find s, given that -8/15*s**3 - 62/3*s**2 + 76/15 - 226/15*s = 0.
-38, -1, 1/4
Let o be (14/8)/((-16)/(-128)). Factor -6*m + 11*m + m**2 + o*m + 49 - 31.
(m + 1)*(m + 18)
Let c(g) = 388*g**2 + 22200*g + 1376. Let o(y) = -1035*y**2 - 59200*y - 3668. Let i(q) = -21*c(q) - 8*o(q). Factor i(k).
4*(k + 56)*(33*k + 2)
Let g = 12/2033 - -329262/14231. Let q = g - 796/35. Factor q*h**2 + 0*h - 8/5.
2*(h - 2)*(h + 2)/5
Let k(x) be the first derivative of -4*x**5/5 + 12*x**4 + 188*x**3 - 304*x**2 + 1241. Let k(y) = 0. What is y?
-8, 0, 1, 19
Let v(u) be the second derivative of 5*u**7/168 + 3*u**6/8 + 11*u**5/16 - 145*u**4/48 - 25*u**3/2 - 35*u**2/2 - 5*u + 208. Determine a, given that v(a) = 0.
-7, -2, -1, 2
Let o(x) = 3*x**2 - 546*x - 4. Let c(j) = 6*j**2 - 1092*j - 9. Let y(h) = -4*c(h) + 9*o(h). Determine f, given that y(f) = 0.
0, 182
Let r(f) be the second derivative of -2/15*f**6 - 8*f**2 - 8*f**3 - 6/5*f**5 - 6 - 12*f - 13/3*f**4. Factor r(u).
-4*(u + 1)**2*(u + 2)**2
Let k(q) be the second derivative of 33/40*q**5 - 253/4*q**3 + 1/80*q**6 + 2 + q + 219/16*q**4 + 1587/16*q**2. Factor k(p).
3*(p - 1)**2*(p + 23)**2/8
Let j = -275 - -275. Suppose j = -35*b + 6*b + 58. Determine m so that 3/2*m**3 + m**b + 1 - 7/2*m = 0.
-2, 1/3, 1
Factor 18*t + 391 + 14*t**3 - 788*t**2 - 668*t - 1604*t + 499 - 182.
2*(t - 59)*(t + 3)*(7*t - 2)
Let h(o) = 4*o**2 + 6*o. Let x(n) = -3*n**2 - 5*n. Suppose 0 = -2*a - 3*a + 50. Suppose 5 + a = 3*d. Let t(w) = d*h(w) + 6*x(w). Find z, given that t(z) = 0.
0
Let x(s) = 67*s + 1343. Let v be x(-20). Let f(o) be the first derivative of -6 - 72/7*o - 12/7*o**2 - 2/21*o**v. Factor f(a).
-2*(a + 6)**2/7
Let q(l) be the second derivative of -l**7/14 - 3*l**6/10 + 33*l**5/10 + 3*l**4 - 36*l**3 + 1416*l. Find j, given that q(j) = 0.
-6, -2, 0, 2, 3
Let r(n) be the second derivative of 0*n**2 - 323/20*n**4 - 47*n - 21/20*n**5 + 3 - 289/10*n**3 - 1/50*n**6. Determine t, given that r(t) = 0.
-17, -1, 0
Let n(f) be the first derivative of 10/3*f - 2/27*f**3 + 14/9*f**2 - 66. Factor n(h).
-2*(h - 15)*