- 16. Let m(k) = 8*o(k) + 7*w(k). Solve m(t) = 0 for t.
-9, 0, 3/2
Factor -129554216/5 - 768108/5*w - 1/5*w**3 - 1518/5*w**2.
-(w + 506)**3/5
Suppose 3*i + 14 = 19*l - 17*l, 10 = 4*l + 3*i. Let p(a) be the first derivative of 23 - 4*a**2 - l*a - 4/3*a**3. Determine z so that p(z) = 0.
-1
Let v(s) be the first derivative of -s**6/720 - s**5/120 + s**4/6 - 25*s**3/3 - 2*s**2 - 75. Let c(m) be the third derivative of v(m). Factor c(p).
-(p - 2)*(p + 4)/2
Let d = -575 + 574. Let q be ((-141)/(-470))/(d/(-10)). Suppose 5/3*m + 0 + 5/6*m**q + 5/2*m**2 = 0. What is m?
-2, -1, 0
Let q be (0/((-25)/(-300)*(1 - -11)))/(-6). Solve 3/5*t - 3/5*t**2 + q = 0.
0, 1
Let h be (-4)/((-16)/1) + (-175190)/(-360). Let k = 488 - h. Factor -14/9*c - k*c**3 - 2*c**2 - 2/9*c**4 - 4/9.
-2*(c + 1)**3*(c + 2)/9
Let l(j) = -51*j**5 + 150*j**4 - 270*j**3 + 192*j**2 - 75*j - 18. Let z(o) = -o**5 - o**4 - o**3 - o - 2. Let u(g) = l(g) - 12*z(g). Factor u(v).
-3*(v - 1)**4*(13*v - 2)
Let b = 1/1576 - -785/4728. Let g(o) be the second derivative of 0 - 12*o - 1/20*o**5 + 0*o**4 + b*o**3 + 0*o**2. Factor g(v).
-v*(v - 1)*(v + 1)
Let b(f) be the second derivative of -28 + 1/48*f**4 - 23/12*f**3 - 2*f + 529/8*f**2. Suppose b(g) = 0. Calculate g.
23
Let m = 113541 - 113539. Let 0*s + 2*s**m + 0 - 1/3*s**3 = 0. What is s?
0, 6
Let b(u) = -u**5 - 5*u**4 - u**3 + 31*u**2 - 18*u + 12. Let g(l) = -l**4 - l**3 - l - 6. Let w(a) = -2*b(a) - 4*g(a). Factor w(x).
2*x*(x - 1)**2*(x + 4)*(x + 5)
Let x(p) = 9*p**2 + 1. Let w(m) = m**3 - m**2 + m + 1. Let s(r) = w(r) + x(r). Let b be s(0). Factor 2/5*n**4 + 0 - 2/5*n**b + 2/5*n**3 + 0*n - 2/5*n**5.
-2*n**2*(n - 1)**2*(n + 1)/5
Let r = 126 + -124. Factor -r + 3*w - 84*w**2 - w**3 + 84*w**2.
-(w - 1)**2*(w + 2)
Factor 19*s**2 - 10*s + 68 - s**4 + 69 + 75 - 212 - 8*s**3.
-s*(s - 1)**2*(s + 10)
Let k(n) = -n**3 + 8*n**2 - 4*n + 2. Let f be k(2). Suppose 4*a = -a - x + 12, -f = -4*a + 2*x. Solve -3*g**3 + g**3 - 2*g**3 + 2*g**a - 2*g**2 = 0.
-1, 0
Let p(q) be the second derivative of q**4/36 + q**3/9 - 323*q**2/6 - 3107*q. Factor p(t).
(t - 17)*(t + 19)/3
Let w = -2053265/6726 - -19380/59. Let l = 444/19 - w. Factor -1/3*n + 0 - l*n**2.
-n*(n + 2)/6
Let s(r) be the first derivative of r**6/90 - r**5/30 - 10*r**4/3 + 86*r**3/3 - 134. Let i(b) be the third derivative of s(b). Factor i(n).
4*(n - 5)*(n + 4)
Let n(p) = 9*p**3 + 7242*p**2 - 6. Let j(o) = -11*o**3 - 7241*o**2 + 8. Let w(b) = 3*j(b) + 4*n(b). Solve w(a) = 0 for a.
-2415, 0
Suppose -2 + 14 = -x. Let j be ((-224)/x)/(-8)*(-12)/21. Factor 2/3*y**5 + 0*y**4 + 2*y + 4/3*y**2 - 8/3*y**3 - j.
2*(y - 1)**3*(y + 1)*(y + 2)/3
Suppose -7*p = -22*p + 75. Suppose 0 = -6*v + 4*v + 10, 5*q + p = 4*v. Factor 0 - 2/3*x**q - 2/3*x**2 - 2/9*x - 2/9*x**4.
-2*x*(x + 1)**3/9
Factor -7*r**3 - 42*r - 61/2*r**2 - 18 - 1/2*r**4.
-(r + 1)**2*(r + 6)**2/2
Let r(x) be the first derivative of 1/4*x**3 + 1/32*x**4 - 1/80*x**5 + 0*x + x**2 - 36. Let u(t) be the second derivative of r(t). Let u(c) = 0. What is c?
-1, 2
Suppose 2 = -38*j + 39*j. Let f = 27 + -12. Find b such that -f*b + 18*b**j - 4 - 5 + 6 = 0.
-1/6, 1
Suppose -23*q + 17*q + 150 = 0. Suppose -9*r - q = -133. Find s, given that 16/3 - 8*s - r*s**2 - 10/3*s**3 = 0.
-2, 2/5
Let r = -81 - -62. Let d be r/(-2)*4 - 2. Factor 549*v**3 + d*v + 67*v**2 - 7*v**2 + 4*v**4 - 521*v**3.
4*v*(v + 1)*(v + 3)**2
Let n(b) be the first derivative of 1/27*b**6 + 65/9*b**2 - 1/9*b**4 + 101 - 92/27*b**3 - 50/9*b + 14/45*b**5. Factor n(o).
2*(o - 1)**3*(o + 5)**2/9
Solve -73*p**2 - 456*p + 71*p**2 + 782*p + 996 = 0.
-3, 166
Let n(d) be the first derivative of -2*d**5/11 - 169*d**4/22 - 8*d**3 - 2934. Factor n(q).
-2*q**2*(q + 33)*(5*q + 4)/11
Let b(y) be the first derivative of 0*y + 4/35*y**5 - 1/21*y**6 + 179 + 3/14*y**4 - 4/7*y**2 - 8/21*y**3. What is f in b(f) = 0?
-1, 0, 2
Let n be ((-885)/60 - -15)/(-2) - 58/(-432). Let x(g) be the second derivative of 3*g + 0 - 1/2*g**2 + 1/9*g**3 - n*g**4. Determine q so that x(q) = 0.
3
Let h be 15/35 - (-5)/(70/22). Suppose 5*b**3 - 139*b**2 + 73*b**h + 76*b**2 - 40*b = 0. Calculate b.
-4, 0, 2
Let o(y) be the second derivative of -y**6/40 - y**5/30 + y**4/24 + 20*y**2 + 45*y. Let a(r) be the first derivative of o(r). Factor a(x).
-x*(x + 1)*(3*x - 1)
Suppose 13*l = 6 + 59. Suppose 198 = -l*q + 14*q. Suppose -h**2 - 22 + q + h = 0. Calculate h.
0, 1
Let b = -10103 - -363713/36. Let p(j) be the second derivative of 0*j**2 + 1/126*j**7 + b*j**4 - 1/9*j**3 - 1/90*j**6 - 1/20*j**5 - 16*j + 0. Factor p(r).
r*(r - 1)**3*(r + 2)/3
Let p(y) be the second derivative of y**8/4200 - y**6/900 - y**3/6 + y**2 + 2*y + 19. Let q(s) be the second derivative of p(s). Factor q(f).
2*f**2*(f - 1)*(f + 1)/5
Let b(i) be the third derivative of i**7/1470 - i**6/56 + 43*i**5/420 + 11*i**4/8 - 70*i**3/3 + 2472*i**2. Suppose b(u) = 0. Calculate u.
-4, 5, 7
Let v(k) be the first derivative of -11*k**3/8 - 183*k**2/8 - 33*k/8 + 432. Solve v(r) = 0 for r.
-11, -1/11
Let v(a) be the first derivative of a**5/10 - a**3/3 + 85*a - 48. Let b(g) be the first derivative of v(g). Factor b(x).
2*x*(x - 1)*(x + 1)
Determine s so that -3/4*s**5 - 7/4*s**4 - 27 + 79/4*s**3 - 81*s + 27/4*s**2 = 0.
-6, -2, -1/3, 3
Let b be (-330)/(-1540) + (-679)/(-1470)*3. Factor 8/5 + b*k - 6/5*k**2.
-2*(k - 2)*(3*k + 2)/5
Let a(i) be the first derivative of -1/3*i**6 + 0*i + 0*i**2 - 6/5*i**5 - 2/3*i**3 - 3/2*i**4 - 32. Factor a(v).
-2*v**2*(v + 1)**3
Factor 3655/6*v**2 - 13/2*v**4 + 4624*v - 1/6*v**5 - 29478 - 97/2*v**3.
-(v - 6)**2*(v + 17)**3/6
Let b(x) be the second derivative of -1/2*x**3 + 1/60*x**4 + 222*x + 0 + 7/5*x**2. Factor b(l).
(l - 14)*(l - 1)/5
Let g(j) be the first derivative of j**6/6 + j**5/2 - 5*j**4/4 - 112*j + 231. Let t(k) be the first derivative of g(k). Factor t(x).
5*x**2*(x - 1)*(x + 3)
Factor -9/5*t**3 + 18/5 + 51/5*t - 12/5*t**2.
-3*(t - 2)*(t + 3)*(3*t + 1)/5
Suppose 0 = r - 3. Suppose -39 = -2*a - r*m, 5*a - 6*m = -2*m + 40. Find c, given that -2*c**4 + 4*c**5 + 7*c**2 - 34*c**5 - a*c**2 + 37*c**4 = 0.
-1/3, 0, 1/2, 1
Factor -8/5*n**3 + 48/5*n**2 + 4 - 4/5*n**4 - 56/5*n.
-4*(n - 1)**3*(n + 5)/5
Let a(q) be the third derivative of -7*q**5/12 - 5905*q**4/4 - 5060*q**3/3 + q**2 + 5*q + 266. Factor a(u).
-5*(u + 1012)*(7*u + 2)
Determine y, given that -112*y**3 - 239*y**3 - 1915*y**4 + 5*y**2 - 1500*y**5 - 74*y**3 - 15*y**2 = 0.
-1, -1/4, -2/75, 0
Let a be (0/(-6))/((-3 + 0)/3). Let u(s) be the second derivative of 1/40*s**6 - 1/16*s**5 + 3*s + 0 + a*s**3 + 0*s**2 + 1/24*s**4. Solve u(w) = 0 for w.
0, 2/3, 1
Let q = -3260081 - -1339894667/411. Let s = q + -2/137. Factor 23/3*u + 10/3 - u**3 + s*u**2.
-(u - 5)*(u + 1)*(3*u + 2)/3
Let k be 4 + 55/(-50) - (-85)/850. Factor -1/9*j**4 + 0*j - 16*j**2 - 8/3*j**k + 0.
-j**2*(j + 12)**2/9
Let j(c) be the third derivative of c**5/75 - 433*c**4/15 + 374978*c**3/15 - 1488*c**2. Determine s, given that j(s) = 0.
433
Let u(m) = 4*m**2 + 23*m - 11. Suppose -6*p = -0*p - 132. Let y(b) = -232*b**2 + 215*b**2 + 43 - 52*b - 41*b. Let h(j) = p*u(j) + 6*y(j). Factor h(k).
-2*(k + 4)*(7*k - 2)
Let c(w) = -7*w**4 - 55*w**3 + 106*w**2 + 172*w + 6. Let t(v) = -12*v**4 - 110*v**3 + 211*v**2 + 342*v + 11. Let p(s) = 11*c(s) - 6*t(s). Solve p(o) = 0.
-1, 0, 4, 8
Let s(z) be the first derivative of -z**6/150 + 3*z**5/50 + 4*z**4/15 - 73*z - 81. Let q(i) be the first derivative of s(i). Factor q(u).
-u**2*(u - 8)*(u + 2)/5
Let u be (-9)/(-5) + (-2)/(-10). Let a = u - -2. Determine z, given that -46*z**a - 6*z**2 + 12*z**5 + 7*z**4 + 38*z**3 - 5*z**3 = 0.
0, 1/4, 1, 2
Suppose -3*t - 5*b = -41, 17*b + 74 = 4*t + 14*b. Suppose 5*i + 17 - t = 0. Suppose 8/5 - 2*c**2 + 2/5*c**4 + 0*c**3 + i*c = 0. What is c?
-2, -1, 1, 2
Let q(c) = -13*c**2 - 2*c + 12. Let b(d) = 37*d**2 + 6*d - 34. Let w(v) = 6*b(v) + 17*q(v). Let n(f) = -258*f - 5808. Let x(r) = -n(r) + 3*w(r). Factor x(t).
3*(t + 44)**2
Suppose -109*a = -118*a + 135. Suppose 5*i + j = 15, a*j = -i + 9*j + 3. Suppose -1/2*m**4 + 0*m - m**i + 0*m**2 + 0 = 0. What is m?
-2, 0
Suppose -1 = 3*d - 10. Suppose 12*n + 24 = 16*n. Solve 4*b - 12*b**5 - n*b**4 + 6*b**3 + 20*b**2 - 14*b**4 - b**3 + d*b**5 = 0 for b.
-2, -1, -2/9, 0, 1
Let a(w) = -8*w**5 - 36*w**4 - 220*w**3 - 396*w**2 - 204*w + 11. L