 - 86. Let x be (-54)/24 - 70/40. Let f(z) = -9*z**2 - 393*z - 684. Let w(c) = x*f(c) + 33*i(c). Suppose w(g) = 0. What is g?
-2, 17
Factor 10*f**4 + 25*f**3 - 506*f - 20*f**2 - f**5 + 3*f**5 - 129 + 426*f - f**5 + 193.
(f - 1)**2*(f + 4)**3
Let x(i) be the third derivative of i**6/1260 - i**5/420 - 8*i**3/3 - 9*i**2 + 1. Let s(u) be the first derivative of x(u). Suppose s(r) = 0. Calculate r.
0, 1
Let p(l) be the third derivative of 5*l**8/336 - l**7/42 - 3*l**6/8 - 11*l**5/12 - 5*l**4/6 - 2712*l**2. Solve p(z) = 0 for z.
-1, 0, 4
Let j be ((-7)/(-3))/((-1716)/(-384384)). Factor -1/6*b**2 - j - 56/3*b.
-(b + 56)**2/6
Let q(i) be the second derivative of -2*i**6/15 + 19*i**5/5 - 122*i**4/3 + 592*i**3/3 - 384*i**2 - 151*i + 11. Suppose q(v) = 0. What is v?
1, 4, 6, 8
Suppose 4*q = 100 - 92, 4*z = 4*q + 8. Solve -4*n + 2/11*n**5 - 16/11 + 10/11*n**z + 2/11*n**3 - 34/11*n**2 = 0.
-4, -1, 2
Let s be (-50)/15 + (5 - -3*(-4)/8). Let v = 2/19 - -13/57. Factor v + s*g**2 + 1/2*g.
(g + 1)*(g + 2)/6
Let u = -1335 - -1335. Let d(f) be the first derivative of -1/3*f**3 + 0*f + 13/28*f**4 + u*f**2 - 8 - 1/42*f**6 - 1/7*f**5. Let d(c) = 0. What is c?
-7, 0, 1
Suppose -325/2*u + 80 + 5/2*u**5 + 5*u**2 - 85*u**4 + 160*u**3 = 0. What is u?
-1, 1, 32
Find d, given that 0 - 3/2*d + 3*d**2 - 3/2*d**3 = 0.
0, 1
Let p(b) be the third derivative of 3*b**7/50 - 31*b**6/50 + 177*b**5/100 + 9*b**4/20 - 32*b**2 + 3. Suppose p(c) = 0. What is c?
-2/21, 0, 3
Let m(q) be the first derivative of 364/3*q**3 - q**4 + 173 - 8464*q - 4048*q**2. Solve m(n) = 0 for n.
-1, 46
Determine r so that 311750*r**2 + 1091095*r + 223554*r**3 + 3*r**5 + 117526*r**2 + 1632*r**4 + 881292 - 2626852*r = 0.
-271, -4, 1
Let m be (-5254)/(-185) + (-4)/10. Suppose m*l - 57 = 9*l. Suppose 1/3*d**5 - 5/3*d**4 + 3*d**2 + 0*d + 0 + d**l = 0. Calculate d.
-1, 0, 3
Let b(q) be the third derivative of 1/224*q**8 - 5/2*q**3 - 8/5*q**5 - 1/10*q**7 + 0*q + 0 - 11*q**2 + 41/16*q**4 + 23/40*q**6. Factor b(c).
3*(c - 10)*(c - 1)**4/2
Let h be 6/(-15) + 23/(-5) + 7. Factor -9*a**h + 0*a**2 - 11 + 9 + 3*a**4 - 10*a**3 - 16 + 33*a + a**3.
3*(a - 3)*(a - 1)**2*(a + 2)
Suppose -208*u + 398*u = 139*u + 153. Let x(n) be the third derivative of 0*n + 1/60*n**4 + 2/75*n**5 + 1/300*n**6 + 23*n**2 - 2/5*n**u + 0. Factor x(q).
2*(q - 1)*(q + 2)*(q + 3)/5
Let i(x) be the first derivative of -3*x - 1/9*x**3 - x**2 - 49. Factor i(k).
-(k + 3)**2/3
Let l(u) be the second derivative of u**6/60 + 11*u**5/5 + 121*u**4 + 10648*u**3/3 + 58564*u**2 - 1101*u. Factor l(f).
(f + 22)**4/2
Let y(a) be the third derivative of -a**6/320 + 367*a**5/160 - 2093*a**4/4 - 2116*a**3 + a**2 + 427*a - 2. Suppose y(k) = 0. What is k?
-1, 184
Let y(p) be the first derivative of -p**4/4 + 656*p**3 - 645504*p**2 + 282300416*p - 1509. Factor y(n).
-(n - 656)**3
Let n(s) = s - 1. Let m(r) = -r - 3. Let v(c) = -m(c) - 2*n(c). Let p be v(1). Factor 28*j**3 + 6*j - 5*j**2 + p*j - 168*j**3.
-5*j*(4*j - 1)*(7*j + 2)
Factor -3/2*b**3 + 0 - 32*b - 193/2*b**2.
-b*(b + 64)*(3*b + 1)/2
What is j in -52*j**2 - 93*j - j**3 + 986 + 4*j**3 - 1985 + 961 = 0?
-1, -2/3, 19
Factor -8*a**2 - a**5 + 8046*a**3 - 10*a**4 + 8*a**2 - 8071*a**3.
-a**3*(a + 5)**2
Let s = 333 - 270. Factor -33*o**2 - 3*o**5 + 0*o**5 - 39*o**4 - s*o**3 + 3*o**4 + 3*o**2.
-3*o**2*(o + 1)**2*(o + 10)
Let c(j) be the third derivative of j**6/15 - 28*j**5/5 + 663*j**4/4 - 1521*j**3 - 19*j**2 + 9*j - 13. Factor c(l).
2*(l - 3)*(2*l - 39)**2
Let g(b) = -17*b**4 + 44*b**3 + 9*b**2 + 30*b. Let p(f) = -53*f**4 + 132*f**3 + 27*f**2 + 95*f. Let a(v) = -19*g(v) + 6*p(v). Factor a(y).
y**2*(y - 9)*(5*y + 1)
Let n(p) be the second derivative of 0 + 1/20*p**5 - 13/12*p**4 + 23/6*p**3 + 144*p - 11/2*p**2. Solve n(y) = 0 for y.
1, 11
Let o = 10/6173 - -18499/12346. Suppose -6*y + 6*y**3 + 15/2 + o*y**4 - 9*y**2 = 0. Calculate y.
-5, -1, 1
Suppose -22241*w**2 - 1560 + 170*w + 22245*w**2 - 122*w + 188*w = 0. What is w?
-65, 6
Factor 2028*w + 3/4*w**5 + 666*w**3 + 42*w**4 + 2184*w**2 + 0.
3*w*(w + 2)**2*(w + 26)**2/4
Factor 15*p**4 - 27*p - 1082 + 10*p**5 - 2*p**2 + 1069 + 10*p**3 - 9*p**5 + 16*p**3.
(p - 1)*(p + 1)**3*(p + 13)
Find f, given that -50*f**3 + 10*f**2 + 118*f**2 + 87*f**2 - 59*f + 174*f + 85*f - 5*f**4 - 780 = 0.
-13, -2, 2, 3
Suppose -8*t = -16*t. Suppose -3*y + h + 5 = 0, 3*y = -t*y + 5*h + 1. Factor -1/4*s + 1/4*s**y + 0.
s*(s - 1)/4
Let x(s) be the third derivative of -s**7/385 + 7*s**6/110 - 69*s**5/110 + 35*s**4/11 - 100*s**3/11 + 1435*s**2. Factor x(y).
-6*(y - 5)**2*(y - 2)**2/11
Determine p, given that -27/4 + 1/4*p**4 - 2*p**3 - 7/2*p**2 + 12*p = 0.
-3, 1, 9
Let g(y) be the first derivative of -35/12*y**4 - 7 + 15*y**2 + 95/6*y**3 - 2*y. Let u(f) be the first derivative of g(f). Suppose u(a) = 0. What is a?
-2/7, 3
Let c(z) be the first derivative of 1/9*z**3 + 5/2*z**2 - 34/3*z - 300. Determine a, given that c(a) = 0.
-17, 2
Let k be ((-26)/65)/((-1)/(-20)). Let s = k - -10. Factor -4*p**3 - 1 + p**4 + 9*p**s - 5 + p**3 - 4*p**4 + 3*p.
-3*(p - 1)**2*(p + 1)*(p + 2)
Let o(s) be the second derivative of -s**5/50 - s**4/6 - 1487*s. Suppose o(p) = 0. Calculate p.
-5, 0
Let x = -110854/65 + 22176/13. What is b in -16/5 - x*b**2 + 18/5*b = 0?
1, 8
Let u(o) = -8*o + 88. Let y be u(0). Factor -57*v - 60*v + 29*v + 70*v**2 - 4*v - y - 74*v**2.
-4*(v + 1)*(v + 22)
Solve 69*x**2 + 397*x + 5*x**3 - 26*x**2 + 17*x**2 + 270 + 377*x - 549*x = 0.
-6, -3
Let y = -1876608 + 16889474/9. Suppose -y*b**2 - 6962/9 + 236/9*b = 0. What is b?
59
Let t be (-26394)/(-1743)*8/212. What is i in -248/7 + 132/7*i - t*i**2 = 0?
2, 31
Suppose -30 = -5*g, -165*w + 3*g - 15 = -164*w. Let n(b) be the first derivative of 117*b**2 - 1089/8*b**4 - 108*b + 77*b**w + 31. Factor n(d).
-3*(3*d + 2)*(11*d - 6)**2/2
Let r be (9 + 0)/(-1)*(-44 + 4585/105). Suppose -34/3*f**2 - 2/3*f**r + 54 - 42*f = 0. Calculate f.
-9, 1
Let b = -36 - -144. Let v be 300/b - (-4)/18. Let -11*z**2 + 6 + 13*z**4 + 19*z**3 - 13*z + 8*z**4 - 16*z**4 - 6*z**v = 0. Calculate z.
-3, -1, 2/5, 1
Let l(q) = 7*q**2 - 9138*q - 2872. Let d(k) = -3*k**2 + 4569*k + 1428. Let y(z) = 11*d(z) + 6*l(z). Find j such that y(j) = 0.
-1/3, 508
Solve 37*j - j**3 + 158*j + 13*j**3 + 59*j - 520 + 254*j**2 = 0.
-20, -13/6, 1
Let d = 472 + -470. Determine m, given that -252*m + m**2 + 249*m + m**2 - 9 + 0*m**d = 0.
-3/2, 3
Let s(o) = -2*o**3 + 22*o**2 + 21*o - 36. Let m be s(12). Let z be 32/m + 116/99. Find b such that 0 - 8/11*b**2 - 2/11*b**5 - 2/11*b - 12/11*b**3 - z*b**4 = 0.
-1, 0
Suppose 208 = -316*i + 303*i. Let t(f) = -2*f**3 - 32*f**2 - f - 12. Let o be t(i). Factor -6*h**2 - 72/7*h**3 + 0 - 4/7*h - 34/7*h**o.
-2*h*(h + 1)**2*(17*h + 2)/7
Let d(l) be the third derivative of -1/2*l**5 - 1/24*l**6 + 0*l**3 - 11*l**2 + 0*l + 0 - 25/24*l**4. Factor d(f).
-5*f*(f + 1)*(f + 5)
Suppose 603 + 1556 = 465*s + 689 - 855. Suppose -5*y**3 + 5/3*y**s + 0 - 50/3*y + 85/3*y**2 - 25/3*y**4 = 0. Calculate y.
-2, 0, 1, 5
Suppose -10*j + 24*j = -48*j + 13*j. Let x(f) be the second derivative of 0*f**2 - 3/10*f**5 + j*f**6 + 0*f**4 + 1/2*f**3 + 1/14*f**7 + 4*f + 0. Factor x(g).
3*g*(g - 1)**2*(g + 1)**2
Let i(n) = n**3 + 26*n**2 + 32*n - 6. Let k be i(-22). Let a = k + -3670/3. Determine u, given that 0 + 0*u**2 + 2/3*u**4 - a*u + 2*u**3 = 0.
-2, 0, 1
Suppose -5*k = -3*k + 37*k - 156. Let m(p) be the third derivative of -1/66*p**k + 0*p + 0 - 1/660*p**5 + 3*p**2 - 1/22*p**3. Find c, given that m(c) = 0.
-3, -1
Let f = -1/97771 + 293317/391084. Suppose 0 = -5*m + 20, -m + 2*m - 2 = d. Determine w, given that -9/4*w + 0 - f*w**d = 0.
-3, 0
Determine m, given that -86/3*m**3 - 4114/3*m - 374*m**2 - 2/3*m**4 + 5324/3 = 0.
-22, -11, 1
Determine i so that -1106/3 + 2/9*i**2 + 116/9*i = 0.
-79, 21
Let y(q) be the third derivative of q**8/336 - 127*q**7/210 + 723*q**6/20 - 9731*q**5/30 + 26413*q**4/24 - 3721*q**3/2 + 13*q**2 - 21*q + 1. Factor y(s).
(s - 61)**2*(s - 3)*(s - 1)**2
Let 54 - 1453*d**4 - 74*d**2 + 115*d - 82*d + 1473*d**4 - 32*d**3 - d**5 = 0. What is d?
-1, 1, 3, 18
Let v(s) be the first derivative of 21*s**4/46 + 296*s**3/69 + 176*s**2/23 - 640*s/23 - 1752. Solve v(i) = 0 for i.
-4, 20/21
Suppose 14*u = -24*y + 10*u, -5*u + 9 = 4*y + 61. Factor 3/5*f**y + 3*f + 12/5.
3*(f + 1)*(f +