 82. Let p be b(-13). Factor 17*s**p + 234*s**2 - 86*s - 226*s**3 - 56 + 29*s**4 + 60 + 28*s**4.
2*(s - 1)**3*(37*s - 2)
Let b(f) = f**2 - f - 3. Let l(y) = -14*y**3 - 8348*y**2 - 1240864*y + 355240. Let x(q) = -8*b(q) - l(q). Solve x(j) = 0 for j.
-298, 2/7
Let p = 5 + -4. Let m(d) = -d**3 - d**2 - d. Suppose 39*r + 3*y + 12 = 36*r, 0 = y. Let i(l) = -12*l**2 - 4*l. Let a(q) = p*i(q) + r*m(q). Factor a(f).
4*f**2*(f - 2)
Let i be (-723)/(-482) + 246/20 + -13. Factor 32/5*l + 64/5 + i*l**2.
4*(l + 4)**2/5
Let m(n) be the first derivative of n**4 - 8*n**3 - 122*n**2 + 264*n + 361. Factor m(a).
4*(a - 11)*(a - 1)*(a + 6)
Let s(a) be the first derivative of 2*a**6/15 - 72*a**5/25 + 123*a**4/5 - 1576*a**3/15 + 1152*a**2/5 - 1152*a/5 - 1210. Determine r, given that s(r) = 0.
1, 3, 4, 6
Let b(y) be the first derivative of y**5/35 + 61*y**4/28 + 232*y**3/21 + 114*y**2/7 + 400. Determine a so that b(a) = 0.
-57, -2, 0
Let j = 1265 - 3865/3. Let o = j - -212/9. What is f in -2/9*f + 0 + o*f**2 = 0?
0, 1
Let b(w) be the third derivative of w**6/30 - 383*w**5/15 - 193*w**4/3 + 512*w**3 + w**2 - 1390*w - 1. Determine h so that b(h) = 0.
-2, 1, 384
Let b = 11356 - 11350. Let n(z) be the third derivative of 1/24*z**b + 35/12*z**4 + 7/12*z**5 + 0 + 20/3*z**3 + 0*z - 34*z**2. Factor n(f).
5*(f + 1)*(f + 2)*(f + 4)
Let -278*k**4 + 270*k**4 - 660*k**3 - 1080*k + 340 + 1684*k**2 - 276*k = 0. What is k?
-85, 1/2, 1
Let u be -14 - ((-27593)/48)/41. Let g(z) be the second derivative of 1/80*z**5 + 10*z - 1/24*z**3 - u*z**4 + 1/8*z**2 + 0. Suppose g(r) = 0. What is r?
-1, 1
Let c = 98/993 - -77774/16881. Factor 2/17*x**4 + 16/17*x**3 - c*x + 12/17*x**2 + 50/17.
2*(x - 1)**2*(x + 5)**2/17
Suppose n + 7 = 2*b, 0*n = 5*b - 5*n - 15. Suppose 0 = b*h + 23 - 39. Factor -3*a**h + 2*a**3 - 1437*a**2 + 5*a**4 - 8*a + 1429*a**2.
2*a*(a - 2)*(a + 1)*(a + 2)
Let n(b) be the third derivative of -b**5/120 - 11*b**4/12 + 15*b**3/4 - 80*b**2. Let n(d) = 0. What is d?
-45, 1
Let d(j) = j**2 + 5*j - 55. Let h be d(-11). Suppose 1 + 9 = a. Find u such that -4*u**2 - h*u + u**2 + a*u - 27 - 17*u = 0.
-3
Let b(t) be the third derivative of t**8/672 + t**7/60 + 7*t**6/240 - 23*t**5/120 - t**4/6 + 4*t**3/3 - 19*t**2 + 1. Determine g so that b(g) = 0.
-4, -1, 1
Let d(f) be the first derivative of f**4/46 + 314*f**3/69 + 6083*f**2/23 - 12482*f/23 - 1249. Factor d(j).
2*(j - 1)*(j + 79)**2/23
Let o(v) = 2*v**3 + 3*v + 7. Let b(l) = -14*l**3 + 288*l**2 - 588*l + 242. Let n(i) = b(i) + 6*o(i). Factor n(z).
-2*(z - 142)*(z - 1)**2
Suppose 0 = 5*a + 2*m - 1 - 17, 0 = -3*a - 4*m + 22. Let i = -5 - -9. Factor -6*n**2 - 3*n**2 + 3*n**i - 9 + 3*n**a + 12.
3*(n - 1)**2*(n + 1)**2
Suppose -112/9 - 2/9*p**5 - 388/9*p**2 - 194/9*p**3 - 40/9*p**4 - 344/9*p = 0. What is p?
-14, -2, -1
Let a(b) = 4*b**2 + b - b**2 - 22 - 4*b**2 + 16*b. Let j(o) = 2*o**2 - 33*o + 42. Let n(t) = -11*a(t) - 6*j(t). Solve n(g) = 0.
1, 10
Suppose -143 + 40 = -5*g + 2*o, 5*g - 83 = -3*o. Let z = -17 + g. Suppose 2*s**z - 24 + 4*s**3 + 17*s**2 + 2*s - 6*s + 5*s**2 = 0. What is s?
-6, -1, 1
Let r = 108 + -100. Suppose -74*p + 76*p - 5*p**2 + r*p**2 - p**4 = 0. Calculate p.
-1, 0, 2
Let v = -34863 - -34865. Factor -5/7*f - 1/7*f**v - 6/7.
-(f + 2)*(f + 3)/7
Let l be (21 - (-473)/(-22))/((-1)/2). Let b be (1 - l)*(-5 - 108/(-24)). Find a such that 5/6*a**3 + b*a - 5/2*a**2 + 10/3 = 0.
-1, 2
Let g(a) be the second derivative of a**5/40 - 5*a**4 - 249*a**3/4 - 567*a**2/2 - 6135*a. Let g(l) = 0. What is l?
-3, 126
Let d(x) be the first derivative of 0*x + 1/15*x**6 + 60 - 1/5*x**2 + 0*x**4 + 1/5*x**5 - 1/3*x**3. Let d(l) = 0. What is l?
-2, -1, -1/2, 0, 1
Let a be (-5)/(-10)*-6 + -85. Let t be 3 + -6 + a/(-16). Factor -1/2*o**2 + t*o + 0.
-o*(o - 5)/2
Let j(c) be the third derivative of c**7/945 + c**6/540 - c**5/9 + 2*c**2 - 31*c - 6. Solve j(l) = 0.
-6, 0, 5
Let x be -33 + 28 - (-171)/27. Let m(w) be the third derivative of 0*w + 1/6*w**4 + 0 - 19*w**2 + 1/15*w**5 - x*w**3. Factor m(t).
4*(t - 1)*(t + 2)
What is o in -29/2*o + 10 + 5/2*o**2 = 0?
4/5, 5
Let f be 6/(-4) + 12/(-144)*-30. Let j be f/(4/16*(-68)/(-2)). Factor 6/17 - 8/17*s + j*s**2.
2*(s - 3)*(s - 1)/17
Let 45*d**2 - 855*d - 30980*d**4 + 30985*d**4 - 1020 + 90*d**3 + 115*d = 0. What is d?
-17, -2, 3
Suppose 42*g - 430 - 128 = -51*g. Let y(p) be the second derivative of 0 + 1/27*p**4 - 2/9*p**2 - 1/9*p**3 + g*p. Let y(b) = 0. Calculate b.
-1/2, 2
Let y(v) = -13*v**2 + 182*v + 760. Let k(c) = -32*c**2 + 448*c + 1900. Let u(x) = 5*k(x) - 12*y(x). Solve u(l) = 0 for l.
-5, 19
Suppose 7*f + 15 = 10*f. Let p(x) = 13*x**2 + x + f*x - x**2. Let n(q) = -q**2. Let j(r) = -10*n(r) - p(r). Factor j(w).
-2*w*(w + 3)
Factor 121*p**4 - 28*p - 252*p**4 - 181*p**2 + 111*p**4 - 480*p**3 + 676*p**2 - 97*p.
-5*p*(p + 25)*(2*p - 1)**2
Let s(q) = q - 6. Let t be s(9). Suppose -6*x = -3*x - t. Let p(z) = 2*z**3 - 6*z**2 - 12*z + 25. Let b(y) = y**3 - 1. Let l(n) = x*p(n) + b(n). Solve l(d) = 0.
-2, 2
Let m = 32 + -26. Suppose -3*k = -9 - m. Factor 5*x**3 - 4*x**3 + 9*x**4 - 11*x**4 + k*x**3.
-2*x**3*(x - 3)
Let t(n) = -7*n**4 + 7*n**3 + 7*n**2 - 13*n - 6. Let i(s) = 8*s**4 - 8*s**3 - 8*s**2 + 15*s + 7. Let d(c) = -6*i(c) - 7*t(c). Let d(z) = 0. What is z?
-1, 0, 1
Suppose 824*z - 17352 = -2068*z. Suppose 14/3*m**4 - z - 34/3*m - 2/3*m**5 + 4/3*m**2 + 12*m**3 = 0. What is m?
-1, 1, 9
Let z be 351/(-135) - 3/(-1). Let g = 3287/5 - 657. Determine x so that -g + z*x + 2/5*x**5 - 2/5*x**4 + 4/5*x**2 - 4/5*x**3 = 0.
-1, 1
Let n(u) be the second derivative of -59/3*u**3 - 31/6*u**4 - 1/10*u**5 + 0 + 104*u - 29*u**2. Let n(o) = 0. What is o?
-29, -1
Let m(b) be the first derivative of -4/5*b**3 + 6/25*b**5 + 6/5*b + 46 + 1/5*b**2 - 1/5*b**4 + 1/15*b**6. Suppose m(o) = 0. Calculate o.
-3, -1, 1
Let z(r) be the first derivative of -2*r**3/27 - 401*r**2/9 - 800*r/9 + 1663. Factor z(a).
-2*(a + 1)*(a + 400)/9
Let a(g) = -g**2 - g - 1. Suppose c + 0*c = 12. Let n(q) be the second derivative of -q**4/3 - 5*q**3/6 + 92*q + 1. Let h(k) = c*a(k) - 4*n(k). Factor h(b).
4*(b - 1)*(b + 3)
Let z(x) be the first derivative of 62*x**4 + 884*x**3/3 + 28*x**2 - 602. Find o such that z(o) = 0.
-7/2, -2/31, 0
Let s(k) be the third derivative of 5329/39*k**3 + 0 - 73/78*k**4 + 6*k + 6*k**2 + 1/390*k**5. Factor s(a).
2*(a - 73)**2/13
Let i(o) be the third derivative of -135*o**2 - 8/5*o**3 + 1/5*o**5 - 2/15*o**4 + 1/30*o**6 + 0 - 1/420*o**8 + 0*o - 2/175*o**7. Let i(w) = 0. Calculate w.
-3, -2, -1, 1, 2
Factor -15548318282/3*y + 0 + 7844760*y**3 + 11884/3*y**4 + 15524772116/3*y**2 + 2/3*y**5.
2*y*(y - 1)*(y + 1981)**3/3
Let z(g) be the second derivative of g**6/50 + 33*g**5/100 + 6*g**4/5 - 18*g**3/5 + 40*g - 25. Solve z(c) = 0 for c.
-6, 0, 1
Find o such that -1/6*o**4 + 17/6*o**3 - 50/3*o**2 + 38*o - 24 = 0.
1, 4, 6
Let q(j) be the third derivative of 0 - 65*j**2 - 17*j**4 + 10*j**3 + 81/112*j**8 + 0*j + 643/40*j**6 + 37/20*j**5 + 531/70*j**7. Solve q(m) = 0.
-5, -1, 2/9
Let s(r) be the second derivative of -16/13*r**3 - 185/78*r**4 - 42/65*r**6 - 267/130*r**5 - 5*r - 4/13*r**2 + 6. Determine y, given that s(y) = 0.
-1, -2/3, -2/7, -1/6
Let p = 53397877/1476945 - -42/32821. Let q = 374/9 - p. Factor 3/5*v**3 + 81/5*v + q*v**2 + 81/5.
3*(v + 3)**3/5
Let p(t) be the first derivative of -t**4/6 + 622*t**3/9 - 206*t**2 - 1172. Factor p(r).
-2*r*(r - 309)*(r - 2)/3
Let l = 894 + -891. Let p(t) be the first derivative of -3/2*t**4 + 9 + 0*t**l + 0*t**2 + 0*t + 3/5*t**5. Let p(h) = 0. Calculate h.
0, 2
Let y = -512 - -516. Factor 657 - 681 + 25*o + 3*o**2 - y*o**2.
-(o - 24)*(o - 1)
Let j(x) = x**3 - 11*x**2 + 15*x + 21. Let u be j(9). Let p be u/(-24) - (-366)/8. Factor 15*f**2 + p*f**3 + 47*f**3 - 96*f**3.
-3*f**2*(f - 5)
Factor -855/2*y - 3/8*y**3 - 27*y**2 + 2166.
-3*(y - 4)*(y + 38)**2/8
Find l, given that 529*l**3 + 742*l**3 + 4340*l**2 + 5*l**5 + 160*l**4 + 348*l**3 + 2940*l - 64*l**3 = 0.
-14, -3, -1, 0
Let n(s) = 131*s**2 - 20*s + 32. Let d be n(2). Factor d*h - h**2 - 4899 - 2*h**2 - 204*h + 0*h**2 - 3213.
-3*(h - 52)**2
Let k = -239915/4 - -59980. Factor k - b - 1/4*b**2.
-(b - 1)*(b + 5)/4
Let f(h) = -22*h**3 - 9152*h**2 - 9054*h + 18260. Let w(g) = 2*g**3 + 832*g**2 + 823*g - 1660. Let d(j) = 3*f(j) + 32*w(j).