e the third derivative of i**6/900 - 4*i**5/25 - 52*i**4/15 - 256*i**3/9 - 9*i**2 + 3. Determine x so that u(x) = 0.
-4, 80
Suppose -3*n + w = -29, -5*n + 50 = -w + 1. Suppose 3*u + 2*u - n = 0. Factor 31*c**2 - 2*c + 8*c - 2*c**3 - 31*c**u - 4.
-2*(c - 1)**2*(c + 2)
Let o(d) be the third derivative of d**7/315 - 11*d**6/180 - d**5/9 + 56*d**4/9 + 128*d**3/3 + 42*d**2 + 2*d. Suppose o(s) = 0. What is s?
-3, -2, 8
Suppose -3*w = 5*z + 9, -5*z - 2 = 4*w + 5. Factor w*y**2 + 49 - 49 + 10*y.
2*y*(y + 5)
Suppose 17*x - 376*x = -1077. Determine g, given that -1/4*g**3 + 4*g + x + 3/4*g**2 = 0.
-2, -1, 6
Let t(b) = b**5 + 144*b**4 + 233*b**3 + 353*b**2 + 144*b. Let i(o) = 2*o**5 + 208*o**4 + 350*o**3 + 529*o**2 + 216*o. Let g(c) = 5*i(c) - 7*t(c). Factor g(d).
d*(d + 3)**2*(d + 4)*(3*d + 2)
Let o(r) be the third derivative of -r**7/105 + 47*r**6/120 - 107*r**5/60 + 7*r**4/4 + 7675*r**2. Factor o(j).
-j*(j - 21)*(j - 2)*(2*j - 1)
Let c(m) be the second derivative of 6 - 2*m + 0*m**2 + m**3 - 1/20*m**5 - 1/12*m**4. Factor c(l).
-l*(l - 2)*(l + 3)
Let h(j) = -j**2 - 1. Let n(y) = -y**2 + 4*y - 19. Let m(q) = -2*h(q) + n(q). Let r be m(-7). Let 5*t + 0*t - 12*t**4 - 8*t**3 - r*t**5 - 5*t = 0. Calculate t.
-2, -1, 0
Suppose 37 = 2*d + 27. Let u be 6/15 - ((-43)/d + -2). Find w, given that -2*w**5 + 4*w**5 + 5*w + 3*w**5 - u*w**3 + w**3 = 0.
-1, 0, 1
Let v(w) be the second derivative of 0*w**2 + 0 + 109*w + 1/12*w**4 + 1/4*w**3 - 1/10*w**5 + 1/84*w**7 - 1/30*w**6. Factor v(l).
l*(l - 3)*(l - 1)*(l + 1)**2/2
Let d(a) = 5*a - 119. Let y be d(24). Let b be 8/y + 124/(-16). Suppose 0 + q**2 - q - b*q**3 = 0. Calculate q.
0, 2
Let c(s) be the second derivative of -s**6/165 + 9*s**5/110 - 3*s**4/22 - 85*s**3/33 + 150*s**2/11 + 57*s - 5. Find k, given that c(k) = 0.
-3, 2, 5
Let c(z) be the second derivative of -3/4*z**2 - 1/15*z**6 + 1/56*z**7 + 5/24*z**3 + 7/24*z**4 + 2 + 6*z - 1/10*z**5. Suppose c(b) = 0. What is b?
-1, 2/3, 1, 3
Let u(n) be the second derivative of 121/2*n**2 + 0 - 1133/12*n**3 - 97/40*n**5 + 1/15*n**6 + 96*n + 57/2*n**4. Determine i so that u(i) = 0.
1/4, 2, 11
Let n(v) be the first derivative of 2*v**3/33 + 8*v**2 - 360*v/11 + 1709. Let n(q) = 0. What is q?
-90, 2
Let f = 1 + -1. Let l be 23 + (1162/(-70)*1 - 6). Factor -6/5*u**4 + 6/5*u**3 + 2/5*u**5 + 0*u + f - l*u**2.
2*u**2*(u - 1)**3/5
Let r(m) be the first derivative of m**4/4 - 4*m**3 + 45*m**2/2 + 273*m - 235. Let y(u) be the first derivative of r(u). Solve y(q) = 0.
3, 5
Let m(c) be the second derivative of -1/5*c**5 + 0*c**2 + 1/45*c**6 - 8/9*c**3 - 141*c - 5/6*c**4 + 0. Factor m(a).
2*a*(a - 8)*(a + 1)**2/3
Let m(k) be the first derivative of -k**6/540 - 2*k**5/135 + 5*k**4/108 - 69*k**2 - 111. Let l(t) be the second derivative of m(t). Solve l(d) = 0 for d.
-5, 0, 1
Let u(f) be the third derivative of f**7/165 + 19*f**6/660 + 4*f**5/165 - f**4/33 + 615*f**2 - f. Solve u(w) = 0 for w.
-2, -1, 0, 2/7
Let i = -141406 - -707032/5. Factor -12/5 - i*n**2 + 14/5*n.
-2*(n - 6)*(n - 1)/5
Let y(u) be the first derivative of -68 + 55*u + 30*u**2 + 5/3*u**3. Find z, given that y(z) = 0.
-11, -1
Let v = -16482/5 + 3316. Let i(h) be the second derivative of 0 + v*h**2 - 31*h + 1/15*h**4 + 28/15*h**3. Solve i(f) = 0.
-7
Suppose -g + 7*y - 229 = -273, 16 = -4*g - 4*y. Suppose 3 + 1/5*c**g + 8/5*c = 0. What is c?
-5, -3
Let g be 69490/(-186) + (-186)/2883. Let u = 375 + g. Suppose 1 + 5*o**4 + u*o**3 - 6*o**2 + 4/3*o**5 - 8/3*o = 0. What is o?
-3, -1, 1/4, 1
Let x(k) be the second derivative of 27*k + 1/50*k**5 + 0 + 0*k**4 + 0*k**2 + 2/25*k**6 + 0*k**3. Factor x(q).
2*q**3*(6*q + 1)/5
Let t(i) be the third derivative of -i**5/420 - 83*i**4/168 - 41*i**3/21 - 84*i**2 - 1. Factor t(z).
-(z + 1)*(z + 82)/7
Let r(i) be the third derivative of i**6/1080 + 11*i**5/360 + i**4/4 + 49*i**3/6 - 11*i**2 + 3. Let z(a) be the first derivative of r(a). Factor z(p).
(p + 2)*(p + 9)/3
Let n be 534/15 + 36/15 + -2. Let p = -32 + n. Factor 35*a**2 + 8*a**4 - 20*a**2 - 15*a**3 - 3*a**p - 2*a - 3*a.
5*a*(a - 1)**3
Suppose 0 = -15*f + 30*f - 480. Factor 209*k**2 - f - 115*k**3 + 20*k**4 - 67 - 64*k + 35 + 3*k**3 - 17*k**2.
4*(k - 2)**3*(5*k + 2)
Let p = -6 + 6. Suppose p = -6*f + f + 20. Determine q, given that -f + 0*q**2 - 20*q - 18*q + 2*q**2 + 36*q = 0.
-1, 2
Let y = 2763 - 2760. Let k(n) be the first derivative of 8*n**2 + 4 + 4/3*n**y + 16*n. Factor k(o).
4*(o + 2)**2
Let n = -3 + 5. Let h be (2 + -4 + 3)*n. Factor o**3 - 84*o + 95*o - 6 - 2*o**3 - 4*o**h.
-(o - 1)**2*(o + 6)
Let g = -444 + 448. Let p(l) = l**3 + 1 + l**2 - 1 - l**4. Let r(w) = -3*w**4 + 4*w**3 + w**2 - 2*w. Let n(i) = g*p(i) - r(i). Factor n(y).
-y*(y - 2)*(y + 1)**2
Factor 77*k**3 - 132*k**3 + 120*k**3 + 54*k + 81*k**4 + 100*k**3 - 645*k**3 + 693*k**2.
3*k*(k - 3)**2*(27*k + 2)
Let u(b) be the third derivative of b**2 + 0*b**3 - 57*b + 1/64*b**4 + 0 - 1/480*b**5. Factor u(c).
-c*(c - 3)/8
Factor 38/3*s + 11/3*s**2 + 1/3*s**3 + 40/3.
(s + 2)*(s + 4)*(s + 5)/3
Factor -h**3 - 881*h**4 + 1773*h**4 + 87*h**2 + 3*h**3 + 0*h**3 - 979*h**4 - 2*h.
-h*(h - 1)*(h + 1)*(87*h - 2)
Let m(j) be the second derivative of 2*j**6/45 + j**5/15 - 4*j**4/3 + 8*j**3/9 + 32*j**2/3 + 10*j + 83. Let m(k) = 0. What is k?
-4, -1, 2
Determine b so that 216*b**2 + 39/7*b**3 + 15219/7*b + 10830/7 = 0.
-19, -10/13
Suppose -3*s - 2*m = -42, -63 = -8*s + 4*s - 5*m. Let a be 6/(-45) - s/(-90). Determine d so that 16/3*d + 2/3*d**4 + 4*d**3 + a + 8*d**2 = 0.
-2, 0
Factor 4*r**3 + 425100*r + 339904 + 4238*r**2 - 6850*r**2 + 87812.
4*(r - 327)**2*(r + 1)
Let t = 46/13 + -327/52. Let r = 7/4 - t. Factor 15/2*j - 7/2*j**2 - r + 1/2*j**3.
(j - 3)**2*(j - 1)/2
Let x(g) = 25*g**3 - 17*g**2 - 2*g + 198. Let t(q) = 42*q**3 - 34*q**2 - 2*q + 394. Let h(s) = 6*t(s) - 10*x(s). Find k such that h(k) = 0.
-3, 4, 16
Suppose 0 = -4*m + 5*t + 32, 64*t + 49 = 3*m + 54*t. Solve -15*v**m + 27 + 12*v**2 - 3*v**4 + 3/2*v**5 + 99/2*v = 0.
-2, -1, 3
Let a be -10*(4 + (-18)/4). Suppose -g + 3*g = -3*h + 7, -h + 11 = a*g. Factor -2 - 2*q**g + 3*q - q**2 + 3*q**2 - q**3.
-(q - 1)**2*(q + 2)
Let o = 289/330 - 93/110. Let l(r) be the second derivative of 0 + 0*r**2 + 1/110*r**5 - o*r**4 + 0*r**3 - 27*r. Solve l(c) = 0.
0, 2
Solve 100*x**3 - 2*x**4 - 201*x**3 + 87*x**3 + 24*x**2 - 224 + 136*x = 0 for x.
-7, -4, 2
Let c = 4645169/22512 + 49/3216. Let q = c + -303/2. Let 1024/7 - 2/7*x**3 - q*x + 48/7*x**2 = 0. Calculate x.
8
Factor -5395*x - 30*x**2 + 4*x**3 - 27365*x - 331*x**2 - 12396 - 20004 - 5*x**3.
-(x + 1)*(x + 180)**2
Let x be 44/(-55)*-5 - (-4)/(-3). Let f(l) be the first derivative of 0*l - 5 - x*l**3 + 1/2*l**4 + 8/5*l**5 - l**2. Solve f(w) = 0.
-1, -1/4, 0, 1
Let w(n) be the second derivative of -n**5/170 + 201*n**4/34 - 40401*n**3/17 + 8120601*n**2/17 - n + 9. Factor w(c).
-2*(c - 201)**3/17
Let z(j) be the second derivative of -j**5/10 - 4*j**4/3 + 3*j**3 - 13*j - 9. What is f in z(f) = 0?
-9, 0, 1
Let f(y) be the third derivative of 9*y**6 - 33/2*y**5 - 25*y**2 + 40/3*y**4 + 0*y - 35/6*y**3 - 9/14*y**7 - 5. Factor f(h).
-5*(h - 7)*(3*h - 1)**3
Suppose -3427 = -1963*j - 513*j + 1249 + 276. Determine l so that 14 + 111/2*l + 40*l**j - 3/2*l**3 = 0.
-1, -1/3, 28
Let g(k) be the third derivative of -k**5/330 - 545*k**4/132 + 182*k**3/11 + 4985*k**2. Factor g(m).
-2*(m - 1)*(m + 546)/11
Let s = 1783 + -1797. Let c be (-214)/107*(1 - (-54)/s). Suppose -4/7*o**3 + 144/7 + c*o**2 - 132/7*o = 0. Calculate o.
3, 4
Let y(j) be the third derivative of -j**5/12 + 1855*j**4/4 + 11135*j**3/6 - 84*j**2 + 2*j - 18. Factor y(b).
-5*(b - 2227)*(b + 1)
Let a(j) be the third derivative of -7*j**5/36 + 505*j**4/24 - 215*j**3/9 + 170*j**2 + 2. Factor a(o).
-5*(o - 43)*(7*o - 2)/3
Let p be ((-186)/1023 + 212/198)/(5/10). Factor -2/9*j**3 - 8/9*j**4 + 8/9*j - p - 2/9*j**5 + 20/9*j**2.
-2*(j - 1)**2*(j + 2)**3/9
Let c(i) be the first derivative of 9/10*i**5 + 3*i**2 + 0*i + 33/8*i**4 + 34 + 6*i**3. Find n, given that c(n) = 0.
-2, -1, -2/3, 0
Let c(y) be the third derivative of 0*y**3 - 1/105*y**7 + 0*y - 2*y**2 - 1/6*y**6 + 6 - 14/15*y**5 - 2*y**4. Factor c(w).
-2*w*(w + 2)**2*(w + 6)
Let b(n) = 6*n**4 - 54*n**2 + 72*n. Let f(s) = -2*s**3 + s**2 - 2*s. Let g(h) = -b(h) - 8*f(h). Solve g(a) = 0 for a.
-7/3, 0, 1