the second derivative of -k**4/108 + 5*k**3/27 - 10*k + 31. Find x such that q(x) = 0.
0, 10
Let t(k) be the third derivative of -k**7/280 + 11*k**6/120 - 9*k**5/80 - 7*k**4/48 - 8*k**2 + 54*k. Find l, given that t(l) = 0.
-1/3, 0, 1, 14
Find s, given that 3/8*s**4 - 57/8*s**3 + 105/2*s + 117/4*s**2 - 75 = 0.
-2, 1, 10
Let z(b) be the third derivative of -b**5/180 - 191*b**4/72 - 21*b**3 + 387*b**2 - 2*b - 2. Factor z(c).
-(c + 2)*(c + 189)/3
Let a(s) = s**3 + 3*s**2 + 2*s - 3. Let i be a(-3). Let k be -1 + i/((-9)/4). Factor -3 + 2*m**2 - 19*m + 18*m - m**3 + k.
-m*(m - 1)**2
Suppose -5*n + 1690 = 3*b, -316 = -n + 4*b - 9*b. Suppose -5*w + 351 - n = 0. Factor -3/2*y + 0 + 1/4*y**w.
y*(y - 6)/4
Let q = -377 + 455. Let x be 12/q - (-202)/39. Find m, given that -4/3*m**3 + 0*m + 0 + x*m**2 = 0.
0, 4
Let o(h) be the first derivative of h**6/90 - 2*h**5/15 + h**4/2 - 8*h**3/9 + 5*h**2/6 + 22*h - 31. Let n(v) be the first derivative of o(v). Factor n(j).
(j - 5)*(j - 1)**3/3
Let g(h) be the first derivative of 0*h**2 - 3*h**4 + 0*h - 2*h**5 + 318 - 8/9*h**3 - 7/18*h**6. Factor g(j).
-j**2*(j + 2)**2*(7*j + 2)/3
Let o(i) = -i**4 + 82*i**3 + 812*i**2 + 1389*i + 645. Let h(c) = -84*c**3 - 812*c**2 - 1392*c - 644. Let b(x) = 3*h(x) + 4*o(x). Factor b(v).
-4*(v - 27)*(v + 1)**2*(v + 6)
Let p(g) = 1176*g - 32928. Let y be p(28). Factor y*j**2 + 0 - 5/3*j**5 + 0*j + 0*j**3 + 2/3*j**4.
-j**4*(5*j - 2)/3
Let x(f) be the second derivative of 7*f**4/6 + 22*f**3 + 80*f**2 + 5*f - 100. Factor x(q).
2*(q + 8)*(7*q + 10)
Factor 9/7*v**4 + 10/7*v**3 - 71/7*v**2 - 116/7*v - 12/7.
(v - 3)*(v + 2)**2*(9*v + 1)/7
Let t(w) = -w**2 - 1069*w + 7533. Let o be t(7). Factor -o + 1/4*u**2 - 3/4*u.
(u - 4)*(u + 1)/4
Let w(i) be the third derivative of i**6/24 - i**5/4 - 15*i**4/8 + 45*i**3/2 - 1540*i**2 + i. Suppose w(a) = 0. What is a?
-3, 3
Let k(y) = -90*y**2 - 455*y + 665. Let a(q) = -7*q**2 - 35*q + 51. Let x(u) = 40*a(u) - 3*k(u). Factor x(l).
-5*(l - 1)*(2*l + 9)
Let c(m) = -3*m**5 + 72*m**4 - 95*m**3 + 24*m**2 - 2*m + 2. Let i(h) = -h**5 + h**3 + h**2 + h - 1. Let r(n) = c(n) + 2*i(n). Determine d, given that r(d) = 0.
0, 2/5, 1, 13
Let l(j) be the second derivative of 81/8*j**3 + 1/80*j**5 - 2*j + 5 - 9/16*j**4 - 729/8*j**2. Factor l(s).
(s - 9)**3/4
Let b(a) be the second derivative of a**6/50 - 48*a**5/25 + 29*a**4/10 + 156*a**3/5 + 567*a**2/10 - 1305*a. Find g, given that b(g) = 0.
-1, 3, 63
Let v be (-2)/(0 - (-6)/(-60)). Suppose v*b**5 + 529 + 8*b**4 - 529 + 16*b**2 + 16*b - 60*b**3 = 0. What is b?
-2, -2/5, 0, 1
Let k be -357*55/(-7480)*6/(-21)*-3. Let k*t**2 - 24 - 69/2*t = 0. What is t?
-2/3, 16
Let y(l) be the first derivative of 18/11*l**3 + 2/11*l**5 + 9/11*l**2 + 0*l + 23/22*l**4 - 44. Let y(u) = 0. What is u?
-3, -1, -3/5, 0
Let r(f) be the second derivative of f**4/10 - 314*f**3/5 + 73947*f**2/5 - 1112*f. Factor r(n).
6*(n - 157)**2/5
Suppose 2246/11 + 204*m - 2/11*m**2 = 0. What is m?
-1, 1123
Let d(w) be the third derivative of 2*w**4 + 0 + 4/15*w**5 - 68*w**2 + 0*w**7 + 1/84*w**8 - 3/10*w**6 + 0*w + 0*w**3. What is c in d(c) = 0?
-3, -1, 0, 2
Suppose 38*p - p = 3552. Determine w so that 8 - 56*w**4 - 7 + 114*w - p*w**3 + 8*w**2 - 4*w**5 + 47 - 14*w = 0.
-12, -1, 1
Suppose -3*b = 3*l - 0*b - 1299, 4*l - 2*b = 1726. Let z = l + -428. Suppose 45/2*q**3 + 42*q**z + 18*q**5 - 3 - 27/2*q - 12*q**2 = 0. Calculate q.
-1, -1/2, 2/3
What is k in 896 + 936 - 12*k**4 - 360 + 6491*k + 3180*k**2 - 1691*k - 1070*k**3 = 0?
-92, -2/3, -1/2, 4
Let p be 144/792 + (-90309)/(-187). Let z = p + -483. Factor -z*h**5 - 6/17*h**4 - 2/17*h**2 + 0 - 6/17*h**3 + 0*h.
-2*h**2*(h + 1)**3/17
Let v = -974 - -979. Let r be 4/((-60)/(-21)) + (v - 6). Factor 0 - r*h**2 - 4/5*h.
-2*h*(h + 2)/5
Let p(j) = -j**2 + 128*j + 144. Let w(h) = -h**2 - 4*h. Let c(g) = -p(g) + 5*w(g). Suppose c(i) = 0. What is i?
-36, -1
Determine n so that -33*n + 521 - 501*n**3 + 147*n**5 - 1158 + 798*n**2 - 168*n**4 - 123*n + 517 = 0.
-2, -2/7, 1, 10/7
Let u(a) be the second derivative of a**4/48 - 25*a**3/12 + a + 1368. Factor u(s).
s*(s - 50)/4
Suppose -242*z = -232*z - 40. Suppose 4*b + z = 0, b = -5*o - 0 + 9. Solve -2/15*p**o - 8/15*p + 0 = 0 for p.
-4, 0
Factor 0 - 282/7*b - 1/7*b**4 + 421/7*b**2 - 138/7*b**3.
-b*(b - 2)*(b - 1)*(b + 141)/7
Let u(z) be the first derivative of 1/8*z**4 + 0*z + 1/480*z**6 + 2*z**3 + 0*z**2 - 1/40*z**5 + 8. Let t(k) be the third derivative of u(k). Factor t(y).
3*(y - 2)**2/4
Factor -780 - 82*a - 2*a**2 + 126*a - 266*a + 7*a**2 - 158*a.
5*(a - 78)*(a + 2)
Suppose -5*j - 23 = -2*g, -4*j - 4 = 5*g - 3*g. Factor -11 + 4*v**g + v**4 + 150*v**2 - 140*v - 60*v**3 + 56.
5*(v - 9)*(v - 1)**3
Determine s, given that -1/4*s**5 + 7/2*s**2 + 5*s + 2 - 1/4*s**3 - s**4 = 0.
-2, -1, 2
Suppose -2*o + 16 = -2*d, 2*d = -15 + 7. Let q(w) be the second derivative of 0 + 1/4*w**o - w**3 + 0*w**2 + 3/20*w**5 + 6*w. Factor q(p).
3*p*(p - 1)*(p + 2)
Let g(x) be the second derivative of -x**6/10 - 495*x**5/2 - 678973*x**4/4 + 681450*x**3 - 1023414*x**2 - x + 89. Factor g(y).
-3*(y - 1)**2*(y + 826)**2
Let j(b) be the third derivative of -19/108*b**4 + 1/540*b**5 + 26*b + 361/54*b**3 - 2*b**2 + 0. Factor j(n).
(n - 19)**2/9
Let l(z) = z + 17. Let w be l(-17). Factor w*h**3 - 130*h**2 + 2*h**3 + 126*h**2.
2*h**2*(h - 2)
Let x(c) be the second derivative of -4*c**5/15 - 53*c**4/6 - 26*c**3/3 - 38*c**2 + 34*c. Let k(d) be the first derivative of x(d). Factor k(s).
-4*(s + 13)*(4*s + 1)
Let m(h) be the second derivative of -h**8/560 - h**7/280 + h**6/60 + 7*h**3/6 - 4*h**2 - 4*h + 7. Let w(b) be the second derivative of m(b). Factor w(v).
-3*v**2*(v - 1)*(v + 2)
Let v = 11797/33 + -3914/11. Factor 2/3*r**3 - 2/3 + 1/3*r + v*r**2.
(r + 1)*(r + 2)*(2*r - 1)/3
Let j(p) be the second derivative of p**4/42 - 1004*p**3/21 + 252004*p**2/7 + 1503*p. Determine m so that j(m) = 0.
502
Let i(x) be the second derivative of x**7/105 - x**6/15 + x**5/10 + x**4/3 - 4*x**3/3 - 51*x**2/2 - 65*x. Let a(p) be the first derivative of i(p). Factor a(q).
2*(q - 2)**2*(q - 1)*(q + 1)
Let l(y) = 9*y + 3. Let x be l(0). Suppose 0 = 4*u - 3*d - 20, 0*d = x*u + 5*d + 14. Factor 4/3*v**3 - 1/6*v**4 - 8/3 - 4*v**u + 16/3*v.
-(v - 2)**4/6
Let l(g) be the third derivative of 0*g + 0 + 1/140*g**7 - 1/120*g**5 - 1/120*g**6 + 238*g**2 + 0*g**4 + 0*g**3. Factor l(a).
a**2*(a - 1)*(3*a + 1)/2
Solve 1/4*j**4 - 188 + 751/4*j**2 - 63/4*j + 63/4*j**3 = 0 for j.
-47, -16, -1, 1
Let w be (-1)/12*-2 - (-1025)/6. Factor -w*v + 347*v - 9*v**3 - 3*v**4 - 176*v + 12*v**2.
-3*v**2*(v - 1)*(v + 4)
Suppose -2*h + 4*n + 12 = 0, 4*n = h + 4*h - 18. Let c = 539829/674705 + -13/134941. Find b, given that -24/5*b**h - 32*b**3 - c + 32/5*b - 20*b**4 = 0.
-1, 1/5
Let p(u) be the first derivative of 3*u**5/100 - u**4/4 - u**3/10 + 3*u**2/2 + 93*u - 87. Let h(b) be the first derivative of p(b). Solve h(w) = 0 for w.
-1, 1, 5
Let -56*r**2 + 480 - 34*r**2 - 96*r + 33*r**3 - 420*r**4 + 417*r**4 = 0. Calculate r.
-2, 4, 5
Let b(x) be the first derivative of -x**6/120 - x**5/40 + x**4/48 + x**3/12 + 22*x - 31. Let j(f) be the first derivative of b(f). Find l such that j(l) = 0.
-2, -1, 0, 1
Let u(p) be the third derivative of -p**8/112 - 6*p**7/35 + 29*p**6/20 - 23*p**5/5 + 63*p**4/8 - 8*p**3 + 1109*p**2 + 1. Factor u(d).
-3*(d - 1)**4*(d + 16)
Let b(k) = k**3 + 385*k**2 - 694*k - 334. Let u(n) = 1540*n**2 - 2775*n - 1335. Let q(m) = -25*b(m) + 6*u(m). Factor q(v).
-5*(v - 2)*(v + 17)*(5*v + 2)
Let d(t) be the second derivative of t**4/78 - 284*t**3/39 + 564*t**2/13 + 526*t. Solve d(l) = 0.
2, 282
Determine k, given that 540*k**2 + 142/3*k**4 + 725/3*k - 250/3 + 3*k**5 + 778/3*k**3 = 0.
-5, -1, 2/9
Suppose 2*r = -5*r + 3*r. Suppose 0 = -4*w - r*w + 20. Determine j, given that -6*j - w*j**2 + 6*j + 0*j**2 + 5*j = 0.
0, 1
Suppose -5/4*b**2 - 1495/4*b - 745/2 = 0. Calculate b.
-298, -1
Determine b, given that 2/9*b**3 - 52/9 + 22/9*b + 28/9*b**2 = 0.
-13, -2, 1
Solve -22*n**4 + 1886*n**2 - 1001*n**2 + 8*n**4 - 939*n**2 + 17*n**4 - 21*n**3 = 0.
-2, 0, 9
Let s(y) = 11*y + 28*y**2 + 17*y**3 + 15 + 20*y**2 - 11*y**2. Let m(c) = -25*c**3 - 55*c**2 - 17*c - 21. Let z(b) = -5*m(b) - 7*s(b). Factor z(k).
2*k*(k + 2)*(3*k + 2)
Let d be (3/(-7))/(733/(-4398)). Factor 0*j**