y - 104. Suppose y*l - 7*l + 3*k - 2 = 0, 4*k + 2 = l. Factor 12*m**l + 4*m**3 + 20*m**2 - 3*m**3 - 5*m**3.
-4*m**2*(m - 8)
Let p(c) = c**3 + 495*c**2 + 58575*c + 58087. Let z(v) = 3*v**3 + 1483*v**2 + 175723*v + 174260. Let q(u) = 17*p(u) - 6*z(u). Determine d so that q(d) = 0.
-241, -1
Let d(s) be the second derivative of -s**4/78 - 58*s**3/39 + 59*s**2/13 + 1231*s. Factor d(v).
-2*(v - 1)*(v + 59)/13
Let k(n) be the second derivative of 20/3*n**3 - 41*n + 1 - 300*n**2 - 1/18*n**4. What is w in k(w) = 0?
30
Suppose 0 = -25*r + 97*r. Let l(c) be the second derivative of -8*c - 2/11*c**3 + 1/22*c**4 + r + 0*c**2 + 3/110*c**5. Solve l(h) = 0 for h.
-2, 0, 1
Let l(n) be the second derivative of 3*n**6/50 - 3*n**5/10 + 9*n**4/20 - n**3/5 - 2*n + 477. Determine x, given that l(x) = 0.
0, 1/3, 1, 2
Let i(k) be the third derivative of k**6/360 + k**5/10 + 5*k**4/6 + 28*k**3/9 + 2400*k**2. Factor i(j).
(j + 2)**2*(j + 14)/3
Let n(t) = -t**2 - 2*t. Let f(s) = 9*s**5 - 210*s**4 + 388*s**3 + 1068*s**2 + 527*s + 84. Let w(q) = 5*f(q) - 90*n(q). Solve w(i) = 0 for i.
-1, -1/3, 4, 21
Let 36/13*q**3 + 40/13*q - 2/13*q**4 + 6*q**2 + 0 = 0. Calculate q.
-1, 0, 20
Suppose 3*u + 2 = 2*p - u, 13 = 4*p + u. Factor -331*f**2 - 2*f**3 + 2*f**4 - 48 - 88*f + 287*f**2 + 0*f**p.
2*(f - 6)*(f + 1)*(f + 2)**2
Let v(w) = -3*w**2 + w + 8. Let j be v(2). Let c be (-3 - -7)*(18/7 + j). Solve -4/7 - t**2 - c*t = 0.
-2, -2/7
Let q(r) be the first derivative of r**4/34 + 64*r**3/51 - 4*r**2 - 1317. Determine i, given that q(i) = 0.
-34, 0, 2
Let j(f) be the third derivative of f**6/40 - 49*f**5/10 - f**4/8 + 49*f**3 + 149*f**2 - 3*f. Factor j(n).
3*(n - 98)*(n - 1)*(n + 1)
Let g(c) be the first derivative of -3*c**5/5 - 9*c**4/4 + 34*c**3 - 72*c**2 + 1649. Suppose g(m) = 0. Calculate m.
-8, 0, 2, 3
Solve -2056/9*j**2 - 356/9*j**4 - 1384/9*j**3 - 4/9*j**5 - 340/9 - 1364/9*j = 0 for j.
-85, -1
Factor -12*g - 2/3*g**2 - 34/3.
-2*(g + 1)*(g + 17)/3
Let a(r) = -7*r + 274. Let w be a(33). Factor -24*g + 5*g**4 - 39 - 85*g**3 + 109*g - w + 75*g**2 + 2.
5*(g - 16)*(g - 1)**2*(g + 1)
Let s be -41 + 47 + 2*8. Let w be (3/s)/(21*(-6)/(-672)). Determine i, given that -w*i + 2/11*i**3 - 16/11 + 4/11*i**2 = 0.
-2, 2
Factor 490/3 + 2/3*j**2 - 36*j.
2*(j - 49)*(j - 5)/3
Let j be 12/3 + (-4 - -1) + 3. Suppose -c + 3*v + 15 = 5*v, -j*c + 4*v = -36. Factor 7*x**2 - 10*x - c*x**2 + 10*x.
-4*x**2
Suppose -48*i = -29*i + 304. Let c be i/8 - 8/(-4). Factor 6/13*b**3 - 2/13*b**4 + 0*b + c - 4/13*b**2.
-2*b**2*(b - 2)*(b - 1)/13
Factor -2/11*x**3 - 3150/11*x**2 - 289406250/11 - 1653750/11*x.
-2*(x + 525)**3/11
Suppose 29*b - 16 = 24*b + 4. Let q(z) be the first derivative of 0*z - 1/16*z**b - 1/4*z**2 + 25 + 1/4*z**3. Factor q(d).
-d*(d - 2)*(d - 1)/4
Find c such that -3430 - 126*c**2 - 1/8*c**4 + 1078*c + 13/2*c**3 = 0.
10, 14
Suppose f + 27 = 33. Let l be (8 + 20)/(f/(-2 - -5)). Factor -19*c**4 - 3 - 5*c**2 + 13 + 0*c + 15*c**3 + l*c**4 - 15*c.
-5*(c - 2)*(c - 1)**2*(c + 1)
Let n(b) be the third derivative of -b**5/20 + 3*b**4/8 + 14*b**3 + 3*b**2 + 158. Determine u, given that n(u) = 0.
-4, 7
Let l = -2/991 + 1051/29730. Let d(r) be the second derivative of 0*r**6 - 1/63*r**7 + l*r**5 + 0*r**3 + 0 - 32*r + 0*r**4 + 0*r**2. Factor d(n).
-2*n**3*(n - 1)*(n + 1)/3
Let q(w) be the third derivative of -w**6/100 + 71*w**5/50 - 186*w**4/5 + 2124*w**3/5 - 3433*w**2. Find t such that q(t) = 0.
6, 59
Let b be 6 + (-14)/6 + (-43)/(-129). Let k(f) be the first derivative of 92/3*f**3 - 8 + 120*f**2 - 144*f + 2*f**b. Factor k(a).
4*(a + 6)**2*(2*a - 1)
Let j(a) = -a**2 + 33*a - 59. Let k be j(31). Factor -h**k - 4*h**3 + 60*h**2 - 157*h + 250 - 68*h.
-5*(h - 5)**2*(h - 2)
Let u(v) = -8*v - 43. Let s be u(-14). Let w = s + -69. Solve 2*l**3 - 2*l**2 + w*l**3 + 0*l**2 - 2*l**2 = 0.
0, 2
Let h(z) be the third derivative of z**5/40 - 21*z**4/16 + 5*z**3 - 49*z**2 + 29*z. Let h(n) = 0. What is n?
1, 20
Suppose 21*o - 2471 - 175 = 0. Factor -195*u + 30 + 3*u**2 + 42 - 6*u**2 + o*u.
-3*(u - 1)*(u + 24)
Suppose 25 = -h + 5*t, 1185 - 1180 = t. Let x(u) be the second derivative of -2/45*u**3 + 0*u**5 - 1/225*u**6 + 1/30*u**4 + 0 + h*u**2 - 17*u. Solve x(b) = 0.
-2, 0, 1
Let y(x) = 3*x + 64. Let r be y(-20). Let g(u) = -4*u**3 + 2*u**2 + 31*u - 44. Let m(a) = a**3 - a**2 + a. Let d(p) = r*m(p) + 4*g(p). Solve d(n) = 0.
-11/3, 2
Let m be 4 + -8 - (-5100)/1233. Let p = -2/685 + m. Factor p*c**2 - 16/15*c + 32/15.
2*(c - 4)**2/15
Suppose -195*n + 606 - 275 = -254. Let y be 44/10 + 6/(-15). Find s, given that 22/19*s - 20/19*s**2 - 12/19*s**n - 6/19 + 26/19*s**y - 10/19*s**5 = 0.
-1, 3/5, 1
Let u = -235 - -240. Factor 6*o + u*o**2 + 14*o + 0*o**2 + 70 - 50.
5*(o + 2)**2
Determine z so that 160*z**4 - 4391*z**3 + 30475*z**2 - 104709 - 211600*z + 165*z**4 + 348049 + 5*z**5 + 10966*z**3 = 0.
-23, 2
Let u(d) be the second derivative of 0 + 2/9*d**2 - 5/18*d**4 - 1/27*d**3 + 103*d. Factor u(z).
-2*(3*z - 1)*(5*z + 2)/9
Let 2896/9 + 1444/9*l - 2/9*l**2 = 0. What is l?
-2, 724
Let r be (-6545)/561*(3 - 292/84). Determine f, given that -80/3*f**3 + 368/9*f**2 - 64/3*f + r*f**4 + 32/9 = 0.
2/5, 2
Suppose 0 = -4*y - v + 444, 4*y - 4*v - 418 = 26. Suppose y*w - 2 = -2. Factor 1/9*q**3 + 2/9 + w*q**2 - 1/3*q.
(q - 1)**2*(q + 2)/9
Let h(o) be the first derivative of -81/7*o - 6/7*o**4 + 3/35*o**5 + 0*o**2 - 263 + 18/7*o**3. Factor h(f).
3*(f - 3)**3*(f + 1)/7
Suppose 0 = -4*n - 4*n + 24. Suppose 4*t + n = 15. Factor 8*l**3 - 3*l**5 - 8*l**3 + 15*l**t - 2*l**5 - 10*l**2.
-5*l**2*(l - 1)**2*(l + 2)
Let i be 74 - 1 - 1/((-2)/10). Factor -25*h**2 + 2*h**2 + 3*h**3 + i*h - 10*h**2 - 12*h**2.
3*h*(h - 13)*(h - 2)
Suppose 160/3 + 1968*f**2 - 1856/3*f - 2992/3*f**3 + 242/3*f**4 = 0. Calculate f.
2/11, 2, 10
Suppose -3*h + 3*g + 27 = 0, 79*h + 4*g + 6 = 77*h. Let v(w) be the third derivative of 0*w + 0 + 18*w**2 + 2/105*w**h - 5/84*w**4 + 1/21*w**3. Factor v(a).
2*(a - 1)*(4*a - 1)/7
Factor -928 - 2/7*p**3 - 6504/7*p - 1632/7*p**2.
-2*(p + 2)**2*(p + 812)/7
Solve 6789/4*c + 961/4 + 435/4*c**2 + 7/4*c**3 = 0 for c.
-31, -1/7
Let l = 32134 - 32130. Let h(u) be the second derivative of 5/7*u**l + 9/20*u**5 - 27*u - 3/14*u**3 + 0 - 3/7*u**2. Let h(d) = 0. What is d?
-1, -2/7, 1/3
Solve -k**3 - 1609*k + 501*k - 424*k**2 + 263*k - 422 = 0 for k.
-422, -1
Factor 276/5*h + 416/5*h**2 + 0 + 3/5*h**3.
h*(h + 138)*(3*h + 2)/5
Let g be (-76)/10*23/184. Let k = g - -211/180. Factor 2/9*m - 2/9 + k*m**2 - 2/9*m**3.
-2*(m - 1)**2*(m + 1)/9
Solve -b**2 + 1752/7*b - 500/7 = 0 for b.
2/7, 250
Let y = 5694 + -5690. Factor -y*d**2 + 40/3*d - 4.
-4*(d - 3)*(3*d - 1)/3
Let q(p) be the second derivative of -p**5/50 + 7*p**4/5 - 31*p**3/3 + 114*p**2/5 - 3007*p. Let q(r) = 0. What is r?
1, 3, 38
Find d, given that -13/5 + 1/5*d**2 + 12/5*d = 0.
-13, 1
Let w(k) be the second derivative of k**7/7 - k**6/15 - 13*k**5/10 - k**4/2 + 14*k**3/3 + 8*k**2 - 18*k + 37. Solve w(c) = 0.
-1, 4/3, 2
Let 40/17*b**3 - 40/17*b + 44/17*b**2 - 2/17*b**4 - 42/17 = 0. Calculate b.
-1, 1, 21
Suppose 1150 = 17*l - 193. Suppose 0 = -91*q + l*q + 60. Let 0*n**4 - n**3 + 0 + 0*n**2 + 1/2*n**q + 1/2*n = 0. What is n?
-1, 0, 1
Suppose -4*q = -12 - 24, -105*x - 5*q = -110*x - 30. Factor 2/15*y**2 + 0 + 2/15*y**x - 4/5*y.
2*y*(y - 2)*(y + 3)/15
Let u = 6130/573 - 6/191. Let d(p) be the first derivative of 32/5*p**5 + 0*p - 12 - u*p**3 - 15*p**4 - 2/3*p**6 + 32*p**2. What is r in d(r) = 0?
-1, 0, 1, 4
Let q(n) be the third derivative of -1/210*n**7 + 0*n + 3 - 5/12*n**6 - 6*n**2 - 50*n**4 - 673/60*n**5 - 96*n**3. Suppose q(d) = 0. Calculate d.
-24, -1
Let -166 + 44 - 46 + 171*o - 41*o + 36*o**2 + 2*o**3 = 0. Calculate o.
-12, -7, 1
Let o(p) = -12*p**3 + 796*p**2 + 80*p + 16. Let c(q) = q**3 + q**2 - 5*q - 1. Let a(m) = -16*c(m) - o(m). Find b such that a(b) = 0.
-203, 0
Let h(q) be the third derivative of -q**6/80 + 53*q**5/12 + 237*q**4/16 + 89*q**3/6 - q**2 + 72. Factor h(s).
-(s - 178)*(s + 1)*(3*s + 1)/2
Let t be ((-56)/7 - (-2552)/154)/1 - 8. Factor -t - 2/7*r + 4/7*r**2 + 2/7*r**3.
2*(r - 1)*(r + 1)*(r + 2)/7
Let d(z) = z**2 + 7134*z + 78353. Let v be d(-11). Factor 0*s + 4/3*s**4 - 8/3*s**3 - 4*s**2 + v.
4*s**2*(s - 3)*(s + 1)/3
Let m = -87679 - -87681. What is k in 38/7*k**4 - 72/7 + 110/7