Factor l(s).
-2*(s - 973)*(3*s + 2)**2
Let j(y) be the first derivative of -2/3*y - 16/9*y**3 + 65 + 3*y**2. Factor j(n).
-2*(n - 1)*(8*n - 1)/3
Find s such that -287*s**2 - 159875*s**3 + 2142*s**4 + 268*s**4 + 450280*s**3 + 5*s**5 + 287*s**2 = 0.
-241, 0
Let f(a) be the third derivative of a**8/784 + 11*a**7/490 - 53*a**6/280 - 387*a**5/140 + 270*a**4/7 - 1350*a**3/7 + 598*a**2. Solve f(v) = 0.
-10, 3
Let s(k) = 3*k**2 - 148*k + 904. Let x(r) = -20*r**2 + 895*r - 5425. Let l(v) = 25*s(v) + 4*x(v). Factor l(z).
-5*(z - 6)*(z + 30)
Let k(c) be the second derivative of -c**5/20 + 41*c**4/4 - 620*c**3 - 1922*c**2 + 9022*c. Factor k(m).
-(m - 62)**2*(m + 1)
Let t be 35/84 + (-110)/(-88). Let n(b) be the third derivative of 25/24*b**4 + 14*b**2 - 1/3*b**5 + 1/24*b**6 - t*b**3 + 0 + 0*b. Let n(x) = 0. What is x?
1, 2
Let s = 33349/18 - 16562/9. Suppose 2523/2*o - 435/2*o**2 + s*o**3 - 24389/10 = 0. Calculate o.
29/5
Suppose -2*r**5 - 62*r**2 - 224/3*r + 41/3*r**3 + 29/3*r**4 - 32/3 = 0. What is r?
-2, -1, -1/6, 4
Let x(j) = -14*j**4 - 184*j**3 - 591*j**2 - 579*j - 92. Let q(d) = -70*d**4 - 920*d**3 - 2954*d**2 - 2896*d - 456. Let f(o) = 5*q(o) - 24*x(o). Solve f(w) = 0.
-9, -2, -1/7
Suppose 4*r + o - 36 = -r, -2*r - o = -15. Suppose x - r = 18. Factor -35*n - 2*n**3 + 4*n**3 + 15 - 7*n**3 + x*n**2.
-5*(n - 3)*(n - 1)**2
Let o = 464476 + -464474. Factor 0 - 9/8*z**o + 0*z - 3/8*z**3.
-3*z**2*(z + 3)/8
Let v = 8454197/469 - 18026. Let b = v - -1867/1407. Suppose -8/3*j**2 + 128/15 + 10/3*j**3 + 2/15*j**5 - 32/3*j + b*j**4 = 0. What is j?
-4, 1
Let w be (1854/(-224))/(120/(-160)). Let g = w - 43/4. Solve 0 + 2/7*z**2 + 2/7*z - g*z**4 - 2/7*z**3 = 0.
-1, 0, 1
Suppose 5*h = -4*y + 659 + 1346, -h - 5*y = -380. Let o = h + -402. Factor 6/13*b**o + 0*b - 4/13*b**4 + 0 + 0*b**2 - 2/13*b**5.
-2*b**3*(b - 1)*(b + 3)/13
Let d(k) be the third derivative of k**5/600 - 359*k**4/60 + 128881*k**3/15 + 1405*k**2. Suppose d(u) = 0. What is u?
718
Determine u, given that -654/11*u**3 - 72/11 - 400/11*u - 214/11*u**4 - 10/11*u**5 - 778/11*u**2 = 0.
-18, -1, -2/5
Let q(a) be the first derivative of 2*a**6/9 - 188*a**5/45 + 76*a**4/3 - 640*a**3/9 + 896*a**2/9 - 64*a + 1319. Find i such that q(i) = 0.
2/3, 2, 9
Determine t so that 3720 + 7353*t - 504300*t**3 - 301896*t**2 - 347072*t**2 - 3747 + 152048*t**2 = 0.
-1, 3/410
Suppose x + 60 + 61 = 129. Factor -4/3*m**4 + x*m**3 + 0 + 0*m - 12*m**2.
-4*m**2*(m - 3)**2/3
Let j(q) = q**2 + 3*q - 37. Let o be (2 - 14/6)/(36/(-540)). Let k be j(o). Factor -2*y + 2/3*y**k + 0*y**2 - 4/3.
2*(y - 2)*(y + 1)**2/3
Let c = 880/7 + -4358/35. Let c*v**2 + 6/5 + 3*v = 0. Calculate v.
-2, -1/2
Let m(q) be the second derivative of q**6/50 - 201*q**5/100 - 3*q**4/20 + 203*q**3/10 - 201*q**2/5 - 549*q. Determine j, given that m(j) = 0.
-2, 1, 67
Let t be 7 - (-10 - -25 - 11). Factor -t*g**2 - 3/2*g**3 - 1/4*g**4 + 0 - 2*g.
-g*(g + 2)**3/4
Let l(t) = -272*t**3 - 544*t**2 - 132*t - 24. Let n = -524 + 525. Let s(u) = u**3 - 2*u**2 + 1. Let x(c) = n*l(c) + 16*s(c). Factor x(o).
-4*(o + 2)*(8*o + 1)**2
Let a(g) = 3*g**5 + 4*g**4 - 3*g**3 - 4*g**2 + 4*g. Let u be 8/16*(0 + 2). Let r(z) = z**5 + z**4. Let l(d) = u*a(d) - 2*r(d). Solve l(x) = 0 for x.
-2, 0, 1
Let t(x) = -x**2 + 11*x + 117. Let l be t(9). Suppose 0 = -j - 5*p + 15, 9*j - l = 5*j - 5*p. Solve -j - 2/5*d**2 + 8*d = 0 for d.
10
Let c(w) = w**2 - 1018*w + 15048. Let r be c(15). Factor 1/3*t**5 + t**r + 0 + 1/3*t**2 + 0*t + t**4.
t**2*(t + 1)**3/3
Let h(f) = -95*f**2 + 148820*f + 79097940. Let j(s) = -7*s**2 + 10630*s + 5649853. Let w(b) = 4*h(b) - 55*j(b). Solve w(i) = 0 for i.
-1063
Let z = 2569491/5 + -513887. Find x such that -54/5*x**2 + z*x**3 + 6/5*x**4 - 8 - 144/5*x = 0.
-10, -1, -1/3, 2
Let x = 3224 - 3221. Find n such that -n**2 + 0 - 1/4*n**x - n = 0.
-2, 0
Let d(b) be the third derivative of 1/120*b**6 - 1/24*b**4 - 7/120*b**5 + 0*b - 36*b**2 + 0*b**3 + 1/60*b**7 - 1. Factor d(c).
c*(c - 1)*(c + 1)*(7*c + 2)/2
Let d(k) be the third derivative of k**6/30 + 2*k**5/3 - 37*k**4/6 + 52*k**3/3 - 6719*k**2. Factor d(p).
4*(p - 2)*(p - 1)*(p + 13)
Let 3/2*v**5 + 265/2*v**3 + 40*v**4 + 46*v + 0 + 140*v**2 = 0. What is v?
-23, -2, -1, -2/3, 0
Let f(r) be the second derivative of r**7/126 - 2*r**6/45 - r**5/10 + r**4 - 3*r**3/2 + 3821*r. Factor f(s).
s*(s - 3)**2*(s - 1)*(s + 3)/3
Suppose 2*b = 4*k + 10, 0 = 3*b - 350*k + 352*k - 15. Let 20/3*z**2 - 8/3*z - 20/3*z**4 - 28/3*z**b + 0 + 12*z**3 = 0. What is z?
-1, 0, 2/7, 1
Suppose -495 - 243*u**2 - 3/2*u**3 + 1479/2*u = 0. Calculate u.
-165, 1, 2
Let v(x) be the third derivative of 1/480*x**6 - 5/1344*x**8 - x + 0*x**3 + 1/24*x**4 + 1/20*x**5 - 1/70*x**7 - 34*x**2 + 0. Suppose v(h) = 0. Calculate h.
-2, -1, -2/5, 0, 1
Let i(q) = -3*q**2 - 4848*q - 1958580. Let f(t) = -6*t**2 - 9696*t - 3917157. Let h(c) = -4*f(c) + 9*i(c). Suppose h(o) = 0. What is o?
-808
Let y be (-6027)/(-4655)*2 - (-16)/76. Suppose 24/5*v + 16/5 - 4/5*v**2 + 0*v**4 - y*v**3 + 2/5*v**5 = 0. Calculate v.
-2, -1, 2
Suppose 24*g - 22*g - 31*g = 55*g. Factor 4/5*f**3 + g - 4/5*f**5 + 4/5*f**2 - 4/5*f**4 + 0*f.
-4*f**2*(f - 1)*(f + 1)**2/5
Let m(i) be the second derivative of 3/2*i**6 + 5/2*i**2 + 5*i**3 + 35/6*i**4 + 2 + 4*i**5 + 2*i + 5/21*i**7. What is v in m(v) = 0?
-1, -1/2
Let k(s) = 3*s**3 + 45*s**2 - 6*s - 42. Let i be k(-15). Factor 34*b + 36*b - 3*b**2 + 81 - 196*b + i*b.
-3*(b - 1)*(b + 27)
Find q, given that 2788*q**2 + 623*q**3 + q**4 - 1833*q**2 + 96721*q + 96388*q**2 = 0.
-311, -1, 0
Factor -5*d + 5/4*d**2 - 120.
5*(d - 12)*(d + 8)/4
Suppose 2*b - 55 = -5*h, -5*b - 3*h - 2 = -92. Let a(i) be the first derivative of 1/10*i**6 - 3/4*i**4 - 3/25*i**5 + 0*i**2 - 3/5*i**3 - b + 0*i. Factor a(p).
3*p**2*(p - 3)*(p + 1)**2/5
Let q(o) be the first derivative of 6*o**5/5 + 8*o**4 + 2*o**3 - 10*o**2 + 174. Solve q(u) = 0 for u.
-5, -1, 0, 2/3
Suppose 316*g - 314*g - 2 = 3*i, g - 11*i = -18. Determine l so that 0*l - 15/2*l**3 + 9/4*l**g + 0 + 3/4*l**5 + 0*l**2 = 0.
-5, 0, 2
Let z = -419912 - -419918. Factor -16/3*t**3 - 20/3*t**2 + 2/3*t**4 + 16/3*t + z.
2*(t - 9)*(t - 1)*(t + 1)**2/3
Let x(f) be the third derivative of -f**8/112 + 11*f**7/14 + 117*f**6/40 - 163*f**5/20 - 113*f**4/2 - 114*f**3 - 108*f**2 + 8*f. Determine u so that x(u) = 0.
-2, -1, 2, 57
Let u(k) be the first derivative of 130*k**4 - 210*k**3 + 105*k**2/2 + 5*k - 4558. Let u(o) = 0. Calculate o.
-1/26, 1/4, 1
Let q(a) = 848*a + 11074. Let l be q(-13). Suppose -15/2*o - 3*o**2 + 1/2*o**3 + l = 0. What is o?
-4, 5
Let c(t) be the first derivative of 1/90*t**6 + 0*t**4 - 29/3*t**3 + 1/15*t**5 + 0*t**2 + 0*t - 1. Let f(j) be the third derivative of c(j). Factor f(o).
4*o*(o + 2)
Let 480 - 1832/5*m - 4/5*m**3 + 324/5*m**2 = 0. Calculate m.
2, 4, 75
Suppose -10*z = -19*z. Let x(r) be the third derivative of 1/570*r**5 + 0*r**4 + 1/665*r**7 + 1/380*r**6 + 0 - 3*r**2 + 0*r**3 + 1/3192*r**8 + z*r. Factor x(s).
2*s**2*(s + 1)**3/19
Factor 8*i**4 + 10*i**4 - 13*i**4 - 5*i**3 - 97*i**2 - 113*i**2.
5*i**2*(i - 7)*(i + 6)
Let v be -8 - (-19 + 6) - 0/(-4). Let k(w) be the second derivative of -12*w**2 + 2*w**4 - 9*w + 2/3*w**3 - 1/5*w**v + 0. Determine q, given that k(q) = 0.
-1, 1, 6
Let d be (-4)/5 + (-124)/20. Let v be -8*d/84 - 8/12. Factor 0*j - 2/3*j**3 + 0 + v*j**2.
-2*j**3/3
Let z(l) be the third derivative of 0*l + 0*l**4 + 0 - 1/60*l**6 - 1/15*l**5 - 41*l**2 + 0*l**3. Factor z(o).
-2*o**2*(o + 2)
Let i(g) be the first derivative of -4*g**5/5 + 294*g**4 - 29584*g**3 + 169940*g**2 - 252300*g - 2701. Find n such that i(n) = 0.
1, 3, 145
Let h be -235*(-29)/(-2900)*(-4)/3 + -3. Let i(r) be the second derivative of h*r**3 + 0 - 1/15*r**4 - 32*r + 4/5*r**2. Suppose i(x) = 0. What is x?
-1, 2
Let j = 2354/1407 + -3/469. Let v(y) = y**2 - y. Let h be v(0). Factor 5/3*u**2 - j + h*u.
5*(u - 1)*(u + 1)/3
What is v in -1 + 5 + 4773*v + 24*v**2 - 4656*v + 5*v**2 = 0?
-4, -1/29
Let t be 6452/(-95167)*(-118)/4. Factor -1/3*k**4 + t*k**3 - 16/3 - 1/3*k**2 - 8*k.
-(k - 4)**2*(k + 1)**2/3
Let j be 12*3/(-24)*-2. Solve 12*p**2 - 20 + 2*p**3 + 23*p**j - 100*p - 7*p**2 = 0 for p.
-2, -1/5, 2
Let t(p) = 2*p**3 - 9*p**2 + 23*p - 14. Suppose 0 = -16*i + 21*i + 20. Let a(k) = -k**3 - k**2. Let c(l) = i*a(l) - 4*t(l). Factor c(b)