6
Let a(z) = -6 + 3*z**2 + 18 + 6*z + z. Let c be a(-4). Factor -4*s**5 - 8*s**2 - 41*s - c*s + 8*s**4 + 77*s.
-4*s*(s - 1)**3*(s + 1)
Let w be (-31)/14 + 315/70. Determine t, given that 8/7*t**3 - 2/7*t**5 + 0 - 4/7*t**4 + w*t**2 + 0*t = 0.
-2, 0, 2
Let r(g) be the third derivative of g**6/30 + 2*g**5/3 + 37*g**4/24 + 3*g**3/2 + 23*g**2 - 6. Factor r(v).
(v + 9)*(2*v + 1)**2
Determine u, given that 180*u**3 - 62249*u - 8*u**5 + 3*u**5 + 62249*u + 160*u**2 + 15*u**4 = 0.
-4, -1, 0, 8
Let x(g) be the third derivative of -g**8/84 + 2*g**7/15 - 11*g**6/30 + g**5/3 - 2591*g**2. Find c such that x(c) = 0.
0, 1, 5
Let q(h) be the second derivative of -3*h**5/80 - 43*h**4/16 + 89*h**3/8 - 135*h**2/8 + 246*h + 1. Factor q(k).
-3*(k - 1)**2*(k + 45)/4
Let i(z) be the third derivative of z**7/490 - 129*z**6/140 + 16641*z**5/140 + 1452*z**2. Factor i(u).
3*u**2*(u - 129)**2/7
Factor 10364/5*t + 2/5*t**2 + 13426562/5.
2*(t + 2591)**2/5
Let g be ((-2)/(-8))/(((-85)/(-204))/5). Let p(v) be the second derivative of 5*v**g - 7*v + 1/4*v**4 + 0 + 75/2*v**2. Determine r, given that p(r) = 0.
-5
Let l(z) be the first derivative of -10/3*z**6 + 0*z + 25/3*z**3 - 5*z**2 + 15*z**4 + z**5 - 67. Determine u so that l(u) = 0.
-1, 0, 1/4, 2
Let s = -124 + 133. Let h(o) be the first derivative of 17*o**2 + 0*o**3 - s*o**2 + 3*o - 28 + 4*o**3 - 2*o**2. Factor h(d).
3*(2*d + 1)**2
Let g = 71908/65 + -14366/13. Suppose 0 - 18/5*f - 3/5*f**2 + g*f**3 = 0. Calculate f.
-3/2, 0, 2
Let h(i) = i**2 + 12*i + 1. Let u(r) = -7*r**2 + 2806*r - 400447. Let x(k) = -2*h(k) - u(k). Solve x(d) = 0 for d.
283
Factor -276/7 + 276/7*k**2 + 2/7*k**3 - 2/7*k.
2*(k - 1)*(k + 1)*(k + 138)/7
Determine j, given that -160*j**3 - 2816000/19*j - 171200/19*j**2 + 62/19*j**4 - 15680000/19 + 2/19*j**5 = 0.
-20, 49
Let h(l) be the first derivative of l**3/6 + l**2/4 + 24. Find p, given that h(p) = 0.
-1, 0
Let y(m) be the second derivative of m**5/16 - 5*m**4/8 - 225*m**3/8 - 250*m**2 + 2*m - 2049. Factor y(w).
5*(w - 16)*(w + 5)**2/4
Suppose -24*u + 1080 = -16*u. Let t be 3/(u/84) + 30/225. Factor 2*p - 18/7*p**t + 10/7*p**3 - 2/7*p**4 - 4/7.
-2*(p - 2)*(p - 1)**3/7
Suppose 2*k = 5*o - 3003, -2*k - 2*o = 3*k + 7464. Let m = 1496 + k. Factor 2*z + 0 + z**4 - 4*z**m - 1/2*z**3.
z*(z - 2)*(z + 2)*(2*z - 1)/2
Let 17*n**3 + 625/3*n + 1/3*n**4 + 0 + 225*n**2 = 0. What is n?
-25, -1, 0
Let c(t) = t**2 + 65*t - 5. Let f(k) = 3*k**2 + 228*k - 18. Let p(g) = -18*c(g) + 5*f(g). Factor p(a).
-3*a*(a + 10)
Suppose 0 = 53*x - 64*x + 462. Solve 160 - 316 + 156 - 22*p - 2*p**4 + x*p**2 - 18*p**3 = 0.
-11, 0, 1
Let k(d) = -2*d + 489. Let x be k(10). Let j = x + -465. Factor 4/5*u**4 + 36/5*u**2 + j*u**3 + 8/5 + 28/5*u.
4*(u + 1)**3*(u + 2)/5
Determine g so that 0 + 0*g + g**5 + 280/3*g**4 - 190/3*g**2 - 159*g**3 = 0.
-95, -1/3, 0, 2
Let s(l) be the first derivative of 39*l**5 + 1265*l**4/2 - 65*l**3/3 + 2531. Let s(w) = 0. What is w?
-13, 0, 1/39
Factor -800 - 210*w - 5/2*w**2.
-5*(w + 4)*(w + 80)/2
Let f(z) be the second derivative of z**7/189 + 4*z**6/9 + 899*z**5/90 - 10*z**4/9 - 100*z**3/3 + 2642*z. Solve f(v) = 0 for v.
-30, -1, 0, 1
Suppose 0 = -65*f - 96*f + 255*f + 215*f. Let n(k) be the second derivative of 0 + 3/40*k**5 - 1/120*k**6 + f*k**2 + 1/48*k**4 - 1/4*k**3 + 30*k. Factor n(w).
-w*(w - 6)*(w - 1)*(w + 1)/4
Let a(i) = i**2 - 13*i - 12. Let l be a(14). What is w in 7*w**3 + 35*w + 50*w**2 - 25*w**l - 2*w**3 + 15 = 0?
-3, -1
Let w(o) be the second derivative of o**5/30 - o**4 - 28*o**3/3 - 88*o**2/3 - 498*o + 3. Find m such that w(m) = 0.
-2, 22
Let a(w) be the first derivative of 46 + 5/2*w**2 - 25/3*w**3 + 25*w - 5/4*w**4. Solve a(k) = 0.
-5, -1, 1
Let a = -1373 + 1372. Let t be (4/a)/(1560/(-180)). Let -t*w - 2/13 - 6/13*w**2 - 2/13*w**3 = 0. What is w?
-1
Let y(m) be the second derivative of m**6/10 - 11*m**5/20 + 5*m**4/12 + m**3/2 + 855*m. Suppose y(c) = 0. What is c?
-1/3, 0, 1, 3
Let y = -984 + 368. Let v be (-368)/y*7 + -4. Suppose -6/11*r**3 + 0 - v*r**4 + 0*r - 4/11*r**2 = 0. Calculate r.
-2, -1, 0
Let k = 184 - 170. What is j in 15 - 2*j**4 - 21 - 6 + 6*j**2 - 6*j**3 + k*j = 0?
-3, -2, 1
Suppose 0 = -4945*f + 4955*f. Let x(p) be the second derivative of 16*p + 1/3*p**4 + 2*p**2 + f + 4/3*p**3. Factor x(o).
4*(o + 1)**2
Suppose 131 + 130 = 29*h. Factor -6*u**2 + 17*u**2 - 2*u**4 - 7*u + h*u**2 + 14*u**3 - 15*u - 10*u.
-2*u*(u - 8)*(u - 1)*(u + 2)
Let p(t) be the third derivative of 85/12*t**4 + 0*t - 1 + 7225/6*t**3 + 1/60*t**5 + 27*t**2. Find o, given that p(o) = 0.
-85
Let w(i) be the third derivative of -i**8/112 + 59*i**7/70 - 191*i**6/8 + 2521*i**5/20 - 301*i**4 + 392*i**3 - 556*i**2. Solve w(n) = 0 for n.
1, 28
Let c = -32 + 34. Suppose -k + 66 = c*k + 3*z, 76 = 4*k - 2*z. Suppose -k*t - 5*t**3 - t**2 + 20*t = 0. Calculate t.
-1/5, 0
Let c(j) be the second derivative of -j**5/10 + 23*j**4/3 - 88*j**3/3 + 2*j - 1908. What is m in c(m) = 0?
0, 2, 44
Let x(y) be the third derivative of y**6/120 + 121*y**5/30 + 5187*y**4/8 + 18252*y**3 - 2*y**2 - 200*y + 7. Factor x(t).
(t + 8)*(t + 117)**2
Let q(i) = -i**2 + 44*i - 336. Let d be q(10). Suppose -3*w + 2*b - 14 = -17, 0 = -d*w - 4*b + 24. Solve 0 - 2/5*y**w - 6/5*y**2 - 4/5*y = 0 for y.
-2, -1, 0
Let r = -77 - -80. Determine q, given that 50*q + 7*q**2 - q**r + 15*q**2 + 3*q**3 + 56 + 14*q = 0.
-7, -2
Let c be ((-33165)/(-630) - 53)*63/(-60). Let -1/4 - c*a - 1/8*a**2 = 0. Calculate a.
-2, -1
Let o(b) be the first derivative of -b**5/20 + b**4/6 + b**3/2 - 22*b - 83. Let z(l) be the first derivative of o(l). Factor z(n).
-n*(n - 3)*(n + 1)
Let a(z) be the second derivative of z**4/120 + 37*z**3/60 + 58*z**2/5 + 6136*z. Suppose a(l) = 0. What is l?
-29, -8
Let s(a) be the first derivative of a**5/11 + a**4/22 - 56*a + 8. Let l(c) be the first derivative of s(c). Let l(b) = 0. Calculate b.
-3/10, 0
Let q be (-9)/15*(15600/64)/(-15). Determine a, given that -q*a + 5/3*a**2 - 1/12*a**3 + 27/2 = 0.
2, 9
Let y(b) be the first derivative of -7*b**3/3 + 27*b**2/8 + b/4 + 1586. Suppose y(g) = 0. Calculate g.
-1/28, 1
Let s(q) be the first derivative of 4/7*q**3 + 50/7*q**2 + 32/7*q + 89. Let s(l) = 0. What is l?
-8, -1/3
Suppose 28134*i + 4*v = 28137*i - 41, 0 = -2*i - 3*v - 18. Solve 0 + 8*x**2 + 0*x + 4/5*x**4 + 28/5*x**i = 0 for x.
-5, -2, 0
Let w = -233264 - -1166321/5. Suppose -4/5*j + 1 - 6/5*j**2 + 4/5*j**3 + w*j**4 = 0. Calculate j.
-5, -1, 1
Let y(l) be the first derivative of 1/2*l**6 + 0*l**2 + 0*l**3 + 0*l + 220 - 3/2*l**5 + 3/4*l**4. Factor y(z).
3*z**3*(z - 2)*(2*z - 1)/2
Suppose 0 = 34*t - 14*t + 100. Let r be 15/t - (-4 + -2). Solve 4/3*g**4 + 2*g - 8/3*g**r + 2/3*g**5 - 4/3*g**2 + 0 = 0 for g.
-3, -1, 0, 1
Let n = 7535/1239 + -655/177. Factor -52/21*c + 2/21*c**2 + n.
2*(c - 25)*(c - 1)/21
Factor -x**4 + 15097*x**3 - 64 - 5*x**4 - 64*x + 8*x**4 + 12*x**2 - 15083*x**3.
2*(x - 2)*(x + 1)*(x + 4)**2
Let p(x) = -x + 4. Let m = 41 + -41. Let q be p(m). Determine b so that -21*b**2 - b**4 + 17*b**4 + 8*b**3 - 12*b**5 + q*b + 5*b**2 = 0.
-1, 0, 1/3, 1
Let r(u) = u**2 + 29*u - 555. Let g be r(-31). Let z = -2463/5 - g. Determine v, given that 12/5*v + 18/5 - z*v**4 - 16/5*v**2 - 12/5*v**3 = 0.
-3, -1, 1
Let y be (81031 + -81029)/(7/6 + 2/(-3)). Factor -1/4*c**2 + y*c - 15/4.
-(c - 15)*(c - 1)/4
Let a(k) be the second derivative of -k**6/240 - 67*k**5/160 - 1277*k**4/96 - 5177*k**3/48 - 2883*k**2/8 - 1584*k. Solve a(z) = 0 for z.
-31, -3, -2
Let f(h) be the third derivative of h**8/110880 + h**7/3080 - h**6/396 + 21*h**5/5 + 3*h**2 + 16. Let i(c) be the third derivative of f(c). Factor i(s).
2*(s - 1)*(s + 10)/11
Let s(k) be the first derivative of k**4/6 - 40*k**3/9 + 68*k**2/3 - 128*k/3 + 984. Solve s(c) = 0 for c.
2, 16
Let m(a) = -17*a**3 + 38*a**2 - 60*a + 24. Let f(o) = 14*o**3 - 38*o**2 + 62*o - 26. Let v(y) = -5*f(y) - 4*m(y). Factor v(z).
-2*(z - 17)*(z - 1)**2
What is d in -224/9 - 2/9*d**2 + 116/9*d = 0?
2, 56
Let r(g) be the first derivative of 4*g**5/5 - 14*g**4 + 116*g**3/3 + 352*g**2 - 768*g + 116. Factor r(m).
4*(m - 8)**2*(m - 1)*(m + 3)
Let j(t) be the second derivative of -t**5/4 + 415*t**4/12 - 1585*t**3/2 - 5175*t**2/2 + 9239*t. Solve j(u) = 0.
-1, 15, 69
Suppose -29*y = -3*y - 25*y - 3. What is m in -35/4*m**4 + 33/2