he third derivative of r**6/30 + 38*r**5/5 + 111*r**4/2 - 4982*r**2. Factor z(y).
4*y*(y + 3)*(y + 111)
Let l = -62960 + 314812/5. Factor 2/5*j**3 + 0 + l*j**2 + 18/5*j.
2*j*(j + 3)**2/5
Let v(f) be the first derivative of 1/2*f**6 - 24/5*f**5 - 3/4*f**4 - 15 + 0*f + 0*f**2 + 8*f**3. Factor v(q).
3*q**2*(q - 8)*(q - 1)*(q + 1)
Let g = 261347 - 261343. Determine t so that 0 + 0*t**g + 0*t**2 + 0*t - 1/3*t**3 + 1/3*t**5 = 0.
-1, 0, 1
Let f(o) = 6*o**4 - 61*o**2 - 5*o**4 + 5 - 21*o - 13*o**3 - 31*o**2 + 115*o**2. Let l(y) = y**3 - y**2 + y. Let c(u) = f(u) + 5*l(u). Solve c(x) = 0 for x.
1, 5
Let w(x) be the second derivative of -4/9*x**4 - 1/30*x**5 + 3 + 1/9*x**3 + 8/3*x**2 + 15*x. Factor w(y).
-2*(y - 1)*(y + 1)*(y + 8)/3
Let z(d) be the first derivative of -7/9*d**2 + 2/27*d**3 + 20/9*d - 115. Factor z(v).
2*(v - 5)*(v - 2)/9
Let l be (2 + 216/(-21))/((-66)/(-15)). Let v = l + 27/11. What is m in 2/7*m**5 + 8/7*m**3 - 10/7*m - 8/7*m**4 + 4/7*m**2 + v = 0?
-1, 1, 2
Suppose -4*y + 2*o + 18 = 0, 3*y - 4*o = 2*y + 22. Let m(d) = -2*d**2 + 9*d + 11. Let k be m(5). Factor -5*h**y - 3 + 4 - k - 10*h.
-5*(h + 1)**2
Let z be 14 + 5 - (81096/(-217))/(-24). What is k in -1/7*k**2 + 6/7*k**3 - 1/7*k**4 - 16/7 - z*k = 0?
-1, 4
Suppose 160/11*s**3 + 368/11*s**2 + 2/11*s**5 - 288 - 1824/11*s - 38/11*s**4 = 0. What is s?
-2, 6, 11
Let k(d) be the second derivative of -d**6/105 + d**5/35 + 13*d**4/14 - 40*d**3/21 - 400*d**2/7 - 776*d. Factor k(l).
-2*(l - 5)**2*(l + 4)**2/7
Let g(h) be the first derivative of 4*h**3/3 + 48*h**2 - 100*h - 2650. Find y such that g(y) = 0.
-25, 1
Suppose 4*b = -q - 0*b - 1, -3*q + 7 = 2*b. Let z = 554/183 - 144/61. Determine r, given that 19/6*r**q + z + 11/2*r**2 + 7/2*r + 1/2*r**4 = 0.
-4, -1, -1/3
Let n(o) be the first derivative of 4/7*o**3 - 12/35*o**5 - 10/7*o**2 + 0*o + 19/28*o**4 + 1/42*o**6 - 147. Solve n(t) = 0 for t.
-1, 0, 1, 2, 10
Let x = 1629 - 768. Determine z, given that -801*z - 6*z**2 + 12 + x*z - 27*z**2 = 0.
-2/11, 2
Let a be ((-4488)/(-170) + -12)*5. Let -96 - 27/2*w**2 + a*w + 3/4*w**3 = 0. Calculate w.
2, 8
Let i(s) = 31*s**2 - 78*s - 207. Let j(k) = 57*k**2 - 155*k - 417. Let p(m) = -11*i(m) + 6*j(m). Factor p(g).
(g - 75)*(g + 3)
Let t(k) be the first derivative of -2/25*k**5 - 7/20*k**4 - 1/5*k**3 + 4/5*k**2 - 20 + 4/5*k. Suppose t(s) = 0. Calculate s.
-2, -1/2, 1
Let x(i) be the second derivative of 5*i**7/42 - 51*i**5/2 + 250*i**4/3 - 165*i**3/2 + 175*i + 2. Solve x(o) = 0.
-11, 0, 1, 9
Let l(q) be the first derivative of -q**4/4 - 2*q**3 + 2*q**2 + 24*q - 3858. Factor l(h).
-(h - 2)*(h + 2)*(h + 6)
Let h be -37 + 15 - -32*48/60. Factor 12/5*i**2 + 0 - 6/5*i**3 + h*i.
-6*i*(i - 3)*(i + 1)/5
Let x = -469 + 472. Let s be ((-36)/(-8) + 6/(-2))/x. Factor -s*m**2 - 5*m - 25/2.
-(m + 5)**2/2
Factor 41*t + 29/3*t**2 - 7/3*t**3 - 1/3*t**4 - 120.
-(t - 3)**2*(t + 5)*(t + 8)/3
Let k be -11 + (-11)/((-154)/210). Let c(t) be the second derivative of -1/8*t**5 + 1/120*t**6 + 5/12*t**3 - 11*t + 1/2*t**k + 0 - 25/8*t**2. Factor c(q).
(q - 5)**2*(q - 1)*(q + 1)/4
Factor -2/7*s**5 - 594/7*s**4 - 131420/7*s**2 - 6174 - 18606*s - 44988/7*s**3.
-2*(s + 1)**3*(s + 147)**2/7
Let h = -1601 - -1605. Suppose -b + h = -4*w, 73 = -3*w + 4*b + 57. Find i, given that w - 192/11*i**2 - 24/11*i**4 - 2/11*i**5 - 104/11*i**3 - 128/11*i = 0.
-4, -2, 0
Let t(b) be the second derivative of 1/90*b**5 + 0 - 2/9*b**2 + 1/27*b**4 - 1/27*b**3 - 8*b. Let t(j) = 0. What is j?
-2, -1, 1
Let l(v) be the first derivative of 0*v - 1/8*v**3 - 86 + 15/16*v**2. Suppose l(a) = 0. What is a?
0, 5
Let q(r) be the second derivative of -r**4/8 + 85*r**3 - 21675*r**2 - 844*r. Determine g, given that q(g) = 0.
170
Let m(i) be the third derivative of -i**6/2160 - i**5/90 + 5*i**4/36 + 11*i**3/3 - 36*i**2. Let d(t) be the first derivative of m(t). Find q such that d(q) = 0.
-10, 2
Suppose -30*h - 31*h = 17*h. Let k(j) be the first derivative of 0*j**5 - 2/9*j**4 + 0*j**3 + 1/27*j**6 + h*j**2 - 12 + 0*j. Suppose k(z) = 0. What is z?
-2, 0, 2
Let g(n) = n**2. Let o(w) = 4*w**2 - 469*w + 470*w - 3*w**2. Let c(q) = -q. Let m(j) = 2*c(j) + 4*o(j). Let s(y) = -5*g(y) + m(y). Determine t so that s(t) = 0.
0, 2
Let p(v) be the second derivative of v**6/315 + v**5/105 - 2*v**3/63 - v**2/21 + 1442*v. Factor p(a).
2*(a - 1)*(a + 1)**3/21
Let z(g) be the third derivative of -90*g**2 + 0*g - 1/195*g**6 + 1/130*g**5 + 0*g**4 + 0 + 1/546*g**8 + 0*g**3 - 1/455*g**7. Suppose z(r) = 0. What is r?
-1, 0, 3/4, 1
Let o(i) be the second derivative of -i**5/20 - 5*i**4/6 + 7*i**3/3 + 35*i**2/2 + 31*i. Let v be o(-11). Factor 51*y**3 - 5*y**5 - 50*y**3 + v*y**4 + 6*y**5.
y**3*(y + 1)**2
Let b(p) be the first derivative of -5*p**4/12 + 1465*p**3/9 + 2945*p**2/6 + 1475*p/3 - 792. Factor b(i).
-5*(i - 295)*(i + 1)**2/3
Let j(o) be the third derivative of -o**6/600 + 31*o**5/300 - o**4/4 + 281*o**2. What is k in j(k) = 0?
0, 1, 30
Let f(w) = 3*w + 1. Let j(y) = -y**2 - 17*y - 43. Let z(o) = -2*f(o) - 2*j(o). Let b be z(-10). Determine l so that 0 + 10/3*l**3 + 5*l**b + 0*l + 0*l**2 = 0.
-2/3, 0
Let c(d) be the first derivative of -1/21*d**6 + 2/35*d**5 - 2/21*d**3 + 0*d + 246 + 1/14*d**4 + 0*d**2. Solve c(m) = 0.
-1, 0, 1
Suppose -x - 11*n - 11 - 64 = 0, n + 1 = -3*x. Factor 485/3*f + 5/6*f**x + 47045/6.
5*(f + 97)**2/6
Let w(y) be the third derivative of -y**6/60 - 43*y**5/30 - 10*y**4 + y**2 + 640*y. Find a such that w(a) = 0.
-40, -3, 0
Let n = 44 + -29. Suppose 2*s - 5 = a, 2*a = -8*s + 10*s - 2. Determine h, given that 703*h + h**a + 4*h**3 - 708*h + 15 - n*h**2 = 0.
-1, 1, 3
Let z(g) be the third derivative of 0*g**5 + 1/240*g**6 - 63*g**2 + 0*g**4 + 0 + 0*g**3 + 0*g. Solve z(n) = 0.
0
Let p(r) be the second derivative of -r**6/90 + 13*r**5/60 - 11*r**4/18 + 2866*r. What is u in p(u) = 0?
0, 2, 11
Let d(m) = -8*m - 12. Let a be d(-7). Suppose -1103 - a*j - 3*j**2 + 1175 + 7*j**2 = 0. Calculate j.
2, 9
Let o = -243403/7 + 34772. Factor -1/7*m**2 - o*m + 6/7.
-(m - 2)*(m + 3)/7
Suppose 8 = -u + p, -4*p - 4 = 2*u - 6. Let c be (u*(-2)/42)/((-25)/(-30)). Factor -c*g**3 - 8/7*g**2 + 0 - 8/7*g.
-2*g*(g + 2)**2/7
Let l(u) = -2*u**3 - 259*u**2 + 492*u - 127. Let v(t) = t**2 + 11*t + 1. Let n(w) = 3*l(w) - 24*v(w). Factor n(f).
-3*(f - 1)*(f + 135)*(2*f - 1)
Let f(q) be the third derivative of 28/3*q**3 - 5/6*q**4 + 0*q - 73*q**2 - 8/15*q**5 + 0 - 1/30*q**6. Factor f(m).
-4*(m - 1)*(m + 2)*(m + 7)
Suppose -1520 = -5*z - 2*x, -4*z + 2*z = -3*x - 608. Suppose -296*m - 32 = -z*m. Factor 2/11*u + 2/11*u**5 - 2/11 + 4/11*u**2 - 2/11*u**m - 4/11*u**3.
2*(u - 1)**3*(u + 1)**2/11
Suppose 113*r + 8 = 117*r. Let j = 3898/3 - 1296. Factor j*p**3 + 0 + r*p - 16/3*p**2.
2*p*(p - 1)*(5*p - 3)/3
Let j(x) be the second derivative of -x**6/105 - 4*x**5/35 + x**4/42 + 8*x**3/21 - 422*x. Factor j(k).
-2*k*(k - 1)*(k + 1)*(k + 8)/7
Suppose 4*h + 3*c - 948 = 0, 4*h + c - 1083 = -127. Let o = h - 237. Let -2*p - 1/2*p**o + 0 - 2*p**2 = 0. What is p?
-2, 0
Let r = 1596 - 1612. Let f be (-95)/(-10) + 144/r. Factor -1/2 - f*a**3 + 1/2*a**2 + 1/2*a.
-(a - 1)**2*(a + 1)/2
Suppose 652*z + 3256/5 + 4/5*z**2 = 0. What is z?
-814, -1
Let m(b) be the first derivative of -b**4/2 + 454*b**3/3 + b**2 - 454*b - 3968. Factor m(v).
-2*(v - 227)*(v - 1)*(v + 1)
Suppose -4 + 4 = 8*s. Factor 2*b**4 + b**3 + s*b**3 + 0*b**3 + 3*b**3.
2*b**3*(b + 2)
Let t = -12058 - -12062. Let f(b) be the first derivative of -11 - 5/4*b - 5/8*b**2 - 1/4*b**5 + 5/6*b**3 + 5/8*b**t - 5/24*b**6. Solve f(q) = 0.
-1, 1
Let v(p) be the third derivative of 0*p - 1/240*p**5 - 5/8*p**3 - 17*p**2 - 1/12*p**4 + 0. Factor v(a).
-(a + 3)*(a + 5)/4
Let v(t) = t**4 - 138*t**3 + 2016*t**2 - 7682*t - 24580. Let o(a) = -a**4 - a - 2. Let q(l) = -2*o(l) + v(l). Factor q(c).
3*(c - 16)**3*(c + 2)
Let t = -246533/160 - -9245/6. Let g(j) be the third derivative of 0*j - 3/32*j**4 + 0 + 1/6*j**3 - t*j**6 + 26*j**2 + 1/40*j**5. Factor g(n).
-(n - 4)*(n - 1)**2/4
Factor 3/2*s**3 - 39/2*s**2 + 2376 - 180*s.
3*(s - 12)**2*(s + 11)/2
Let n be 11 + (-9 - (-3 - 0)). Let v(x) be the third derivative of 0*x**3 + 15*x**2 + 1/12*x**4 + 0*x - 2/15*x**n + 0. Determine j so that v(j) = 0.
0, 1/4
Suppose 0 = -5*v - 20, -5*t - v + 0 = -11. Factor 6*p**2 - 5*p + 2*p**t + 3*p**2 + 5