e of f**7/504 + f**6/3 - 53*f**4/6 + 213*f**2. Let k(a) be the second derivative of s(a). Factor k(g).
5*g*(g + 48)
Let m(w) be the third derivative of -w**6/1080 - 109*w**5/540 + 56*w**4/27 - 226*w**3/27 + 94*w**2 - 4. Determine n, given that m(n) = 0.
-113, 2
Let p = 143017 + -143015. Let -4/3*a**p + 28*a + 0 = 0. Calculate a.
0, 21
Suppose 5/2*g + g**2 - 1 - 5/2*g**3 = 0. Calculate g.
-1, 2/5, 1
Find x, given that -3/8*x**5 - 3315/8*x - 303/4*x**2 - 2025/8 + 315/4*x**3 - 57/8*x**4 = 0.
-27, -1, 5
Factor 4/3*l**3 - 100/3*l**2 + 868/3 - 772/3*l.
4*(l - 31)*(l - 1)*(l + 7)/3
Let r(s) be the second derivative of 1/56*s**7 - 3/80*s**5 + 1/16*s**4 - 6*s + 2 + 0*s**2 - 1/40*s**6 + 0*s**3. What is q in r(q) = 0?
-1, 0, 1
Let k(w) be the second derivative of w**6/6 - 67*w**5/10 + 3289*w**4/60 + 536*w**3 + 1440*w**2 + 2*w + 100. Factor k(x).
(x - 15)**2*(5*x + 8)**2/5
Let w = -8146 + 8151. Let h(n) be the second derivative of 0*n**3 + 0*n**2 + 3/140*n**w + 0 - 2/105*n**6 + 10*n + 3/14*n**4 - 1/294*n**7. What is m in h(m) = 0?
-3, 0, 2
Let v(u) be the third derivative of -5/3*u**3 + 4/7*u**7 - 1/6*u**6 - 11/6*u**5 + 65/24*u**4 + 30 - 15/112*u**8 - 5*u**2 + 0*u. Determine h so that v(h) = 0.
-1, 1/3, 1, 2
Let c(n) be the first derivative of -n**5 - 15*n**4/4 + 50*n**3/3 + 1559. Solve c(r) = 0.
-5, 0, 2
Let m = 1024/105 - 112/15. Let p(x) be the first derivative of 4/7*x**2 + 1/28*x**4 + 4 + m*x - 1/3*x**3. Factor p(b).
(b - 4)**2*(b + 1)/7
Suppose -20*y**3 - 91343*y**2 + 45661*y**2 + 4870*y + 1200 + 45957*y**2 = 0. What is y?
-10, -1/4, 24
Let o(r) = -12*r + 4*r + 10 + r**2 + 5. Let k be o(7). Find d, given that -14*d**3 + 21*d**4 + 4*d**2 - 2*d**2 - 23*d**4 + k*d + 6*d**3 = 0.
-4, -1, 0, 1
Let k = 49 - 48. Let f be (-7)/7*(k + 0). Let o(h) = h**3 + h**2 + h. Let a(n) = -2*n**3 - 5*n**2 - 2*n. Let s(w) = f*a(w) - 3*o(w). Solve s(j) = 0.
0, 1
Let v(y) be the first derivative of 0*y - 95 - 1/5*y**3 - 1/10*y**6 + 0*y**2 + 3/20*y**4 + 3/25*y**5. Factor v(h).
-3*h**2*(h - 1)**2*(h + 1)/5
Determine l, given that 11*l**2 - 24*l**2 - 6*l**3 + 24 + 16*l - 9*l**2 - 12*l**2 = 0.
-6, -2/3, 1
Let n = -6/7265 - -7301/43590. Factor -1/6*w**3 + 0*w + n*w**4 - 1/3*w**2 + 0.
w**2*(w - 2)*(w + 1)/6
Let i = 32 - 28. Let f(s) = -2494*s + 4991. Let a be f(2). Factor -32/3*d**2 + 0 - 10/3*d**i - 38/3*d**a + 8/3*d.
-2*d*(d + 2)**2*(5*d - 1)/3
Let p(l) = 5*l**5 - 7*l**4 - l**3 + 38*l**2 - 7*l - 31. Let a(h) = 2*h**5 - 2*h**3 + h**2 - h - 1. Let w(m) = -6*a(m) + 2*p(m). Let w(r) = 0. What is r?
-7, -2, -1, 1, 2
Factor 6*n**3 - 193*n**2 + 480*n + 42*n**3 - 256 - n**4 - 78*n**3.
-(n - 1)**2*(n + 16)**2
Let h be ((-432)/(-28))/(-19 - (-20761)/1092). Suppose 27*o**2 + 3/4*o**3 + h + 324*o = 0. What is o?
-12
Let t = -91 - -99. Let a(r) = -r**3 + 7*r**2 + 7*r + 10. Let g be a(t). What is x in 2/9*x**5 + 0*x + 0*x**3 + 0*x**4 + 0 + 0*x**g = 0?
0
Let c(k) be the third derivative of -k**6/480 + 5*k**5/48 + 9*k**4/16 - 2*k**2 + 748. Factor c(a).
-a*(a - 27)*(a + 2)/4
Let v(i) = -13*i**4 + 706*i**3 - 2131*i**2 + 1418*i - 4. Let f(o) = -87*o**4 + 4941*o**3 - 14916*o**2 + 9927*o - 27. Let t(r) = -4*f(r) + 27*v(r). Factor t(p).
-3*p*(p - 2)*(p - 1)*(p + 237)
Let u(w) = w**2 + 23*w + 47. Let b be u(-21). Find r such that 40*r**3 + 20*r**2 + 25*r**4 - r**5 + 5*r**5 + r**b = 0.
-2, -1, 0
Let x(y) be the first derivative of -6*y**5/35 + 81*y**4/14 - 102*y**3/7 + 75*y**2/7 - 883. Determine f, given that x(f) = 0.
0, 1, 25
Let j(g) be the first derivative of -13 + 0*g**3 - 1/24*g**4 + 0*g + 4*g**2 - 1/12*g**5. Let t(l) be the second derivative of j(l). Factor t(i).
-i*(5*i + 1)
Let p(d) be the third derivative of -5*d**8/336 + d**7/6 - 3*d**6/4 + 5*d**5/3 - 5*d**4/3 + 101*d**2. Suppose p(g) = 0. Calculate g.
0, 1, 2
Find h, given that -65/3 - 1/2*h**2 + 197/6*h = 0.
2/3, 65
Suppose 2*o + 28 = -12204*g + 12209*g, 4*g + 5*o = -4. Find v, given that -8/3*v + 0 + 4/3*v**5 + g*v**4 - 4*v**2 + 4/3*v**3 = 0.
-2, -1, 0, 1
Suppose -1065*n**2 - 9 + 243*n - 2750/3*n**4 + 5075/3*n**3 = 0. What is n?
1/22, 3/5
Let j be (-92)/207*3/4*0. Let r(m) be the first derivative of 5/2*m**2 + 17 + j*m + 5/4*m**4 - 10/3*m**3. Suppose r(d) = 0. What is d?
0, 1
Let o(y) be the third derivative of -29/480*y**6 + 8/15*y**5 + 1/420*y**7 + 3*y**3 - 66*y**2 - 67/32*y**4 + 0 + 0*y. Factor o(l).
(l - 8)*(l - 3)**2*(2*l - 1)/4
Let c be (615/4920)/((-9)/(-48)*4). Suppose 5*b - 9 - 1 = 0. Factor -2/3*q - 11/6*q**b + 0 - 1/6*q**4 + c*q**5 - 3/2*q**3.
q*(q - 4)*(q + 1)**3/6
Solve -25/7*y**3 - 3076/7 - 15384/7*y - 19245/7*y**2 = 0 for y.
-769, -2/5
Let s(g) be the second derivative of -g**4/24 - 125*g**3/6 - 15625*g**2/4 + 1488*g. Factor s(j).
-(j + 125)**2/2
Let x(o) = -6*o - 22. Let y be x(-5). Suppose -70 = -y*h - 14. Determine b so that 4*b**5 - 20*b**4 + 0*b - 20*b**2 + 40*b**3 + 4*b - h*b**3 = 0.
0, 1/2, 2
Let v(h) be the second derivative of 11*h**5/100 - 2*h**4 + 33*h**3/10 + h**2 + 3978*h. What is j in v(j) = 0?
-1/11, 1, 10
Let g(w) = -w**2 - w. Let d(i) = -i + 8. Let c be d(5). Let h(l) = -c*l + 3*l + 4*l - 6*l. Let v(q) = -6*g(q) + 5*h(q). Factor v(z).
2*z*(3*z - 2)
Let s(x) be the first derivative of 23 - 10*x**3 + 3*x - 12*x**2 + 1/2*x**4 + 3/4*x**5. Let z(w) be the first derivative of s(w). Factor z(n).
3*(n - 2)*(n + 2)*(5*n + 2)
Let n(p) = 6*p**2 + 11*p + 12. Let l be n(-2). Let -l*r**2 - 5*r**3 + 20*r + 19 + 9*r**2 + 1 = 0. What is r?
-2, -1, 2
Let g(q) be the third derivative of q**6/40 + 941*q**5/20 - 1885*q**4/8 + 943*q**3/2 - 136*q**2 - 8*q. Suppose g(f) = 0. What is f?
-943, 1
Solve 120984 + 3/2*n**2 + 852*n = 0.
-284
Let l(y) be the second derivative of -8*y**6/5 + 67*y**5/5 - 28*y**4 + 22*y**3 - 8*y**2 + 1180*y. Determine c so that l(c) = 0.
1/4, 1/3, 1, 4
Let o(k) = -3*k - 10. Let a be o(-5). Suppose -3 = -3*n, 3*g + n - 15 - 106 = 0. Solve 18*j - 48*j**2 - 41*j**5 + 83*j**5 - g*j**a + 44*j**3 - 16*j**4 = 0.
0, 1, 3
Let l(g) be the third derivative of g**5/12 - 410*g**4/3 + 268960*g**3/3 + 1669*g**2. Factor l(f).
5*(f - 328)**2
Let f(n) be the third derivative of -n**5/21 + 4*n**4/3 - 22*n**3/21 + 47*n**2 + 3*n. Determine o so that f(o) = 0.
1/5, 11
Let s(c) be the second derivative of 9*c + 0*c**5 + 0 - 1/360*c**6 + 0*c**2 - 11/3*c**3 + 1/24*c**4. Let i(x) be the second derivative of s(x). Factor i(f).
-(f - 1)*(f + 1)
Let w be ((-60)/(-54) + -1)*(-2)/80*-270. Let v be (-20)/(-6) - 1/3. Factor -1/4*i**v + w*i**2 + 0 + i.
-i*(i - 4)*(i + 1)/4
Let c(h) be the third derivative of -1/360*h**6 - 1/630*h**7 + 0*h + 0 + 2/45*h**5 + 0*h**3 + 1/6*h**4 - 67*h**2. Factor c(x).
-x*(x - 3)*(x + 2)**2/3
Factor 2/3*t**4 + 42*t**3 + 40 + 122*t**2 + 362/3*t.
2*(t + 1)**3*(t + 60)/3
Suppose 359*k - 136 - 582 = 0. Let t(o) be the first derivative of 45 + 16*o + 76/3*o**3 + 80*o**k. Factor t(j).
4*(j + 2)*(19*j + 2)
Let w(n) = 5*n**3 - 196*n**2 + 604*n + 140. Let r(o) = 2*o**3 + 2. Let z(q) = -10*r(q) - 5*w(q). Factor z(c).
-5*(c - 18)*(c - 4)*(9*c + 2)
Let z(g) be the second derivative of 1/8*g**4 + 0*g**2 + 0 - 7/2*g**3 - 45*g. Factor z(t).
3*t*(t - 14)/2
Let s(r) = 18*r - 355. Let m be s(20). Factor 10*d + 0*d + 6911*d**2 + m - 6906*d**2.
5*(d + 1)**2
Let a(u) be the second derivative of u**6/450 + u**5/150 - 2*u**4/5 - u**3/6 + 7*u**2/2 - 8*u. Let l(j) be the second derivative of a(j). Factor l(p).
4*(p - 3)*(p + 4)/5
Suppose 0*x + 572 = 13*x. Let c be (x/660)/(1/2). What is t in 0*t + 0 - 8/15*t**3 + 2/5*t**2 + c*t**4 = 0?
0, 1, 3
Factor 4255443/4 + 3573/2*o + 3/4*o**2.
3*(o + 1191)**2/4
Let j(n) = 32*n**3 + 29*n**2 - 25*n - 6. Let r(s) = 85*s**3 + 86*s**2 - 75*s - 16. Let g(u) = 8*j(u) - 3*r(u). What is l in g(l) = 0?
0, 1, 25
Let t(b) be the first derivative of -4*b**6/3 + 28*b**5/5 + 3*b**4 - 68*b**3/3 - 10*b**2 + 24*b + 1327. Find n, given that t(n) = 0.
-1, 1/2, 2, 3
Factor -h**2 + 2976*h - 298770 - 3*h**2 + 0*h**2 + 0*h**2 - 254766.
-4*(h - 372)**2
Let o(f) be the second derivative of f**4/21 - 16*f**3/21 - 130*f**2/7 - 1087*f + 1. Factor o(u).
4*(u - 13)*(u + 5)/7
Let a(y) be the third derivative of -4*y**7/105 - 3*y**6/10 + 6*y**5/5 + 71*y**4/6 + 20*y**3 - 3*y**2 + 65*y. Suppose a(f) = 0. What is f?
-5, -2, -1/2, 3
Let u(i) be the third derivative of 0 + 1/450*i**5 + 4*i**2 + 0*i**4 - i - 4/45*i**3. Factor u(x)