 a(f) be the third derivative of -4/135*f**5 + 1/108*f**6 - 7*f**2 + 0*f**3 + 0*f + 0 + 1/27*f**4 - 1/945*f**7. Find k such that a(k) = 0.
0, 1, 2
Let x(s) be the second derivative of 0*s**3 + 1/10*s**5 + 3*s + 0 + 0*s**2 + 2/3*s**4. Suppose x(a) = 0. What is a?
-4, 0
Let a(r) = -r + 39. Let j be a(5). Suppose j*b - 32*b = 10. Let -1/3*h**3 + 0 - 5/6*h**b + 0*h**2 + 0*h + 7/6*h**4 = 0. Calculate h.
0, 2/5, 1
Suppose 160 = 5*k + 5*z - 0*z, -5*k = -4*z - 124. Let v = -139/5 + k. Suppose 0 + 0*x + 0*x**3 - 1/5*x**2 + v*x**4 = 0. Calculate x.
-1, 0, 1
Let p = 285/112 + 5/16. Suppose -2*t - 26 = 5*j, 22*j = 24*j + 12. Factor 4/7*f**4 + 0 - 12/7*f**3 + 4/7*f**5 - 8/7*f - p*f**t.
4*f*(f - 2)*(f + 1)**3/7
Factor 1/2*g**4 - 4*g + 6*g**2 - 3*g**3 + 0.
g*(g - 2)**3/2
Let t be (-3 + 51/9)/(4/6). Factor -14*x**2 + 7*x**4 + 0*x + 7*x**t + 1701*x**3 - 1705*x**3 + 4*x.
2*x*(x - 1)*(x + 1)*(7*x - 2)
Let p be 3*(-6)/63 + 3933/21. Suppose -p = o - 187. Factor -4/9*t + 2/3*t**2 + o.
2*t*(3*t - 2)/9
Let -22/3*t + 1/3*t**3 + 0 + 3*t**2 = 0. Calculate t.
-11, 0, 2
Let d(w) be the first derivative of -w**4/28 + 5*w**3/21 - 3*w**2/14 - 9*w/7 - 531. Factor d(c).
-(c - 3)**2*(c + 1)/7
Let u(d) = -8*d**2 + 6*d + 32. Let m(h) = -7*h**2 + 5*h + 32. Let c(l) = 6*m(l) - 5*u(l). Factor c(y).
-2*(y - 4)*(y + 4)
Let n(x) = 176*x**4 + 64*x**3 - 20*x**2 + 40*x + 40. Let w(q) = 25*q**4 + 9*q**3 - 3*q**2 + 6*q + 6. Let o(i) = 3*n(i) - 20*w(i). Factor o(v).
4*v**3*(7*v + 3)
Suppose -51*a = -46*a + 165. Let q = a - -35. Solve -1 + 1/2*g**3 + 0*g**q - 3/2*g = 0 for g.
-1, 2
Let m = -2146 - -2148. What is p in 4/7 - 1/7*p**3 - 4/7*p**m + 1/7*p = 0?
-4, -1, 1
Let z be (-2)/(-1) + (-83590)/41808. Let n = z - -86819/20904. Find l such that 0 - n*l**4 + 30/13*l**3 - 8/13*l + 32/13*l**2 = 0.
-2/3, 0, 2/9, 1
Suppose 0 = -7*i + 11*i + 8. Let f(u) = -23*u - 3. Let g be f(i). Factor -4*c**2 + c**2 - 46*c + g*c.
-3*c*(c + 1)
Let v be 55/(990/(-72)) + (6 - -1). Suppose -w**v + w**2 + 0 + 0*w + 1/4*w**4 = 0. What is w?
0, 2
Let p = -3006 + 3009. What is u in 0 + 16/3*u - 20/3*u**5 + 4/3*u**p - 16*u**4 + 16*u**2 = 0?
-2, -1, -2/5, 0, 1
What is m in -151*m**2 + 8*m**5 - 2 - 94*m**3 + 80*m - m**5 - 14 + 227*m**3 - 53*m**4 = 0?
4/7, 1, 4
Let b(o) be the first derivative of 14*o**5/5 + 5*o**4 - 8*o**3/3 - 10*o**2 - 6*o - 47. Factor b(d).
2*(d - 1)*(d + 1)**2*(7*d + 3)
Let c(j) = 13*j**4 - 319*j**3 - j**2 + 311*j. Let z(u) = 11*u**4 - 318*u**3 - 2*u**2 + 312*u. Let i(x) = 3*c(x) - 4*z(x). What is h in i(h) = 0?
-1, 0, 1, 63
Let u = 12 - 14. Let g be (u/8)/(2/(-16)). Factor o + 4*o - g*o**2 - 3*o.
-2*o*(o - 1)
Let c(b) be the first derivative of b**9/252 + 3*b**8/560 - b**7/280 - 8*b**3/3 - 2. Let t(s) be the third derivative of c(s). Factor t(q).
3*q**3*(q + 1)*(4*q - 1)
Let f be (-16)/(-7) + 10/(-35). Factor 5*c - 15 + 5*c + 4*c**2 + c**f.
5*(c - 1)*(c + 3)
Suppose 4*p = -v - 0*v + 33, -5*p = -5*v + 90. Factor 8*n**4 - 17*n**3 + 42*n**3 - v*n**3 + 4*n**5.
4*n**3*(n + 1)**2
Factor 447*i - 18579*i**3 + 21*i**2 - 140 + 365 + 18588*i**3 - 702*i**2.
3*(i - 75)*(i - 1)*(3*i + 1)
Factor 0*o + 0*o**2 + 3/4*o**3 + o**4 + 0.
o**3*(4*o + 3)/4
Let l = 209/2 - 95. Let v(f) be the first derivative of l*f**2 - 56/3*f**3 + 8/5*f**5 - 6 - 8/3*f**6 + 47/4*f**4 - 2*f. Determine y, given that v(y) = 0.
-2, 1/4, 1
Let z = -44202 + 88405/2. Let 23*y + z + 529/2*y**2 = 0. What is y?
-1/23
Let b = -66 + 54. Let z be -4 + ((-99)/b - 4). Find s, given that -z*s**2 + 0 - 1/4*s = 0.
-1, 0
Suppose -4*p + 84 = -8*p. Let q be 6/(-21) + (-48)/p. Solve -y + 3 - q*y**2 - y - 3 = 0 for y.
-1, 0
Let i(g) be the second derivative of 2*g**7/105 - g**6/15 + g**5/15 - 19*g**2/2 + 16*g. Let z(j) be the first derivative of i(j). Factor z(u).
4*u**2*(u - 1)**2
Let z be (-5 - (-44)/6) + (-4)/(-6). Suppose -17*d**4 + 6*d**5 + 9*d**2 - 11*d**2 + 10*d**z + 3*d**4 = 0. Calculate d.
0, 1/3, 1
Factor -23/4*w + w**2 + 19/4.
(w - 1)*(4*w - 19)/4
Let a(h) be the first derivative of 0*h + 31 + 2*h**4 - 4/5*h**5 - 4/3*h**3 + 0*h**2. Solve a(j) = 0.
0, 1
Let k(w) = 2*w**3 + 6*w**2 - 2*w - 6. Let u(p) = 3*p**3 + 11*p**2 - 3*p - 11. Let b(q) = -7*k(q) + 4*u(q). Suppose b(i) = 0. Calculate i.
-1, 1
Let f be 2/(-1) + (-4)/(16/(-12)). Let i be f/6*-1*(2 - 11). Determine l, given that -l**3 + 3/2*l**2 + i*l - 1 = 0.
-1, 1/2, 2
Suppose -7*u + 10 = -2*u. Let l = 4 - u. Factor 0*i**l - 72*i**2 - 47*i**3 - 3 - i**3 - 27*i.
-3*(i + 1)*(4*i + 1)**2
Factor 11/5*t + 7/5*t**2 + 1 + 1/5*t**3.
(t + 1)**2*(t + 5)/5
Factor 2/9*y**2 - 22/9 - 20/9*y.
2*(y - 11)*(y + 1)/9
Let b = 512179/8608 + -3/8608. Solve 49/2*p**5 + 2 + b*p**4 - 8*p - 23/2*p**2 + 67/2*p**3 = 0.
-1, 2/7
Let g = 1340 - 1338. Factor 2/3*d**3 + 16/3*d - 14/3*d**g + 32/3.
2*(d - 4)**2*(d + 1)/3
Let t(x) be the first derivative of -3*x**5/5 + 5*x**4 - 15*x**3 + 20*x**2 - 12*x - 54. Find y such that t(y) = 0.
2/3, 1, 2, 3
Let s(r) be the third derivative of 1/60*r**6 - 7/20*r**4 + 1/525*r**7 + 17*r**2 + 0*r - 6/5*r**3 + 1/150*r**5 + 0. Factor s(k).
2*(k - 2)*(k + 1)*(k + 3)**2/5
Suppose 0 - 62/11*a**4 - 2/11*a**3 + 2/11*a**5 + 62/11*a**2 + 0*a = 0. Calculate a.
-1, 0, 1, 31
Let w(v) = v**2 + 6*v - 2. Let f be w(-6). Let q(j) = 2*j - 4. Let h(o) = -o**2 - o + 5. Let b(l) = f*h(l) - 3*q(l). Factor b(x).
2*(x - 1)**2
Let j be ((-125)/15)/25*(-2 + 1). Let m = 245/3 + -81. Find q such that j*q - m + 1/3*q**2 = 0.
-2, 1
Let i be 19/((-14896)/32)*(-2)/(2/7). Find b such that -4/7*b**2 + 2/7 - i*b = 0.
-1, 1/2
Let j = -36691/2 + 18346. Factor -35/4*h**4 - 17/4*h**2 - 39/4*h**3 - j*h - 11/4*h**5 + 0.
-h*(h + 1)**3*(11*h + 2)/4
Let s = 64 + -59. Suppose -5*b - 4*y - 1 = -5, -3*y = -s*b - 3. Find w such that 1/4*w**5 + 1/2*w**4 + 0*w + 0*w**2 + 1/4*w**3 + b = 0.
-1, 0
Let w = -2/751 - -1520/6759. Solve -w*g**2 + 0 - 2/9*g = 0.
-1, 0
Let n(j) be the third derivative of j**10/1512000 - j**9/302400 + j**5/60 + 5*j**3/3 - 6*j**2 - 4. Let c(o) be the third derivative of n(o). Factor c(w).
w**3*(w - 2)/10
Let r(c) be the first derivative of 5/7*c**2 + 1/14*c**4 + 19 + 4/7*c + 8/21*c**3. Let r(f) = 0. Calculate f.
-2, -1
Let r(p) be the first derivative of 4*p**5/35 + 3*p**4/7 - 8*p**2/7 + 210. Factor r(l).
4*l*(l - 1)*(l + 2)**2/7
Suppose 0*g = -3*g + 45. Let h = g - 13. Solve -p**2 + p + 8*p + 3*p**2 - 5*p**h - 6 = 0 for p.
1, 2
Let v(a) be the third derivative of -a**7/420 + a**6/160 + a**5/80 - a**4/48 + 364*a**2. Factor v(k).
-k*(k - 2)*(k + 1)*(2*k - 1)/4
Let p = -5800/3 + 1940. Find j such that -2/3*j**2 + p*j - 50/3 = 0.
5
Suppose 0 = -2*i - 0*i + o, 2*i + 4*o - 20 = 0. Solve 2*n**i + 22*n**3 + 10*n**4 - 4*n**5 - 17*n**3 - 13*n**3 = 0.
0, 1/2, 1
Let b(o) be the first derivative of 4/3*o - 1/3*o**2 + 13 - 2/9*o**3. Suppose b(u) = 0. Calculate u.
-2, 1
Solve -5*t**3 + 0 + 5/4*t**2 + 5*t - 5/4*t**4 = 0 for t.
-4, -1, 0, 1
Let j be (-15)/15*(-3)/(-3)*-3. Let l(x) be the first derivative of -4 - 1/5*x**2 + 0*x - 2/15*x**j. Solve l(k) = 0.
-1, 0
Factor 58/5*m**2 - 54/5*m - 4/5.
2*(m - 1)*(29*m + 2)/5
Let h(w) be the third derivative of -7/108*w**4 + 0 + 13*w**2 + 0*w - 13/945*w**7 - 11/90*w**5 + 2/27*w**3 - 37/540*w**6. Determine y, given that h(y) = 0.
-1, 2/13
Suppose 2*o - 22 = -o + 5*b, -o - 3*b - 2 = 0. Suppose 0*g = -g + o*f + 27, -3*g - 5*f - 4 = 0. Factor g*m**2 + m - 6*m**2 + 4 + 3*m.
(m + 2)**2
Let r(z) be the first derivative of -z**5/80 + 3*z**4/32 + 35*z**2/2 - 10. Let u(h) be the second derivative of r(h). Find q such that u(q) = 0.
0, 3
Let t(d) be the second derivative of 0 + 1/12*d**4 - d + 0*d**2 - 1/3*d**3. Factor t(f).
f*(f - 2)
Suppose -3*m = -4*k + 45, 16 = 5*k + 5*m - 14. Suppose 0 = 5*i + k - 49. Let -i + 4*b**2 + 2*b**3 + 2*b + 8 + 0*b**3 = 0. Calculate b.
-1, 0
Let i be 36/(-15)*(-8 - (-469)/63). Find g, given that 2/3 - i*g + 2/3*g**2 = 0.
1
Let h(w) be the second derivative of 0*w**2 - 1/42*w**7 - 1/4*w**4 + 0 + 23*w + 1/3*w**3 - 1/20*w**5 + 1/10*w**6. Factor h(j).
-j*(j - 2)*(j - 1)**2*(j + 1)
Suppose -4*p = -5*v + 20, -5*p + 37 = 4*v - 4*p. Suppose 10*k - v = 6*k. Find w, given that -k*w**5 + 9*w**4 - 4*w**3 - 9*w**4 - 2*w**5 + 8*w**4 = 0.
0, 1
Let v(o) be the first derivative of -o**4/2 + 2*o**3/3 + 37*o**2 + 70*o + 559. Let v(b) = 0. Calculate b.
-5, -1, 7
Determine d so that 0*d**2 + 0 - 15/2*