 6
Find a, given that -92/7*a**3 - 80/7*a**4 + 24/7 + 8*a**2 + 14*a - 6/7*a**5 = 0.
-12, -1, -1/3, 1
Suppose -5*t + 22 = -3*l, 1 = t - 4*l - 0. Let -11*q**3 + 63*q**5 - 62*q**t + 8 - 7*q**2 - q**4 + q + 9*q = 0. Calculate q.
-2, -1, 1, 4
Let j(l) be the second derivative of 160*l - 1/200*l**5 + 0*l**2 - 7/120*l**4 + 0 + 2/15*l**3. Factor j(p).
-p*(p - 1)*(p + 8)/10
Let j(y) be the first derivative of 4*y**3/9 - 491*y**2 + 1472*y/3 + 2221. Factor j(g).
2*(g - 736)*(2*g - 1)/3
Suppose 4*s - 15420*j = -15415*j - 42, -4*j = -s - 38. Factor 0*l + s*l**2 - 1/4*l**5 + 0 + 5/2*l**4 - 17/4*l**3.
-l**2*(l - 8)*(l - 1)**2/4
Suppose 16*x - 21*x = -40. Suppose -2*v = -x, 4*k = 2*k + v + 6. Factor 94*r**2 - 5*r - 104*r**2 + 0*r - k*r**3.
-5*r*(r + 1)**2
Suppose 0 + 187/3*n**3 + n + 98/3*n**2 + 92/3*n**4 = 0. What is n?
-1, -3/92, 0
Let w = -19/15579 - -187081/109053. Factor 4/7*g**2 - 8/7*g - w.
4*(g - 3)*(g + 1)/7
Let b be (708/357 - 0) + (-3728)/6524. Solve 14/17*i**5 + 48/17*i**2 - b - 24/17*i**4 - 28/17*i**3 + 14/17*i = 0 for i.
-1, 1, 12/7
Let r(p) = -p**3 - 13*p**2 + 529*p + 6497. Let g be r(-12). Determine a so that -4*a**2 + 4*a**4 - 1/4*a**g - 63/4*a**3 + 16*a + 0 = 0.
-1, 0, 1, 8
Let h(i) be the third derivative of -i**6/180 - 37*i**5/90 + i**4/36 + 37*i**3/9 - 2181*i**2. Let h(d) = 0. Calculate d.
-37, -1, 1
What is a in 2/3 + 17/12*a + 5/6*a**2 + 1/12*a**3 = 0?
-8, -1
Let f(z) be the first derivative of 3*z**4/4 + 932*z**3/5 + 130851*z**2/10 + 51894*z/5 + 726. Factor f(t).
3*(t + 93)**2*(5*t + 2)/5
Factor -209*l**2 - 10*l**3 + 50*l**2 - 185*l - 434*l + 104*l - 196*l**2 - 170.
-5*(l + 1)*(l + 34)*(2*l + 1)
Suppose -38*c = -34*c + 20. Let z be 435/50 + -9 + (-4)/c. Suppose -1/2 - z*g**2 + g = 0. What is g?
1
Let c(g) be the third derivative of g**9/98280 - g**7/2340 - g**6/780 + 21*g**4/8 - 121*g**2. Let i(y) be the second derivative of c(y). Factor i(f).
2*f*(f - 3)*(f + 1)*(f + 2)/13
Let c(j) be the third derivative of 11*j**6/240 + 13*j**5/10 + 57*j**4/16 + 13*j**3/6 + 22*j**2 - 59. Factor c(h).
(h + 1)*(h + 13)*(11*h + 2)/2
Let t be (-48)/84*(-7)/2. Factor -13*u**2 + 5*u**2 + 8*u**4 + 4*u**5 + 2*u**5 - t*u**5 - 4*u.
4*u*(u - 1)*(u + 1)**3
Let a = 260 + -256. Find n, given that -36*n**3 - 8*n**2 + 2*n**2 - 6*n - 19*n**2 - 2*n**2 - 12*n**a = 0.
-2, -1/2, 0
Let l(o) = o**2 - 11*o + 26. Suppose -4*p = -4*f + 32, 28 = 4*f - 2*p - 4. Let n be l(f). Factor 0 + n*g**4 + 0*g**2 + 0*g + 1/4*g**5 + 4*g**3.
g**3*(g + 4)**2/4
Suppose -r - 12 = -5*r. Let 6*o - r*o**3 - 6*o**2 - 21*o - 12*o**2 = 0. What is o?
-5, -1, 0
Let n(p) be the first derivative of p**4/7 + 53*p**3/21 + 116*p**2/7 + 48*p + 5669. Suppose n(f) = 0. Calculate f.
-21/4, -4
Let h(f) be the first derivative of -10*f - 8/3*f**3 - 1/4*f**4 + 19/2*f**2 + 115. Find a such that h(a) = 0.
-10, 1
Determine h so that 0*h**4 + 48/5*h**2 - 68/5*h**3 - 192/5 + 208/5*h + 4/5*h**5 = 0.
-4, -2, 1, 2, 3
Factor -291*s - 177*s**2 - 86 - 2*s**3 - 306*s**2 - 76 + 548*s**2.
-(s - 27)*(s - 6)*(2*s + 1)
Let w(a) = 3*a**3 + 2*a. Let i(x) = 22*x**3 - 68*x**2 - 55*x. Let p(q) = -2*i(q) + 14*w(q). Factor p(v).
-2*v*(v - 69)*(v + 1)
Let a = 426 - 414. What is l in -37*l**2 + 32 - 3*l**2 + 120*l**4 - 50*l**2 + a*l**2 + 112*l + 122*l**4 - 308*l**3 = 0?
-4/11, 1
Let r be 27/35*57780/8667. Factor -192/7*a - 256/7 - 2/7*a**3 - r*a**2.
-2*(a + 2)*(a + 8)**2/7
Let g be (-22)/((-1 - 0) + 4 + -4). Suppose -7*v + 43 = g. Factor 1/8*s**2 - 1/8*s**v + 1/4*s + 0.
-s*(s - 2)*(s + 1)/8
Let z = 1175774 - 8230412/7. Solve 3/7*c**3 - 9*c - z*c**2 - 54/7 = 0 for c.
-3, -1, 6
Let b(x) be the second derivative of 203*x**4 + 811*x**3/2 - 3*x**2/2 + 5*x - 95. Factor b(k).
3*(k + 1)*(812*k - 1)
Let a = 3 + -1. Suppose -29*n - 408 = -165*n. Suppose -f**4 + 0*f**2 - 23*f**3 - 23*f**3 + 49*f**n - 2*f**a = 0. What is f?
0, 1, 2
Let b = -109 - -112. What is i in -3*i**b - 173*i**2 + 2*i + i**5 - 2*i**4 + i**4 + 174*i**2 = 0?
-1, 0, 1, 2
Suppose 8 = -2*w + 2*h, 8*h - 16 = -5*w + 7*h. Let l(a) be the third derivative of 1/270*a**5 + 0*a**4 + 0*a + 0 + 14*a**w - 1/27*a**3. Solve l(j) = 0.
-1, 1
Suppose -3*i + 61 = 58. Let t be 2/(10/(-15) + i). Factor t*c - 7*c + c**2 - 7*c + 3 + 4.
(c - 7)*(c - 1)
Let n(g) be the third derivative of g**6/30 - 16*g**5/15 - 77*g**4/6 - 40*g**3 - 87*g**2 - 2*g. Let n(t) = 0. Calculate t.
-3, -1, 20
Let s(r) be the first derivative of -r**6/6 + r**5 - 5*r**4/12 - 5*r**3 - 139*r + 62. Let t(o) be the first derivative of s(o). Factor t(p).
-5*p*(p - 3)*(p - 2)*(p + 1)
Let r(l) be the second derivative of l**7/105 + 82*l**6/75 + 161*l**5/50 + 8*l**4/3 + 2534*l. Factor r(c).
2*c**2*(c + 1)**2*(c + 80)/5
Determine m so that 864*m - 3/2*m**5 + 0 - 72*m**4 + 72*m**2 - 1725/2*m**3 = 0.
-24, -1, 0, 1
Let x be 122/(-122) + 3/(-1) - -7. Factor 16/3*b**x + 0 + 1/3*b + 8/3*b**2.
b*(4*b + 1)**2/3
Solve -64/11*j + 8/11*j**3 + 2/11*j**5 + 0 + 18/11*j**4 - 72/11*j**2 = 0.
-8, -2, -1, 0, 2
Determine q so that 0 + 11/2*q**2 + 3*q + 2*q**3 - 1/2*q**4 = 0.
-1, 0, 6
Let g = 98 - 86. Suppose 7*q = 4*q + g. Factor -q*a**2 - 12 + 12*a - 77*a**3 + 73*a**3 + 8*a.
-4*(a - 1)**2*(a + 3)
Let t(o) be the second derivative of -2 + 588/5*o**3 + 413/5*o**4 - 45*o + 2/105*o**7 + 317/25*o**5 + 0*o**2 - 26/25*o**6. Determine i so that t(i) = 0.
-2, -1, 0, 21
Let w = 2487 + -286007/115. Let o = 906/805 - w. Factor -o*g**2 - 4/7*g + 8/7*g**3 + 4/7 - 4/7*g**5 + 4/7*g**4.
-4*(g - 1)**3*(g + 1)**2/7
Let 335/3*z - 112*z**2 + 0 + 1/3*z**3 = 0. What is z?
0, 1, 335
Let y(c) be the third derivative of -c**5/15 - 7*c**4/3 - 98*c**3/3 + 3110*c**2. Factor y(m).
-4*(m + 7)**2
Let g(m) = -m**2 + 14*m + 5. Suppose -2*p - 2*p + 50 = 5*n, 9 = n + p. Let x be g(n). Factor 25*u + 30 + 10*u**2 + x*u**2 - 24*u**2 + 4*u**2.
-5*(u - 6)*(u + 1)
Let f(o) = -o**2 + 23*o + 8. Let h(s) = -7*s**2 + 131*s + 41. Let b(y) = -11*f(y) + 2*h(y). Factor b(z).
-3*(z - 2)*(z - 1)
Let r(u) = -139*u + 1120. Let i be r(8). Let a(n) be the first derivative of -4/9*n**2 + i - 8/9*n - 2/27*n**3. Factor a(f).
-2*(f + 2)**2/9
Let u(m) be the first derivative of 2*m**3/15 - 10*m + 1465. Determine i so that u(i) = 0.
-5, 5
Let b(k) = -3*k**2 + 36*k + 54. Suppose -7*i = -377 + 258. Let g(w) = -9*w**2 + 105*w + 161. Let u(t) = i*b(t) - 6*g(t). Determine s, given that u(s) = 0.
-2, 8
Let i(h) be the second derivative of 10*h**2 + 5/36*h**4 + 20/9*h**3 + 0 + 36*h. Find l, given that i(l) = 0.
-6, -2
Let j = -370149814/321 + 1153111. Let x = -2/107 - j. Determine v, given that -v**5 + 1/3*v**4 - 8/3*v + v**2 - 4/3 + x*v**3 = 0.
-1, -2/3, 1, 2
Factor -1747 - n**2 - 68*n - 3*n**2 + 2187.
-4*(n - 5)*(n + 22)
Let t = -8263 + 8263. Let j(v) be the first derivative of 1/3*v**2 + t*v - 2/3*v**3 - 2/15*v**5 + 1/2*v**4 + 1. Determine q so that j(q) = 0.
0, 1
Let g(r) be the second derivative of 62*r + 13/66*r**3 - 2 - 6/11*r**2 - 1/132*r**4. Factor g(h).
-(h - 12)*(h - 1)/11
Let y(a) = 7*a**3 + 307*a**2 - 675*a + 361. Let b(u) = -2*u**3 - 102*u**2 + 225*u - 121. Let v(o) = 8*b(o) + 3*y(o). Factor v(n).
5*(n - 1)**2*(n + 23)
Let q = 1166/103 - 2229/206. Factor -h**2 + 0*h - 1/2*h**3 + 0 + q*h**5 + h**4.
h**2*(h - 1)*(h + 1)*(h + 2)/2
Let h(x) be the second derivative of 0*x**2 + 49*x + 17/36*x**4 + 1/9*x**3 + 7/15*x**5 + 0 + 13/90*x**6. Factor h(y).
y*(y + 1)**2*(13*y + 2)/3
Let h(w) be the second derivative of w**5/24 - 5*w**4/8 + 15*w**2 - 18*w - 1. Let m(z) be the first derivative of h(z). Let m(q) = 0. Calculate q.
0, 6
Suppose 9*t**4 - 2251*t**2 + 4371*t**2 - 39*t**3 - 3*t**4 - 126 - 2180*t**2 + 291*t = 0. What is t?
-3, 1/2, 2, 7
Let x(v) be the second derivative of v**7/15 - 11*v**6/45 + 2*v**5/45 - 195*v**2/2 - 53*v. Let b(j) be the first derivative of x(j). Factor b(p).
2*p**2*(p - 2)*(21*p - 2)/3
Let d(b) be the first derivative of -b**4/24 + 3*b**3/4 + 11*b**2/2 - 162*b - 127. Let u(n) be the first derivative of d(n). Find v, given that u(v) = 0.
-2, 11
Let j(q) be the second derivative of q**7/273 - 4*q**6/39 - 21*q**5/130 + 195*q - 26. Factor j(u).
2*u**3*(u - 21)*(u + 1)/13
Let x(q) be the first derivative of 5*q**4/4 + 35*q**3/3 - 5*q**2/2 - 35*q + 352. Factor x(t).
5*(t - 1)*(t + 1)*(t + 7)
Let k(o) = 85*o**2 - 48150*o + 10551390. Let q(d) = -31*d**2 + 17509*d - 3836869. Let t(x) = 11*k(x) + 30*q