0, 1/4, 1
Let l(u) = 5*u**2 - u - 1. Let g be l(-1). Suppose g*r - 4*n = 705, 5*r + 2*n + 2*n - 705 = 0. Factor 4 + 139*w**2 - 2 - r*w**2 + 2*w - 2*w**3.
-2*(w - 1)*(w + 1)**2
Determine m so that -3/7*m - 156/7 + 6/7*m**4 + 321/7*m**3 + 468/7*m**2 = 0.
-52, -1, 1/2
Let p(z) be the first derivative of z**5/36 + 85*z**4/72 - 95*z**3/9 + 90*z**2 + 146. Let l(a) be the second derivative of p(a). Factor l(v).
5*(v - 2)*(v + 19)/3
Let f(a) be the third derivative of 0*a + 5/7*a**3 - 1/140*a**5 - 3/56*a**4 - 123*a**2 + 0. Factor f(k).
-3*(k - 2)*(k + 5)/7
Let g(t) = 3*t**2 - 1604*t + 639992. Let r(z) = -7*z**2 + 3210*z - 1279980. Let y(u) = -15*g(u) - 6*r(u). Let y(p) = 0. What is p?
800
Factor 22*v**2 + 3/2*v**3 - 15/2*v + 0.
v*(v + 15)*(3*v - 1)/2
Let o(k) be the first derivative of 25*k + 24 - 2/3*k**4 + 0*k**2 + 1/10*k**5 + 4/3*k**3. Let z(s) be the first derivative of o(s). Find j, given that z(j) = 0.
0, 2
Factor -285/4*a - 147/4*a**2 - 3/4*a**3 - 141/4.
-3*(a + 1)**2*(a + 47)/4
Let r be 14 + 9 + 0 + -20. Let w(p) be the first derivative of 7/12*p**r + 3*p - 16 - 1/16*p**4 - 2*p**2. Factor w(f).
-(f - 3)*(f - 2)**2/4
Let k(o) = 5*o. Suppose -3*x + 3*r - 4 = -8*x, -2*r - 14 = -5*x. Let f be k(x). Solve 2*s**3 + 2*s**5 - 9*s**4 - 6*s**3 + s**5 + f*s**3 = 0.
0, 1, 2
Let 380*l - 18 + 53*l**2 - 30 - 384*l - 3*l**2 + 4*l**3 - 2*l**4 = 0. Calculate l.
-4, -1, 1, 6
Factor -140000 + 400*g - 2/7*g**2.
-2*(g - 700)**2/7
Let x(z) = 73*z + 7. Let s be x(1). Let q be (29/(-27) + 1)*(-1200)/s. Find j, given that 2/3 - q*j + 2/9*j**3 + 2/9*j**2 = 0.
-3, 1
Let k(t) = t**2 - 7*t + 10. Let b be k(6). Let n = -20 + 22. Factor 91*h**b + 8*h**n + 10*h**3 - 55*h**4 + 15*h**3 + 19*h**3.
4*h**2*(h + 1)*(9*h + 2)
Let b(c) be the second derivative of -7 - c**2 + 1/12*c**4 + c + 1/6*c**3. Factor b(t).
(t - 1)*(t + 2)
Let l(u) = -5*u**2 - 24*u - 16. Suppose -3*g - 27 = -162. Let c = -41 + g. Let o(x) = -20*x**2 - 95*x - 65. Let k(b) = c*o(b) - 15*l(b). Factor k(i).
-5*(i + 2)**2
Let d be ((-6)/8)/(306150/(-328120)). Let u = d - 3/785. Solve -36/5*g**2 + u*g**3 - 36/5*g + 12/5*g**4 - 8/5 = 0.
-1, -1/3, 2
Let q(f) = 3*f**3 - 6*f**2 - 15*f - 2. Let n(d) = -7*d**3 + 16*d**2 + 30*d + 5. Let u(z) = 6*n(z) + 15*q(z). Find o, given that u(o) = 0.
-5, 0, 3
Suppose 0 = -6*f - 1062 - 30. Let z be 28/f + (-644)/(-637). Suppose -z + 16/7*d + 2/7*d**4 - 12/7*d**2 + 0*d**3 = 0. Calculate d.
-3, 1
Let f(v) = -3*v + 38. Let b be f(6). Factor 20*t**3 - 70*t + 22*t**3 - 45*t**2 - 67*t**3 + b*t**3.
-5*t*(t + 2)*(t + 7)
Suppose -5 = -k - l - 1, 3*k = -2*l + 11. Find x such that -14*x**3 - 13*x + x**4 + 26*x**3 - 23*x**k - 25*x**2 = 0.
-1, 0, 13
Let h = -159366 - -159368. Factor 4/5*t + 1/5*t**3 + 12/5 - 7/5*t**h.
(t - 6)*(t - 2)*(t + 1)/5
Suppose -273*w + 14 = -276*w - 5*f, 5*f = 4*w - 28. Determine u, given that 9/2*u**3 - 3*u**4 - 3/2*u + 0*u**w + 0 = 0.
-1/2, 0, 1
Let v(o) be the first derivative of 1/5*o**2 + 1/5*o + 0*o**3 - 71 - 1/10*o**4 - 1/25*o**5. Suppose v(x) = 0. Calculate x.
-1, 1
Find y such that -2/9*y**5 - 82/9*y + 14/9*y**4 + 52/9*y**2 - 22/3 + 28/3*y**3 = 0.
-3, -1, 1, 11
Let -1935*p**3 + 610*p**4 - 43*p**2 + 478*p**2 - 180 + 731*p**5 + 172*p**2 - 691*p**5 + 620*p + 238*p**2 = 0. What is p?
-18, -1/2, 1/4, 1, 2
Let a(z) = -9*z - 43. Let r be a(-5). Suppose -15 = -r*s - 9. Determine p so that 4*p**3 + 22*p**2 - 22*p**s + 12*p**4 - 3*p**5 - 10*p**2 - 3*p = 0.
0, 1
Factor 0 + 4/9*h**4 + 760/9*h**3 + 0*h - 764/9*h**2.
4*h**2*(h - 1)*(h + 191)/9
Suppose 0 = -4*s - t - 6, -3*t = -4*s + 65 - 15. Solve -24/5*l**s - 1/5 - 11/5*l = 0 for l.
-1/3, -1/8
Let k = -68 + 82. Suppose -17*u + 45 = -k*u. Find d, given that u + 21*d**2 - 11 + 14 + 69*d = 0.
-3, -2/7
Let h(q) be the second derivative of 3/8*q**2 + 0 - 108*q + 1/16*q**4 + 1/4*q**3. Solve h(p) = 0.
-1
Let g(s) = -4*s**3 - 36*s**2 + 56*s - 44. Let o(w) = 3*w**3 + 29*w**2 - 45*w + 35. Let b(n) = 11*g(n) + 14*o(n). Factor b(m).
-2*(m - 3)*(m - 1)**2
Let n(j) be the second derivative of 0 - 7/27*j**3 + 1/9*j**2 + 33*j + 1/9*j**4. Determine t so that n(t) = 0.
1/6, 1
Let m = -633 - -636. Let r(x) be the third derivative of 1/120*x**6 + 15*x**2 + 0*x**m + 1/120*x**4 + 0 + 0*x - 1/50*x**5. Suppose r(a) = 0. Calculate a.
0, 1/5, 1
Suppose -d + g + 32 = 27, d + 5*g + 13 = 0. Let x be 7*2/12 + d/(-4). Suppose -x*a**4 + 0*a + 2/3*a**5 - 2/3*a**3 + 2/3*a**2 + 0 = 0. What is a?
-1, 0, 1
Let h(n) be the second derivative of n**5/60 - 11*n**4/12 + 97*n**3/9 - 52*n**2 + 8394*n. Find t, given that h(t) = 0.
3, 4, 26
Let u be 761 - (-12)/(-54)*-3. Let d = -751 + u. Find h such that 12 + 10*h + 2*h**3 - d*h**2 = 0.
-2/3, 3
Let x = 16 - 12. Solve i**3 + 12*i - 4*i**3 - 17*i + 4*i**2 + x*i**3 = 0.
-5, 0, 1
Let o be (-1)/174*8/((-1568)/(-21)). Let a = o - -3257/14616. Let -2/9*m**5 - a*m + 0*m**2 + 0*m**4 + 4/9*m**3 + 0 = 0. Calculate m.
-1, 0, 1
Let r(s) be the third derivative of -17*s**7/1155 - 29*s**6/220 - 13*s**5/55 - 2*s**4/33 + 366*s**2. Find x, given that r(x) = 0.
-4, -1, -2/17, 0
Let i = -37302 + 113942/3. Let b = -678 + i. Factor b*w**2 + 0*w**3 - 2/9*w**4 + 0 + 4/9*w.
-2*w*(w - 2)*(w + 1)**2/9
Let 39/5*z**3 + 9/5*z**4 + 72/5 - 12*z - 102/5*z**2 = 0. Calculate z.
-6, -1, 2/3, 2
Suppose -56/3*t**3 + 7/3*t**2 + 44/3*t + 5/3*t**4 + 0 = 0. Calculate t.
-4/5, 0, 1, 11
Find s such that 46/11*s**2 - 48 - 268/11*s + 28/11*s**3 + 2/11*s**4 = 0.
-11, -4, -2, 3
Suppose 0 = 9*x - 33 + 15. Let s = 16 + 0. Let 2*t**2 + 9*t + 5*t - 2*t - s + 2*t**x = 0. Calculate t.
-4, 1
Suppose -15428 = -19*z - 5814. Find u such that 5*u**4 - 365*u - 392 - 60*u**3 - z*u**2 - 7*u**4 - 475*u = 0.
-14, -1
Let q(j) be the third derivative of 0*j + 0*j**3 + 1/3*j**4 - j**2 + 0*j**5 - 1/60*j**6 + 5. Factor q(x).
-2*x*(x - 2)*(x + 2)
Suppose 39*l + 5097 = 5214. Let u(w) be the second derivative of -5/28*w**4 - 3/70*w**5 + 0*w**2 + 0 + 1/7*w**3 - l*w + 1/14*w**6. Let u(y) = 0. What is y?
-1, 0, 2/5, 1
Let y = 3257 - 3257. Let g(c) be the first derivative of -2*c**4 - 28/5*c**5 + 0*c**3 + y*c**2 + 0*c + 21 + 8/3*c**6. Determine d so that g(d) = 0.
-1/4, 0, 2
Let g(l) be the third derivative of l**5/20 - 163*l**4/4 + 5*l**2 + 213. What is p in g(p) = 0?
0, 326
Let q(t) be the first derivative of -t**6/720 + 17*t**5/40 - 867*t**4/16 - t**3/3 - 137*t**2/2 + 254. Let s(z) be the third derivative of q(z). Factor s(j).
-(j - 51)**2/2
Determine z so that 36*z**2 + 2942*z - 33*z**2 + 4498*z + 4612800 = 0.
-1240
Let q(o) = -36*o - 413. Let x be q(-12). Suppose -4*r = -x*r + 60. Let -14/9*i**3 - 10/3*i**2 - 2/9*i**r + 0 - 2*i = 0. Calculate i.
-3, -1, 0
Let l be 58*4/(-480) + (-1)/(5/(-3)). Let m(b) be the third derivative of -31/24*b**4 + 28*b**2 + 0 + 0*b - l*b**6 - b**3 - 13/20*b**5. What is j in m(j) = 0?
-3/2, -1, -2/7
Let f(r) be the third derivative of r**6/15 - 19*r**5/10 - 95*r**4/6 + 17*r**3 + 913*r**2. Factor f(c).
2*(c - 17)*(c + 3)*(4*c - 1)
Let u(s) be the first derivative of 2/39*s**3 + 0*s**2 + 0*s + 2/65*s**5 - 1/13*s**4 - 2. Factor u(r).
2*r**2*(r - 1)**2/13
Factor 120*c + 75*c**2 + 32 - 169*c + 3*c**3 + 56 + 101 + 310*c.
3*(c + 1)*(c + 3)*(c + 21)
Suppose 784 + 96 = 5*y + 5*v, 3*y - 528 = -5*v. Factor -y + 82 + 62 + 360*p**2 + 700*p**3 - 48*p.
4*(5*p + 2)**2*(7*p - 2)
Let u be -9 + (-15 - (-1781)/143)/((-21)/77). Suppose 40/3 - 6*s - u*s**2 = 0. What is s?
-20, 2
Let y(p) = -p**3 - p - 16. Let q(i) = 9*i**3 + 339*i**2 - 2556*i + 5232. Let v(n) = -q(n) - 12*y(n). Factor v(k).
3*(k - 105)*(k - 4)**2
Let d(j) be the third derivative of -7/6*j**3 - 31*j**2 + 0*j + 1/60*j**5 + 0 + 1/4*j**4. Factor d(f).
(f - 1)*(f + 7)
Suppose -925 = -20*r - 345. What is i in -r*i**4 + 15*i**4 + 44*i**3 - 2 - 48*i**2 + 0 + 4*i + 16*i = 0?
1/7, 1
Let 0*z**2 + 74 + z**2 - 57*z + 56 - 259 - 71*z = 0. What is z?
-1, 129
Let x(k) = -10*k - 38. Let h be x(-4). Suppose 0 = -5*z - 4*q + 14, -h*q = -z - 0*z. Factor -304*g**2 + 303*g**z + 0*g - g.
-g*(g + 1)
Let b(v) be the first derivative of v**5/15 - 23*v**4/30 + 8*v**3/5 - 47*v**2/2 - 14. Let o(l) be the second derivative of b(l). Determine j so that o(j) = 0.
3/5, 4
Let v(i) be the third derivative of i**6/90 + 7*i**5/15 + 13*i**4/6 - 11*i**3/2 - 2*i**2 + 29. Let x(f) be the first derivative of v(f). Factor x(k).
4*(k + 1)*(k + 13)
Let w(f) b