t p(o) be the third derivative of -o**8/504 + o**6/45 - o**5/45 - o**4/12 + 2*o**3/9 - o**2 - 182*o. Determine f, given that p(f) = 0.
-2, -1, 1
Suppose -1 = -r - 4*u + 1, -3*u + 6 = 3*r. Let 30*y - 16*y**2 + 4 - 7*y**r + 5 + 4*y**3 = 0. What is y?
-1/4, 3
Let h(r) be the second derivative of -1/231*r**7 - 7/165*r**6 + 0 - 39*r + 0*r**2 - 9/55*r**5 - 10/33*r**4 - 8/33*r**3. Determine n so that h(n) = 0.
-2, -1, 0
Suppose -10*j = -74 + 24. Let q(h) be the second derivative of -h**3 + 5/8*h**4 - 3/4*h**2 + 0 - j*h. Factor q(w).
3*(w - 1)*(5*w + 1)/2
Suppose 2*x = -4*i - 4, 0 = 2*x - 4*i - 13 - 23. Suppose 5*n - x = -4*u, -3*u + 6 = -3*n + 7*n. Solve 0*q**3 - q**3 - u*q**2 - 8*q**3 = 0.
-2/9, 0
Let l(p) = 7 - 3*p**2 + 6*p**2 - 4*p**2 + 14*p - 8*p. Let f be l(7). Factor 0*i**2 + f - 4/9*i**3 + 14/9*i**4 + 0*i.
2*i**3*(7*i - 2)/9
Let n(j) be the second derivative of j**5/10 - j**4/2 - 2*j**3 + 8*j**2 - 5*j + 29. Factor n(x).
2*(x - 4)*(x - 1)*(x + 2)
Let k(h) = 9*h + 10. Let j be k(11). Let s = 113 - j. Factor -3/2*d**s + 0*d - 3/2*d**3 + 0*d**2 + 0.
-3*d**3*(d + 1)/2
Suppose 5 - 17 = 4*m, 2*t + 2*m = -118. Let h = -167/3 - t. Suppose -2/3*w - h + 2/3*w**3 + 1/3*w**4 + 0*w**2 = 0. Calculate w.
-1, 1
Let q(o) = -7*o**3 - o. Let c be q(-1). Let h(y) = y**3 - 8*y**2 + 2. Let f be h(c). Factor 4/5*z - 8/5 + 4/5*z**f.
4*(z - 1)*(z + 2)/5
Let h be 1 + (-5)/225 - (-160)/(-360). Factor -2/15*k**2 - h - 8/15*k.
-2*(k + 2)**2/15
Let l(w) = 2*w**2 + 22*w + 61. Let p be l(-7). Let n(o) be the third derivative of -1/15*o**p + 0*o + 0 + 1/60*o**6 + 0*o**3 + 5*o**2 + 1/12*o**4. Factor n(v).
2*v*(v - 1)**2
Let t(h) be the first derivative of 2*h**7/7 - 4*h**6/15 - 3*h**5/5 + 2*h**4/3 + 9*h - 7. Let m(d) be the first derivative of t(d). Let m(i) = 0. Calculate i.
-1, 0, 2/3, 1
Let u(l) be the first derivative of l**4 + 648*l**3 + 157464*l**2 + 17006112*l - 455. Factor u(z).
4*(z + 162)**3
Let h(l) be the first derivative of 8*l**3/3 + 50*l**2 + 48*l + 52. Factor h(d).
4*(d + 12)*(2*d + 1)
Let f(g) be the second derivative of -g**5/20 + 7*g**4/4 - 33*g**3/2 - 121*g**2/2 - g - 6. Suppose f(o) = 0. Calculate o.
-1, 11
Let h(t) = -3*t**2 - 362*t - 11163. Let o(k) = -3*k**2 - 363*k - 11163. Let a(y) = 3*h(y) - 4*o(y). Find z such that a(z) = 0.
-61
Factor -40/7*v + 0 - 2/7*v**2.
-2*v*(v + 20)/7
Let l(x) be the first derivative of x**5/10 + x**4/2 + 5*x**3/6 + x**2/2 - 78. Factor l(g).
g*(g + 1)**2*(g + 2)/2
Find n, given that 1 + 4*n - 3 + 2 + 3 - 6 - n**2 = 0.
1, 3
Let x(v) be the second derivative of -v**5/5 - 13*v**4/15 + 52*v**3/15 - 16*v**2/5 - 4*v + 14. Let x(c) = 0. Calculate c.
-4, 2/5, 1
Let t(o) be the first derivative of o**7/315 + o**6/60 + o**5/45 - 5*o**2/2 + 6. Let j(p) be the second derivative of t(p). Factor j(h).
2*h**2*(h + 1)*(h + 2)/3
Solve -8/7 - 2/7*m**2 + 8/7*m = 0 for m.
2
Suppose -2*a + 489*g - 492*g + 4 = 0, 5*a - 10 = 5*g. Factor -1/2*j - 7/4*j**3 + 9/4*j**a + 0.
-j*(j - 1)*(7*j - 2)/4
Let w(k) be the second derivative of k**4/12 - k**3/2 + k**2 + k + 41. Let w(h) = 0. What is h?
1, 2
Let o = -471 + 3306/7. Solve 0*a + 3/7*a**2 + 0 - 6/7*a**3 - o*a**4 = 0.
-1, 0, 1/3
Suppose -2552 = -2*w - 2*w. Let b = -4454/7 + w. Determine x, given that 2/7*x**5 + 8/7*x**2 + 2/7*x + 0 + b*x**3 + 8/7*x**4 = 0.
-1, 0
Let a(j) = j**3 - 8*j**2 + 6*j + 9. Let v be a(7). Solve 2*i**5 - 21*i**2 - 6*i - 8*i**4 + 4*i**3 + 49*i**2 - 20*i**v = 0.
-1, 0, 1, 3
Find t such that 12*t**4 + 35*t**5 - 130*t**3 - 4*t**2 + 48*t**4 - 6*t**2 - 124*t**3 + 269*t**3 = 0.
-1, 0, 2/7
Let f(a) be the second derivative of a**5/200 + a**4/40 - 3*a**3/10 - 2*a - 6. Factor f(s).
s*(s - 3)*(s + 6)/10
Let z(x) be the third derivative of 1/560*x**8 + 0 + 0*x - 1/100*x**6 + 0*x**3 + 0*x**5 + 10*x**2 + 0*x**7 + 1/40*x**4. Solve z(m) = 0.
-1, 0, 1
Let z(o) be the second derivative of 46*o + 1/24*o**5 + 0 - 5/18*o**4 + 0*o**2 + 5/9*o**3. Factor z(t).
5*t*(t - 2)**2/6
Suppose 0 = -2*t - 3*k + 515, 5*t - 5*k - 801 = 2*t. Find b, given that -t*b + 260*b + 7 + b**2 - 6 = 0.
1
Let d(r) be the first derivative of r**6/450 + r**5/25 - 7*r**4/30 - r**3 + 29. Let c(a) be the third derivative of d(a). Find y, given that c(y) = 0.
-7, 1
Let g(l) be the third derivative of -7*l**2 + 1/10*l**5 + 1/12*l**4 + 0*l + 0 + 0*l**3 - 1/15*l**6. Factor g(p).
-2*p*(p - 1)*(4*p + 1)
Let v be 24/18 - 4/3. Let k be v + 1 + -4 + 5. Factor -8*o**2 - 2*o + 0*o**3 - 4*o**3 - 6*o**3 - 8*o**4 - k*o**5 - 2*o**3.
-2*o*(o + 1)**4
Let y(f) be the first derivative of -f**6/27 - 2*f**5/45 + 4*f**4 - 912. Find q, given that y(q) = 0.
-9, 0, 8
Let c(d) be the second derivative of -5*d**5/18 + 5*d**4/9 - 4*d**3/9 - 8*d**2 + 6*d. Let h(o) be the first derivative of c(o). Find p such that h(p) = 0.
2/5
Let d(k) be the first derivative of -k**4/2 - 86*k**3 - 4095*k**2 + 8450*k + 159. Determine z so that d(z) = 0.
-65, 1
Suppose -3*n - 454 = -4*x - 421, 0 = 5*x + 3*n - 21. Factor -x*d + 3/2*d**2 + 0.
3*d*(d - 4)/2
Suppose 2*r = -h + 2, 4*r - 36 = 30*h - 28*h. Suppose -3*y + 3 = -3. Solve -4/5*t + 14/5*t**y + 2*t**4 - 2/5*t**r + 0 - 18/5*t**3 = 0.
0, 1, 2
Let s(m) be the first derivative of 0*m**2 - 8 + 1/100*m**5 + 0*m + 1/600*m**6 - 5*m**3 + 0*m**4. Let l(h) be the third derivative of s(h). Factor l(a).
3*a*(a + 2)/5
Let w(j) = 60*j**4 - 385*j**3 + 685*j**2 - 360*j - 25. Let z(i) = -5*i**4 + 32*i**3 - 57*i**2 + 30*i + 2. Let o(h) = -2*w(h) - 25*z(h). Factor o(a).
5*a*(a - 3)*(a - 2)*(a - 1)
Let z = 49 + -9. Let v be 7 + -1 - z/10. Factor 16*j + 6 - 18*j**2 + 9*j**v + 2*j**2 + j**2.
-2*(j - 3)*(3*j + 1)
Let n(d) be the first derivative of d**3/12 + 29*d**2/4 + 841*d/4 - 389. Find c such that n(c) = 0.
-29
Let u be (-38)/(-10) + -3 + 48/15. Factor 4 + 177*r**3 - 178*r**3 - 2*r**2 + r**5 + 2*r**u - 4.
r**2*(r - 1)*(r + 1)*(r + 2)
Determine t so that -26/15*t**5 + 4/15*t + 14/15*t**2 - 22/5*t**3 + 0 + 74/15*t**4 = 0.
-2/13, 0, 1
Let v(n) be the first derivative of -n**4/6 + 5*n**3/9 + 11*n**2/3 + 5*n - 402. Factor v(g).
-(g - 5)*(g + 1)*(2*g + 3)/3
Let x(o) = -98*o**2 - 25 + 62*o + 18*o + 18*o - 7*o. Let n(s) = -s + 1. Let z(l) = -14*n(l) - 2*x(l). Factor z(g).
4*(7*g - 3)**2
Let x be (3/2)/(1/2). Let h = -1 + 4. Suppose 2*s**4 + 7*s**x - 2*s**2 + 4*s**2 - 11*s**h = 0. Calculate s.
0, 1
Solve 2*y**3 - 1 + 1/3*y**5 - 2/3*y**2 - 7/3*y + 5/3*y**4 = 0.
-3, -1, 1
Suppose -184 = v - 50*v + 3*v. Let d be (-1)/(-3) + (-2)/6. Determine a so that 0*a**2 + d + 0*a + 1/5*a**v + 2/5*a**3 = 0.
-2, 0
Suppose 35*o - 31*o - 192 = 0. Let -o*q**2 + 50*q - 15 + 8*q**2 - 20*q**2 + 30*q**3 + 0 - 5*q**4 = 0. Calculate q.
1, 3
Let s(c) = 12*c**2 + 19*c + 20. Let x(g) = 5*g**2 + 10*g + 8. Let o(y) = 2*s(y) - 5*x(y). Factor o(n).
-n*(n + 12)
Let d(z) = z**3 + 16*z**2 + 15*z + 4. Let o be d(-15). Factor 7*g**4 + 0*g**5 - 8*g**o - 4*g**5 - 3*g**4.
-4*g**4*(g + 1)
Let p = 16004/34153 + 4/2009. Factor 2/17*d**2 + 8/17 - p*d.
2*(d - 2)**2/17
Let p be 7 - (8/(-8) - 76/(-10)). Factor -2*o**2 - 16/5*o - p*o**3 - 8/5.
-2*(o + 1)*(o + 2)**2/5
Let z(x) be the second derivative of -x**4/16 - 11*x**3/48 - 5*x**2/16 + 353*x. Solve z(k) = 0.
-1, -5/6
Let u = -1350 + 12152/9. Factor 10/9*m**3 - 8/9*m - 4/3*m**2 + 16/9 - u*m**4.
-2*(m - 2)**3*(m + 1)/9
Let z(g) be the second derivative of 4*g**6/15 + 11*g**5/5 + 4*g**4/3 - 10*g**3/3 + 138*g. Factor z(u).
4*u*(u + 1)*(u + 5)*(2*u - 1)
Suppose 5*u + 57 = 5*y + 27, -4*y = 5*u + 12. Factor 14/11*k**5 - 32/11*k**4 + y*k**3 + 0*k + 0 - 4/11*k**2.
2*k**2*(k - 1)**2*(7*k - 2)/11
Let a(u) = 2*u**2 + 8*u + 2. Let f(i) = i**2 - 5 + 4 - 6*i**2 + 6*i**2. Let s(j) = a(j) + 2*f(j). Determine d so that s(d) = 0.
-2, 0
Let b(i) = -i**2 - 4*i + 62. Let c be b(-10). Factor 1/11*p**c - 4/11*p + 3/11.
(p - 3)*(p - 1)/11
Let a(l) be the second derivative of -2*l**7/147 + 31*l**6/105 + 26*l**5/35 - l**4/3 - 50*l**3/21 - 17*l**2/7 - 122*l. Let a(j) = 0. What is j?
-1, -1/2, 1, 17
Let u(j) = 5*j**2 + 8*j + 8. Let f(a) = -7*a**2 - 7*a - 10. Let q(t) = -4*f(t) - 5*u(t). Factor q(y).
3*y*(y - 4)
Let t be 13/(-78) - (-98)/12. Let c(n) be the first derivative of -4/3*n**3 - 6 + 2*n**2 + t*n. Factor c(s).
-4*(s - 2)*(s + 1)
Let h = -5384 - -37694/7. Factor -3/7*f**4 + 3/7 - h*f**3 + 0*f**2 + 6/7*f.
-3*(f - 1)*(f + 1)**3/7
Let x be 2/(-8) - 39/(-12). Let g be 4