0.
0, 1, 2
Let o(n) be the second derivative of n**5/24 + 85*n**4/72 - 70*n**3/3 + 5856*n. Determine r, given that o(r) = 0.
-24, 0, 7
Let j be 14/(-28) + (-459)/(-162). Factor 1/3*p**2 + 2*p - j.
(p - 1)*(p + 7)/3
Let v(f) be the second derivative of f**5/60 + 43*f**4/36 - 22*f**3/9 + 18*f. Solve v(c) = 0 for c.
-44, 0, 1
Let u = 246497/1725577 + 2/246511. Let h be 0 - 2 - 45/(-21). Factor -1/7*j**2 + 0 - h*j**5 + u*j**3 + 0*j + 1/7*j**4.
-j**2*(j - 1)**2*(j + 1)/7
Factor 19511 - 890*a - 19643 + 26*a**3 - 89*a**2 - 115*a**2.
2*(a - 11)*(a + 3)*(13*a + 2)
Let s(n) be the third derivative of -n**9/272160 - n**8/30240 + n**6/810 - n**5/60 - 29*n**4/8 - 29*n**2. Let o(k) be the third derivative of s(k). Factor o(c).
-2*(c - 1)*(c + 2)**2/9
Let f(m) = 25*m**2 - 2831*m + 680. Let y be f(113). Factor 0 - 6/7*t**3 + 4/7*t**y + 0*t + 2/7*t**4.
2*t**2*(t - 2)*(t - 1)/7
Let a = -41080/9 + 164329/36. Factor 2 + a*f**2 + 9/4*f.
(f + 1)*(f + 8)/4
Let y(g) = g**2 - 2*g + 0*g**2 + 21*g**3 - 22*g**3. Let x(k) = k**3 - k**2. Let w(l) = 2*x(l) + y(l). Suppose w(m) = 0. Calculate m.
-1, 0, 2
Let o(a) be the first derivative of -a**6/600 + a**4/40 + a**3/15 - a**2/2 + 37*a + 41. Let f(b) be the second derivative of o(b). Suppose f(n) = 0. What is n?
-1, 2
Let a(k) = 23*k**2 + 5*k - 10. Suppose 46*z = 25*z - 105. Let j(c) = 4*c**2 - 2. Let y(l) = z*a(l) + 20*j(l). Factor y(b).
-5*(b + 1)*(7*b - 2)
Find x such that -593/4*x**2 + 7/4*x**3 - 43 - 193*x = 0.
-1, -2/7, 86
Factor 30565*g**3 + 20*g**2 + 30562*g**3 - 4*g**4 + 12*g - 61123*g**3.
-4*g*(g - 3)*(g + 1)**2
Let d = -358965 + 717981/2. Factor -3/2*r**3 - 57/2 + 111/2*r - d*r**2.
-3*(r - 1)**2*(r + 19)/2
Suppose 4*c = 2*z + 452, -2 = 3*z + 4. Let n be 1/(-7)*2 + c/392. Suppose -4/7*b**3 + 4/7*b**2 + n + 0*b = 0. Calculate b.
0, 1
Let m = 255493 - 255490. Factor -2/11*k**4 + 6/11*k**2 + 0*k - 4/11*k**m + 0.
-2*k**2*(k - 1)*(k + 3)/11
Factor -26 + 58/3*w - 2/3*w**3 + 22/3*w**2.
-2*(w - 13)*(w - 1)*(w + 3)/3
Let p be ((-5)/(-15) + 112/42)/(30/40). Let p*y**2 + 2/11*y**4 - 64/11 - 18/11*y**3 + 0*y = 0. What is y?
-1, 2, 4
Factor 6*t**2 - 3829717*t**3 - 5*t**4 + 3829707*t**3 - t**4 + 2*t**5 + 8*t.
2*t*(t - 4)*(t - 1)*(t + 1)**2
Let o(h) = -180*h**2 + 2881*h - 12. Let c be o(16). Factor 6/7*w**3 - 6/7*w + 0 + 2/7*w**c - 2/7*w**2.
2*w*(w - 1)*(w + 1)*(w + 3)/7
Let -45/2 - 1/4*j**2 + 91/4*j = 0. Calculate j.
1, 90
Let q(b) be the first derivative of -2*b**3/27 + 902*b**2/9 - 406802*b/9 + 661. Factor q(f).
-2*(f - 451)**2/9
Suppose 8379/2*c**2 + 6690*c + 843*c**3 + 3342 + 3/2*c**4 = 0. Calculate c.
-557, -2, -1
Let c(i) = -830*i**2 + i**3 + 1646*i**2 + 6*i - 827*i**2. Let v(r) = -r**3. Let k be (-2)/6 + (-4)/(-3). Let p(l) = k*c(l) - 2*v(l). Factor p(y).
y*(y - 3)*(3*y - 2)
Let g be 750 - (3/2)/(24/(-32)). Factor -728*u**2 - 45*u**5 - 73*u**4 + g*u - 288 + 9*u**4 + 324*u**3 + 49*u**5.
4*(u - 9)*(u - 2)**3*(u - 1)
Let b(y) be the third derivative of y**6/900 - 29*y**5/150 + 841*y**4/60 - 35*y**3/6 + 3*y**2 - 8. Let c(w) be the first derivative of b(w). Factor c(z).
2*(z - 29)**2/5
Let r(d) be the first derivative of d**5 - 80*d**4 - 5*d**3/3 + 160*d**2 - 2055. Determine u, given that r(u) = 0.
-1, 0, 1, 64
Let i(w) be the third derivative of w**7/350 - 11*w**6/120 + 57*w**5/50 - 63*w**4/10 + 36*w**3/5 + 193*w**2. Factor i(o).
(o - 6)**3*(3*o - 1)/5
Suppose -12 - 52 = -16*o. Let k be (-3)/(-6)*(66/15 - o). Suppose -1/5*y + 0 + k*y**3 + 0*y**2 = 0. Calculate y.
-1, 0, 1
Let x be 820/24 - 6/36 - 4. Suppose -2*n - 22 = -x. Factor -1/5*u + 0 + 0*u**3 - 3/10*u**2 + 1/10*u**n.
u*(u - 2)*(u + 1)**2/10
Suppose -v + 6*v = u - 32, -5*u = 5*v - 160. Suppose 8 = -2*i, -3*i + 20 = f + u. Determine g so that 6/7*g + 8/7*g**2 + f + 2/7*g**3 = 0.
-3, -1, 0
Let d(q) = q**2 + 22*q + 23. Let w be d(-21). Suppose 680*u + 106 - w*u**3 - 2*u**3 - 668*u - 16*u**2 - 34 = 0. Calculate u.
-3, 2
Determine c so that 10/7*c**5 - 2*c**4 + 2*c**2 + 0 - 4/7*c - 6/7*c**3 = 0.
-1, 0, 2/5, 1
Suppose 706 + 2187 = 263*g. Let s(k) be the first derivative of 1/2*k**3 + 0*k - 3/16*k**4 + 9/8*k**2 - g. Factor s(n).
-3*n*(n - 3)*(n + 1)/4
Factor 1/2*w**4 - 1/2*w**3 - 2*w**2 + 2*w + 0.
w*(w - 2)*(w - 1)*(w + 2)/2
Let p(w) = 5*w**2 + 2*w - 19. Suppose -5*c + 7*c = 16. Let j be p(c). Factor -4*t - t**3 - t - j*t**2 + 323*t**2.
-t*(t - 5)*(t - 1)
Let w = -76184 + 228553/3. Factor w*m**3 + m - 1/3 - m**2.
(m - 1)**3/3
Let n(i) be the first derivative of 1/3*i - 25/18*i**3 - 23/12*i**2 - 252. Find d, given that n(d) = 0.
-1, 2/25
Suppose -45 = -683*g + 682*g. Let o be (-6)/5*6/((-432)/g). Factor o*p**3 + 0 + 3/4*p**2 - 3/2*p.
3*p*(p - 1)*(p + 2)/4
Suppose -1/2*z**2 + 0 - 45*z = 0. What is z?
-90, 0
Let u be 2/20*2*2850/1254. Factor -75/11 + u*h - 1/11*h**3 + 7/11*h**2.
-(h - 5)**2*(h + 3)/11
Let p(q) be the third derivative of -q**6/600 + 1341*q**5/100 - 1349381*q**4/40 + 4044121*q**3/30 - 10602*q**2. Let p(u) = 0. Calculate u.
1, 2011
Let d be 33/(-55) - (-3)/5. Let g be (-11)/154 + (-406)/(-196). Factor -2/3*k**g + d + 2/3*k**3 - 4/3*k.
2*k*(k - 2)*(k + 1)/3
Let p(r) be the second derivative of 40*r**7/21 - 68*r**6/3 - 75*r**5/4 + 45*r**4/4 - 349*r. Determine y so that p(y) = 0.
-3/4, 0, 1/4, 9
Suppose -157*v - 64 = -189*v. Factor -2*f - 6/5*f**v - 4/5 + 2/5*f**3 + 2/5*f**4.
2*(f - 2)*(f + 1)**3/5
Let p be 48/21 - (3 + -1). Let d be (6/21)/(16/(-16)*1/(-7)). Factor -p*r**4 + 0 - 4/7*r**3 + 6/7*r**d + 0*r.
-2*r**2*(r - 1)*(r + 3)/7
Let f(a) be the third derivative of -47*a**2 + 3*a**4 + 0*a - 108*a**3 - 1/30*a**5 + 0. Factor f(j).
-2*(j - 18)**2
Solve 4/5*d**2 + 56/5 + 62/5*d - 2/5*d**3 = 0.
-4, -1, 7
Let p(c) be the third derivative of -2 - 1/2*c**4 - 8*c**3 + 3/5*c**5 - 1/40*c**6 - 1/70*c**7 + 0*c - 2*c**2. Let p(x) = 0. Calculate x.
-4, -1, 2
Suppose -6*z - 292 = -316. Suppose o - 2 = 0, -2*n + 0 - 4 = -z*o. What is t in -2/3*t - 1/3*t**4 - 5/3*t**n - 4/3*t**3 + 0 = 0?
-2, -1, 0
Let k(f) = 2*f - 11. Let g be k(8). Suppose 21 = g*b - a, 3*b + a = -0*a + 11. Factor 236*l**3 + 16*l**b - 192*l**3 - l**2 - 11*l**2.
4*l**2*(l + 3)*(4*l - 1)
Suppose -3*s = -4*v - 303, 2*s - 11*v - 202 = -6*v. Solve 70 + s*y + 57*y - 22*y**2 - 112*y + 2*y**3 = 0.
-1, 5, 7
Let o = -1/2006 - -3518/15045. Let u(r) be the third derivative of 0 + 22*r**2 - 2*r**4 - 8/3*r**3 + o*r**6 + 0*r + 3/5*r**5. Find d such that u(d) = 0.
-2, -2/7, 1
Factor -328*x + 656*x - 48*x**3 + 16*x**3 - 338*x + 256*x**2 + 65*x**2.
-x*(x - 10)*(32*x - 1)
Let q(k) be the second derivative of -3*k**5/10 + 163*k**4/72 + 83*k**3/36 + 5*k**2/6 + 2*k - 535. Factor q(l).
-(l - 5)*(4*l + 1)*(9*l + 2)/6
Let j(f) = -2*f**2 + 1408*f - 44282. Let q be j(33). Let 44/3*u**3 + 0 + 64*u + 160/3*u**2 + 4/3*u**q = 0. Calculate u.
-4, -3, 0
Suppose k + 33 = 3*d, 3*d - 14 - 46 = 2*k. Let w be (0 + 1)/((-30)/k - 1). Factor 2 - 4*m**2 - w + 3 - 2*m - 6*m.
-4*(m + 1)**2
Let o(s) be the third derivative of 17/4*s**5 + 0*s - 130*s**4 + 0 + 49*s**2 - 1690/3*s**3 - 1/24*s**6. What is x in o(x) = 0?
-1, 26
Let -710803*r - 4*r**3 - 628*r**2 + 4293*r**2 + 268*r**2 + 731*r**2 - 648753*r = 0. What is r?
0, 583
Let s(f) be the first derivative of f**5/30 - 7*f**4/3 + 49*f**3 + 77*f - 87. Let z(h) be the first derivative of s(h). Factor z(i).
2*i*(i - 21)**2/3
Let g(j) be the third derivative of 119*j**2 - 45/8*j**4 + 2*j + 0 + 1/12*j**5 + 125/3*j**3. Factor g(r).
5*(r - 25)*(r - 2)
Let z(b) = -21*b**2 - b + 20. Let c(u) be the second derivative of 0 + 0*u**3 + 10*u + 2*u**2 - 1/3*u**4. Let v(r) = -11*c(r) + 2*z(r). Factor v(a).
2*(a - 2)*(a + 1)
Suppose -15*j + 18*j - 120 = 0. Let v be (36/j)/(14/105). Factor -19/4*d**3 - 2*d + d**4 - 1 + v*d**2.
(d - 2)**2*(d - 1)*(4*d + 1)/4
Let d(i) = -39*i**3 - 197*i**2 + 1411*i + 1625. Let h(g) = -8*g**3 - 39*g**2 + 282*g + 325. Let s(k) = 3*d(k) - 14*h(k). Factor s(f).
-5*(f - 5)*(f + 1)*(f + 13)
Suppose -12 = 4*x, v = 2*x + 40 + 54. Let y be 190/v - 140/112. Factor -y*j**3 + 0 + 2/11*j**4 + 18/11*j + 6/11*j**2.
2*j*(j - 3)**2*(j + 1)/11
Let z(t) be the third derivative of -2*t + 1/70*t**7 - 18*t**2 - t**4 - 1/5*t**5 + 0 + 0*t**3 + 1/20*t**6. Find o, given that z(o) = 0.
-2, 0, 2
Let b be (224 - -1)*1745/47115. Suppose 0 + 6*a + 1/3*a**4 + 2*a**3 - b*a**2 = 0. Calculate a.
-9, 0, 1, 2
Let w = 194 - 371. Let