e -16*(2*-1 + 45/18). Let i be v(b). Determine u so that 4/3*u**i + 8/3*u**2 - 4/3*u - 8/3 = 0.
-2, -1, 1
Let u(n) = 3*n**3 - 16*n**2 + 28*n + 10. Let b(o) = o**3 - 8*o**2 + 13*o + 4. Let f(c) = -5*b(c) + 2*u(c). Find r such that f(r) = 0.
-9, 0, 1
Suppose -213*a + 216*a = 12. Let b(k) be the second derivative of -6*k**3 + 0 - 2*k - 3/2*k**2 - 9*k**a. Let b(h) = 0. Calculate h.
-1/6
Let b(p) be the second derivative of p**4/108 + p**3/27 - 5*p**2/6 - 18*p - 1. Determine q, given that b(q) = 0.
-5, 3
Let i(k) be the first derivative of 7*k**4/30 - 4*k**3/3 + 12*k**2/5 - 16*k/15 - 43. Factor i(c).
2*(c - 2)**2*(7*c - 2)/15
Let h(n) be the second derivative of 0 - n**5 + 1/2*n**6 + 5/3*n**3 - 5/4*n**4 + 5/21*n**7 - 5*n + 0*n**2. Let h(c) = 0. What is c?
-2, -1, 0, 1/2, 1
Factor -33*v + 16*v**2 - 13*v**2 + 16 - v**3 + 0 + 15*v**2.
-(v - 16)*(v - 1)**2
Let r(h) = -h**2 - 1. Let k(f) = 5*f**2 - 7*f + 14. Let w(o) = k(o) + 4*r(o). Factor w(x).
(x - 5)*(x - 2)
Suppose -3275*b + 3270*b = -40. Let w(l) be the first derivative of 2/3*l**3 + 9 - b*l + 0*l**2. Factor w(q).
2*(q - 2)*(q + 2)
Let d = -1/3332 - -6669/16660. What is h in 0 + 0*h + d*h**2 = 0?
0
Let g = -295 + 300. Let q(l) be the third derivative of 0*l + 0*l**4 + 0 + 0*l**3 - 1/60*l**5 + g*l**2. Suppose q(w) = 0. Calculate w.
0
Let h(q) = -q. Let n be h(-8). Suppose 4*g - 2*g = n. Solve m - g*m - 144*m**3 - 193*m**4 + m**4 - 35*m**2 - m**2 = 0.
-1/4, 0
Let b(r) be the third derivative of r**8/504 + 2*r**7/105 - r**6/30 - 22*r**5/45 - 17*r**4/12 - 2*r**3 - 33*r**2 + 2*r. Factor b(l).
2*(l - 3)*(l + 1)**3*(l + 6)/3
Let i(v) be the second derivative of 16*v + 0 - 1/18*v**4 - 7/18*v**3 - 5/6*v**2. Find c such that i(c) = 0.
-5/2, -1
Let x(d) be the second derivative of -d**7/2520 - d**6/360 - 37*d**4/12 - 31*d. Let g(n) be the third derivative of x(n). Factor g(j).
-j*(j + 2)
Factor -14/5*u - 2/5*u**2 - 4.
-2*(u + 2)*(u + 5)/5
Suppose -40*l = -85 - 35. Let a(c) be the first derivative of -7 + 3/4*c**2 + 1/6*c**l + 0*c. Factor a(y).
y*(y + 3)/2
Suppose -37*k = -58*k + 41*k. Find d such that 5*d**2 + 5*d**3 + 5/4*d**4 + 0 + k*d = 0.
-2, 0
Solve -2/19*a**2 + 12/19 + 10/19*a = 0.
-1, 6
Let d(z) be the first derivative of z**5/270 - z**3/27 - 5*z**2/2 - 8. Let a(o) be the second derivative of d(o). Factor a(b).
2*(b - 1)*(b + 1)/9
Let r(v) be the second derivative of 81/10*v**2 - 25*v - 3/5*v**3 + 1/60*v**4 + 0. Determine a so that r(a) = 0.
9
Suppose -15*l**3 - 29*l**3 + l**4 - l**2 + 5*l + 39*l**3 = 0. Calculate l.
-1, 0, 1, 5
Factor -1/6*y**4 + 1/6*y**3 + 1 + 7/6*y**2 - 13/6*y.
-(y - 2)*(y - 1)**2*(y + 3)/6
Let q(j) be the first derivative of 0*j**3 - 1/3*j**4 + 10 + 2*j**2 + 13*j. Let y(u) be the first derivative of q(u). Factor y(k).
-4*(k - 1)*(k + 1)
Let w be -1 + -2 + (15 - 0). Let o = -10 + w. Let -o*u + 0*u + u - u**2 = 0. Calculate u.
-1, 0
Factor 0*l - 5/9*l**3 + 4/9*l**4 - 1/9*l**5 + 0 + 2/9*l**2.
-l**2*(l - 2)*(l - 1)**2/9
Let a(j) be the second derivative of j**9/13608 - j**8/3780 + j**6/810 - j**5/540 + 5*j**3/3 + j. Let q(f) be the second derivative of a(f). Factor q(m).
2*m*(m - 1)**3*(m + 1)/9
Let u be -5 - ((-17)/3 - 57/(-114)). Find n, given that 0 + u*n**4 - 1/6*n + 1/6*n**3 - 1/6*n**2 = 0.
-1, 0, 1
Find u, given that 18*u + 19*u**2 - 2*u + 14*u - 35*u**2 + 19*u**2 = 0.
-10, 0
Let i = -157 + 159. Let s(p) be the second derivative of 0 - p**4 - 1/5*p**6 + i*p + p**2 + 0*p**3 + 4/5*p**5. Factor s(z).
-2*(z - 1)**3*(3*z + 1)
Let o(n) be the second derivative of 3*n**7/280 + n**6/24 - n**5/10 - n**4/2 + 8*n**3/3 + 16*n. Let u(x) be the second derivative of o(x). Factor u(f).
3*(f - 1)*(f + 2)*(3*f + 2)
Let d(q) be the first derivative of q**3/12 - 2*q**2 + 375. Factor d(g).
g*(g - 16)/4
Let d be (-40)/((-16)/4) + -2. Suppose d = 2*z + 4. Determine o so that -2*o**2 - z - 3*o - 2 - 3*o = 0.
-2, -1
Determine t, given that -10*t**2 + 356 + 59*t - 2*t**3 + 8*t - 17*t - 106 = 0.
-5, 5
Let y(f) = -2*f**4 + 2*f**3 + f**2. Let a(x) = 292*x**4 - 772*x**3 - 509*x**2 + 486*x - 81. Let m(s) = a(s) - 4*y(s). Determine j so that m(j) = 0.
-1, 3/10, 3
Let u(g) be the third derivative of g**7/5460 - g**6/390 + 3*g**5/260 - 13*g**3/6 - 6*g**2. Let v(n) be the first derivative of u(n). Factor v(r).
2*r*(r - 3)**2/13
Let p = 69 + -66. Let j(u) be the first derivative of 4*u**2 - 4/3*u**p - 4*u - 1. Factor j(v).
-4*(v - 1)**2
Let k(u) be the third derivative of 2*u**7/105 - u**6/10 - u**5/15 + u**4/2 + 21*u**2 + u. Factor k(j).
4*j*(j - 3)*(j - 1)*(j + 1)
Let u(x) be the second derivative of 0*x**3 + 1/10*x**6 + 0*x**2 - 1/10*x**5 + 4*x + 0 - 1/12*x**4. Suppose u(r) = 0. Calculate r.
-1/3, 0, 1
Let w be (-8)/((-192)/(-257)) - -11. Let b(v) be the third derivative of -2*v**2 + 1/12*v**5 + 1/2*v**3 - w*v**4 + 0*v + 0 - 1/120*v**6. Factor b(h).
-(h - 3)*(h - 1)**2
Suppose 0 = b - 0 + 3, 5*t = 5*b + 30. Let p be ((-2)/(-4 + 0))/1. Factor -p*y**4 + 0 + y**t + 2*y**2 - 4*y.
-y*(y - 2)**2*(y + 2)/2
Let m(o) be the first derivative of o**4/36 - 2*o**2/3 + 46*o + 28. Let c(x) be the first derivative of m(x). Solve c(u) = 0.
-2, 2
Suppose -19 = -5*c + r - 1, 4*r + 21 = 3*c. Suppose 0 = -3*l + 13 - 7. Factor 3*s**l - 2*s - 6 + 5*s - 3*s - c*s.
3*(s - 2)*(s + 1)
Suppose 0*d - 3*d - 4*x + 468 = 0, -4*d = -3*x - 599. Factor -13*l**2 + d*l**3 - 157*l**3 + 25*l - 7*l**2.
-5*l*(l - 1)*(l + 5)
Let z(s) be the third derivative of -s**5/30 + 21*s**4/8 + 16*s**3/3 + 227*s**2. Factor z(p).
-(p - 32)*(2*p + 1)
Let k(r) = -r**2 + 11*r - 6. Let b(x) = 15 + x**2 - 7*x - 4 - 21*x + 7*x. Let v(p) = -6*b(p) - 11*k(p). Factor v(d).
5*d*(d + 1)
Suppose 3*l = 6*l - 90. What is f in -4 + 4 - 25*f**2 + l*f**2 = 0?
0
Let r(b) = -b**2 + 20*b + 227. Let n be r(28). Factor 20/7*j + 4/7*j**2 + 12/7 - 4/7*j**n.
-4*(j - 3)*(j + 1)**2/7
Let y be 0 - -1 - 6106/(-2830). Let z = y + 12/283. Determine n so that -z + 1458/5*n**3 - 972/5*n**2 + 216/5*n = 0.
2/9
Let w(u) be the second derivative of -5/3*u**3 + 0*u**2 + 10*u + 0 + 1/3240*u**6 + 0*u**4 - 1/270*u**5. Let c(h) be the second derivative of w(h). Factor c(y).
y*(y - 4)/9
Suppose 8*o + 10 = 13*o. Let -2/19*r**o - 8/19 + 8/19*r = 0. What is r?
2
Let j be 7/((-441)/(-183)) - 5*(-4)/(-60). Factor -3/7*h**3 + 0 + 15/7*h**2 - j*h.
-3*h*(h - 3)*(h - 2)/7
Let r = 55/82 + -111/410. Determine m so that 1/5*m**5 + 3/5*m**4 - 3/5*m - 1/5 + 2/5*m**3 - r*m**2 = 0.
-1, 1
Suppose -10*s = -15*s. Let o(t) be the second derivative of -4*t + 0 - 1/30*t**6 - 1/42*t**7 + 0*t**2 + 1/20*t**5 + 1/12*t**4 + s*t**3. What is a in o(a) = 0?
-1, 0, 1
Suppose 5*w - 486 = 924. Factor 4122*l**3 + 358*l - 2272*l**2 - 1764*l**4 - 43 + w*l - 21 - 762*l**3.
-4*(3*l - 2)**2*(7*l - 2)**2
Let v(l) be the third derivative of 121*l**6/30 + 11*l**5 + 8*l**4 + 8*l**3/3 + 3*l**2 - l. Find k such that v(k) = 0.
-1, -2/11
Suppose 2*x - 61 = 4*n + 37, -2*x - 5*n + 80 = 0. Let h be 2*4 - x/9. Factor -3/5 + 9/5*b**2 + 4/5*b**h - 2*b.
(b - 1)*(b + 3)*(4*b + 1)/5
Suppose 1 = 4*c + 9. Let v be (c/10)/(9/(-18)). Determine z so that -4/5*z**4 + 6/5*z**3 - 8/5*z + 8/5*z**2 - v*z**5 + 0 = 0.
-2, 0, 1
Factor -360*a + 427*a + 48 + 1323*a**2 + 437*a.
3*(21*a + 4)**2
Let f = 6 - 7. Let j be (-112)/(-77)*1/(-2)*f. Factor -2/11*q**2 - 8/11*q - j.
-2*(q + 2)**2/11
What is h in 1/2 + h**3 - 1/2*h**5 - 1/2*h + 1/2*h**4 - h**2 = 0?
-1, 1
Let r(u) be the second derivative of -2*u**7/21 - 26*u**6/15 + 17*u**5/5 + 37*u**4/3 - 136*u**3/3 + 56*u**2 + 333*u. Factor r(j).
-4*(j - 1)**3*(j + 2)*(j + 14)
Let p be (172/(-12) + 14)*6/(-4). Suppose 25/2 - 5*g + p*g**2 = 0. Calculate g.
5
Let x(s) be the first derivative of s**3/12 + 107*s**2/8 - 815. Suppose x(z) = 0. What is z?
-107, 0
Determine s so that 8*s**3 + 7*s**3 - 7*s**4 - 15*s**2 + 5*s + 9*s**4 - 7*s**4 = 0.
0, 1
Suppose 3*w + 1 = 4*d, 17*w = 21*w - 4*d - 4. Let t(p) be the third derivative of 0 + 1/360*p**w - 7*p**2 + 0*p**4 - 1/36*p**3 + 0*p. Solve t(s) = 0 for s.
-1, 1
Let g = -72 + 76. Let a(m) be the third derivative of -1/12*m**g + 0*m**3 - 1/24*m**6 + 7/60*m**5 + 0 + 0*m + 4*m**2. Factor a(z).
-z*(z - 1)*(5*z - 2)
Determine u, given that -93*u**4 - 209*u**3 + 18*u - 2*u**3 - 12*u**5 + 48*u**2 + 43*u**3 - 18*u = 0.
-4, 0, 1/4
Factor -20/9 - 2/9*m**2 + 14/9*m.
-2*(m - 5)*(m - 2)/9
Suppose 4*n + 4*b