Homework 1: Find the greates common monomial and factor the given polynomials.
1. 3m - 6m^2
2. 16abz - 8xyz
3. 2xy (a + b) — 4x (a + b) 8
4. ax - 2x + 3xy
5. 3abc - 12ab
1. 3m - 6m^2
2. 16abz - 8xyz
3. 2xy (a + b) — 4x (a + b) 8
4. ax - 2x + 3xy
5. 3abc - 12ab
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Here are the solutions to your homework:
3m - 6m^2 = 3m(1 - 2m)
16abz - 8xyz = 8z(2ab - xy)
2xy (a + b) — 4x (a + b) 8 = 2x(a + b)(y - 2)
ax - 2x + 3xy = x(a - 2 + 3y)
3abc - 12ab = 3ab(c - 4)
The greatest common monomial factor is the largest monomial that divides evenly into each term of the polynomial. To find it, you can factor out the greatest common factor of the coefficients and the highest power of each variable that divides evenly into each term. Then, you can divide each term by the greatest common monomial factor to write the polynomial in factored form.
I hope this helps! Let me know if you have any other questions.