Factor the polynomial by grouping:
2x² – 8xy – 9x + 36y
Take out the greatest common factor of each pair of terms. For instance,
• the greatest common factor of 2x² and – 8xy is 2x, so rewrite those terms as a multiple of 2x:
2x² = 2x · x ✔
– 8xy = 2x · (– 4y) ✔
• the greatest common factor of – 9x and 36y is 9, so rewrite those terms as a multiple of 9:
– 9x = 9 · (– x)
36y = 9 · 4y
Instead of factoring out 9, see what happens if you factor out – 9:
– 9x = – 9 · x ✔
36y = – 9 · (– 4y) ✔
That last option is better for what comes next, which is factoring that polynomial by grouping.
Take the polynomial and rewrite it conveniently:
2x² – 8xy – 9x + 36y
= 2x · x + 2x · (– 4y) – 9 · x – 9 · (– 4y)
Just take out common factors. From the first two terms, take 2x out, and for the last two, take out – 9:
= 2x · (x – 4y) – 9 · (x – 4y)
Now, (x – 4y) is a common factor, then just take it out to finally get to the factored form:
= (x – 4y) · (2x – 9) <——— this is the answer.
I hope this helps. =)