Factoring 4x2−2xy−4x+3y−3Why isn't it working?

"Factoring 4x2−2xy−4x+3y−3Why isn't it working?" solved and explained

blitzbabeiy

2022-02-01

Factoring

4 x^{2} - 2 x y - 4 x + 3 y - 3

Why isn't it working?

ataill0k

Beginner2022-02-02Added 18 answers

Step 1
When

2 x = 3

, then the expression becomes

4 x^{2} - 2 x y - 4 x + 3 y - 3 = 9 - 3 y - 6 + 3 y - 3 = 0

Hence the expression can be factored by

(2 x - 3)

, and you can see easily that

4 x^{2} - 2 x y - 4 x + 3 y - 3 = (2 x - 3) (2 x - y + 1)

Emilie Booker

Beginner2022-02-03Added 14 answers

Step 1
Probably not the fastest, but I would like to suggest you use the general factorization method:
We have,

4 x^{2} - 2 x y - 4 x + 3 y - 3 = 4 x^{2} - x (2 y + 4) + (3 y - 3)

\Rightarrow Δ = {(y + 2)}^{2} - 4 (3 y - 3) = {(y - 4)}^{2}

\Rightarrow x_{1} = \frac{y + 2 + (y - 4)}{4} = \frac{y - 1}{2}

\Rightarrow x_{2} = \frac{y + 2 - (y - 4)}{4} = \frac{3}{2}

\Rightarrow 4 x^{2} - 2 x y - 4 x + 3 y - 3 = 4 (x - \frac{3}{2}) (x - \frac{y - 1}{2})

\Rightarrow 4 x^{2} - 2 x y - 4 x + 3 y - 3 = (2 x - 3) (2 x - y + 1)

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