Factor by grouping (sometimes called the ac-method).
$28 x^{2} - x - 2$
First, choose a form with appropriate signs.
Then, fill in the blanks with numbers to be used for grouping. Finally, show the factorization.
Form:
$28 x^{2} + ◻ x + ◻ x - 2$
$28 x^{2} + ◻ x - ◻ x - 2$
$28 x^{2} - ◻ x + ◻ x - 2$
$28 x^{2} - ◻ x - ◻ x - 2$
Factorization:

Answer

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Answer

Thus, the factorization of the given expression $28 x^{2} - x - 2$ is $(4 x + 1) (7 x - 2)$ .

Steps

Step 1 ：First, we multiply the coefficient of the x^2 term (28) by the constant term (-2) to get -56.

Step 2 ：We then need to find two numbers that multiply to -56 and add to -1 (the coefficient of the x term). The numbers that satisfy these conditions are -8 and 7.

Step 3 ：We can then rewrite the middle term of the quadratic as -8x + 7x. This allows us to group the terms and factor by grouping.

Step 4 ：Finally, we factor the expression to get (4x + 1)(7x - 2).

Step 5 ：Thus, the factorization of the given expression $28 x^{2} - x - 2$ is $(4 x + 1) (7 x - 2)$ .

Answer

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