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:
\[
28 x^{2}+\square x+\square x-2
\]
$28 x^{2}+\square x-\square x-2$
$28 x^{2}-\square x+\square x-2$
$28 x^{2}-\square x-\square x-2$
Factorization:
Answer
Thus, the factorization of the given expression \(28 x^{2}-x-2\) is \(\boxed{(4x + 1)(7x - 2)}\).
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 \(\boxed{(4x + 1)(7x - 2)}\).
