Factor by grouping (sometimes called the ac-method).
$5 x^{2} + 6 x - 8$

First, choose a form with appropriate signs.
Then, fill in the blanks with numbers to be used for grouping. Finally, show the factorization.
Form:
$05 x^{2} + ◻ x + ◻ x - 8$
$05 x^{2} + ◻ x - ◻ x - 8$
$05 x^{2} - ◻ x + ◻ x - 8$
$05 x^{2} - ◻ x - ◻ x - 8$
Factorization:
$◻$
Check
$02023 Mc$

Answer

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Answer

The factorization of the given quadratic equation $5 x^{2} + 6 x - 8$ is $(x + 2) (5 x - 4)$ .

Steps

Step 1 ：First, we need to find two numbers that multiply to -40 (which is the product of 5 and -8) and add to 6. The two numbers that satisfy these conditions are 10 and -4.

Step 2 ：We can rewrite the equation as $5 x^{2} + 10 x - 4 x - 8$ .

Step 3 ：Now we can factor by grouping. The first group is $5 x^{2} + 10 x$ and the second group is $- 4 x - 8$ .

Step 4 ：We can factor out a $5 x$ from the first group and a $- 4$ from the second group. This gives us $5 x (x + 2) - 4 (x + 2)$ .

Step 5 ：Now we can factor out the common factor of $(x + 2)$ to get the final factorization.

Step 6 ：The factorization of the given quadratic equation $5 x^{2} + 6 x - 8$ is $(x + 2) (5 x - 4)$ .

Answer

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