Problem of the Week

Updated at Jul 16, 2018 4:32 PM

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Mar 24, 2025

How can we compute the factors of $8{x}^{2}-34x+21$ ?

Below is the solution.

8{x}^{2}-34x+21

Split the second term in

8{x}^{2}-34x+21

into two terms.

Multiply the coefficient of the first term by the constant term.

8\times 21=168

Ask: Which two numbers add up to

-34

and multiply to

168

-6

and

-28

Split

-34x

as the sum of

-6x

and

-28x

8{x}^{2}-6x-28x+21

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8{x}^{2}-6x-28x+21

Factor out common terms in the first two terms, then in the last two terms.

2x(4x-3)-7(4x-3)

Factor out the common term

4x-3

(4x-3)(2x-7)

Done