Problem of the Week

Updated at Feb 5, 2018 3:09 PM

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Mar 24, 2025

To get more practice in algebra, we brought you this problem of the week:

How can we factor $28{x}^{2}-11x+1$ ?

Check out the solution below!

28{x}^{2}-11x+1

Split the second term in

28{x}^{2}-11x+1

into two terms.

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

28\times 1=28

Ask: Which two numbers add up to

-11

and multiply to

28

-4

and

-7

Split

-11x

as the sum of

-4x

and

-7x

28{x}^{2}-4x-7x+1

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28{x}^{2}-4x-7x+1

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

4x(7x-1)-(7x-1)

Factor out the common term

7x-1

(7x-1)(4x-1)

Done