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Video: Factorizing Trinomials by Taking the Highest Common Factor

Bethani Gasparine

Completely factor 4𝑥² − 32𝑥 + 28.

00:43

Video Transcript

Completely factor four 𝑥 squared minus 32𝑥 plus 28.

First thing we can do is take out a greatest common factor of four. Because four, 32, and 28, the highest number that can come out from all of them is four.

Now we need to come up with numbers that multiply to be seven and add to be negative eight. Numbers that multiply to be seven are one and seven and negative one and negative seven, so which ones would add to be negative eight? That would be negative one and negative seven. Therefore, our factors would be 𝑥 minus one and 𝑥 minus seven. So our final answer would be four times 𝑥 minus one times 𝑥 minus seven.