Which polynomial is prime? x2 + 9 x2 – 25 3x2 – 27 2x2 – 8

Mathematics

1 answer:

Charra [1.4K]3 years ago

3 0

<h3>Answer: Choice A. x^2+9</h3>

This is a sum of squares, which cannot be factored over the real numbers. You'll need to involve complex numbers to be able to factor, though its likely your teacher hasn't covered that topic yet (though I could be mistaken and your teacher has mentioned it).

Choice B can be factored through the difference of squares rule. Therefore, choice B is not prime.

Choice C and D can be factored by pulling out the GCF and then use the difference of squares rule afterward. So we can rule out C and D as well.

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Step-by-step explanation:

We are given that BP is the perpendicular bisector of AC. QC is the perpendicular bisector of BD. AB = BC = CD.

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Since the triangle, BPC is a right-angled triangle as $\angle$ PBC = 90°, so we can use Pythagoras theorem in this triangle to find the length of the side PC.