80425
AssignmentMultiple Select

Factoring Polynomials Completely

Question 80425 • Common Core Algebra I B-IC

Which polynomials are prime? Check all that apply.2x2+ 7x + 15x2 – 10x + 53x2 + 84x2 – 25x2 + 36

Answer
A
2x2+ 7x + 1
B
5x2 – 10x + 5
C
3x2 + 8
D
4x2 – 25
E
x2 + 36

Explanation

A polynomial is prime here if it cannot be factored into polynomials with integer coefficients. For A, the discriminant is 7² − 4(2)(1) = 41, which is not a perfect square, so it does not factor. C and E also have no integer-coefficient factorization: their discriminants, −96 and −144, are not perfect squares. B factors as 5(x − 1)², and D factors as (2x − 5)(2x + 5), so those are not prime.

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