Factor completely, then place the factors in the proper location on the grid. x^2n + 10x^n + 16

Mathematics

1 answer:

postnew [5]4 years ago

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Answer:

$(x^n + 2)(x^n + 8)$

Step-by-step explanation:

The polynomial $x^{2n}+10x^n + 16$ can be factored exactly the same as the polynomial $x^2 + 10x + 16$ . Here it factors into two numbers which multiply to 16 but add to 8. These factors are 8 and 2. So it factors into the expression (x+8)(x+2).

For the polynomial $x^{2n}+10x^n + 16$ it factors into the same factors except x ^n is used instead. The factors are $(x^n + 2)(x^n + 8)$

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