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Chapter 6: Problem 2

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}+9 x+8$$

Short Answer

Expert verified
The factorization of the polynomial \( x^{2} + 9x + 8 \) is \( (x + 1)(x + 8) \).

Step by step solution

01

Identify the Coefficients

From the equation \( x^{2} + 9x + 8 \), the coefficients can be identified as: a = 1, b = 9, and c = 8.
02

Find the Factors

To factorise the trinomial, find two numbers such that they add up to 9 (the coefficient of x) and their product is 8. The numbers satisfying this condition are 1 and 8, because 1 + 8 = 9 and 1 * 8 = 8.
03

Write the Factorised Form

Replace in the quadratic equation \( x^2 + 9x + 8 \) by the binomial factors. The factorised form is therefore \( (x + 1)(x + 8) \).
04

Check the Factorization

Use the FOIL method to multiply the binomial factors back together: \nFirst terms: \( x * x = x^2 \);\nOuter terms: \( x * 8 = 8x \);\nInner terms: \( 1 * x = x \);\nLast terms: \( 1 * 8 = 8 \).\nAdding these together yields the original trinomial, \( x^2 + 9x + 8 \), thus confirming that the factorization is correct.

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Most popular questions from this chapter

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