Problem 86 - Introductory Algebra for College Students

Question

Give two helpful suggestions for factoring \(x^{2}-5 x+6\)

Step-by-Step Solution

Answer

The factored form of the given polynomial \(x^{2}-5x+6\) is \((x+2)(x+3)\).

Step 1: Identify 'b' and 'c' from the given polynomial

In this quadratic expression \(x^{2}-5x+6\), 'b' is -5 (the coefficient of x) and 'c' is +6 (the constant term).

Step 2: Identify two numbers

Now, we need to identify two numbers such that they add up to 'b' (-5 in this case) and multiply to 'c' (+6 in this case). After careful consideration, we will see that -2 and -3 will satisfy these conditions as (-2) + (-3) = -5 and (-2) * (-3) = 6.

Step 3: Apply Identified Numbers to Factorize

Substitute -2 and -3, which were identified in step 2, into the standard format (\(x-p\)(\(x-q\)). This will give us the factored form of the given polynomial as \((x+2)(x+3)\).