Factor the polynomial expression. If necessary, use the caret (^) to enter exponents. For example, write x2 as x^2.2x2 + 13x + 15
2x^2 + 13x + 15
(2x+3)(x+5)
To factor the polynomial expression 2x^2 + 13x + 15, we want to break it down into two binomial expressions that, when multiplied together, give us the original polynomial.
Step 1: Multiply the coefficient of the x^2 term (2) by the constant term (15). In this case, 2 * 15 = 30.
Step 2: Find two numbers whose product is equal to 30 and whose sum is equal to the coefficient of the x term (13). In this case, the numbers are 10 and 3, since 10 * 3 = 30 and 10 + 3 = 13.
Step 3: Rewrite the middle term (13x) as the sum of the two numbers found in Step 2. So, 13x becomes 10x + 3x.
Now we can rewrite the polynomial by splitting the middle term:
2x^2 + 10x + 3x + 15
Step 4: Factor by grouping. Group the terms by pairs:
(2x^2 + 10x) + (3x + 15)
Step 5: Factor out the greatest common factor (GCF) from each pair:
2x(x + 5) + 3(x + 5)
Step 6: Notice that both terms now have a common factor of (x + 5). Factor out the common binomial:
(x + 5)(2x + 3)
Therefore, the factored form of the polynomial expression 2x^2 + 13x + 15 is (x + 5)(2x + 3).