How To Factor The Trinomial X<Sup>2</Sup> + 15X + 56

Factor the Trinomial x^215x+56, Where Leading Coefficient a=1, Using from www.youtube.com

Introduction

Factoring is an essential skill in algebra. It is the process of breaking down a polynomial into smaller parts or factors. In this article, we will discuss how to factor a trinomial with the coefficients of x², x, and the constant. We will focus on the trinomial x² + 15x + 56 and provide a step-by-step guide on how to factor it.

Step 1: Look for Common Factors

The first step in factoring any polynomial is to look for common factors. In the case of the trinomial x² + 15x + 56, there are no common factors among the three terms.

Step 2: Find Two Numbers that Multiply to the Constant and Add to the Coefficient of x

The next step is to find two numbers that multiply to the constant term (56) and add up to the coefficient of x (15). These two numbers are called the "magic numbers." In this case, the magic numbers are 7 and 8 because 7 * 8 = 56 and 7 + 8 = 15.

Step 3: Rewrite the Trinomial

Now that we have the magic numbers, we can rewrite the trinomial as follows: x² + 7x + 8x + 56 Notice that we have split the coefficient of x into two parts: 7x and 8x.

Step 4: Group the Terms

The next step is to group the terms as follows: (x² + 7x) + (8x + 56) Notice that we have grouped the first two terms and the last two terms.

Step 5: Factor Out the GCF

The greatest common factor (GCF) of the first group is x, while the GCF of the second group is 8. We can factor out these GCFs as follows: x(x + 7) + 8(x + 7) Notice that we have factored out the GCF of each group and placed the resulting expressions in parentheses.

Step 6: Combine the Terms

Now that we have factored out the GCFs, we can combine the terms as follows: (x + 8)(x + 7) Notice that we have combined the two expressions in parentheses into a single expression using the distributive property.

Step 7: Check Your Answer

To check our answer, we can use the FOIL method to multiply the two factors: (x + 8)(x + 7) = x² + 7x + 8x + 56 Notice that this is the same expression that we started with, which means that our factoring is correct.

Conclusion

Factoring trinomials can be a challenging task, but by following the steps outlined in this article, you can factor any trinomial with ease. Remember to look for common factors, find the magic numbers, rewrite the trinomial, group the terms, factor out the GCF, and combine the terms. With practice, you will become an expert at factoring!