Understanding And Solving "Factor X<Sup>2</Sup> + 6X + 8"

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Introduction

As a professional teacher, it is my responsibility to guide my students through complex mathematical problems. One such problem is "factor x² + 6x + 8". While it may seem daunting at first, breaking down the problem and understanding its components can make it easier to solve.

What is Factoring?

Factoring refers to the process of breaking down a mathematical expression into simpler components. In the case of "factor x² + 6x + 8", we are attempting to find two binomials that, when multiplied together, will result in the original expression.

The Formula for Factoring Quadratic Equations

To factor a quadratic equation in the form of ax² + bx + c, we use the following formula: (x + m)(x + n), where m and n are constants that, when multiplied together, equal c and, when added together, equal b.

Breaking Down "Factor x² + 6x + 8"

In the case of "factor x² + 6x + 8", a = 1, b = 6, and c = 8. Using the formula above, we need to find two constants, m and n, that satisfy the following conditions: m x n = 8 m + n = 6

Solving for m and n

To solve for m and n, we can use trial and error or algebraic methods. One way is to list all the possible factors of 8, which are 1, 2, 4, and 8. We then try different combinations until we find two that add up to 6. In this case, we can see that 2 and 4 satisfy both conditions. Therefore, m = 2 and n = 4.

Writing the Final Answer

Now that we have found m and n, we can write the final answer as (x + 2)(x + 4). Multiplying these two binomials together will result in x² + 6x + 8.

Checking Our Answer

To check if our answer is correct, we can use the FOIL method to multiply (x + 2)(x + 4). FOIL stands for First, Outer, Inner, Last and refers to multiplying the terms in each binomial in a specific order. When we multiply (x + 2)(x + 4) using the FOIL method, we get x² + 6x + 8, which is the original expression.

Conclusion

Factoring quadratic equations can be challenging, but by breaking down the problem and using the formula, we can find the solution. In the case of "factor x² + 6x + 8", we found that the answer is (x + 2)(x + 4). It is important to check our answer using the FOIL method to ensure its accuracy.