First, factor out the common term 2: 2(x^2 + 4x + 3). Then, factor the quadratic: 2(x + 3)(x + 1).
Factor the expression 2x^2 + 8x + 6.
Practice Questions
Q1
Factor the expression 2x^2 + 8x + 6.
2(x + 3)(x + 1)
2(x + 2)(x + 3)
2(x + 1)(x + 3)
2(x + 4)(x + 1)
Questions & Step-by-Step Solutions
Factor the expression 2x^2 + 8x + 6.
Step 1: Look at the expression 2x^2 + 8x + 6 and find the common factor for all terms. The common factor is 2.
Step 2: Factor out the common term 2 from the expression. This gives you 2(x^2 + 4x + 3).
Step 3: Now, focus on the quadratic expression inside the parentheses: x^2 + 4x + 3.
Step 4: To factor x^2 + 4x + 3, look for two numbers that multiply to 3 (the constant term) and add up to 4 (the coefficient of x). The numbers are 3 and 1.
Step 5: Rewrite the quadratic as (x + 3)(x + 1).
Step 6: Combine this with the factor you took out earlier. The final factored form is 2(x + 3)(x + 1).
Factoring – The process of breaking down an expression into simpler components that, when multiplied together, give the original expression.
Common Factor – Identifying and extracting the greatest common factor from all terms in the expression.
Quadratic Factoring – Factoring a quadratic expression into the product of two binomials.
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