What is the expression in factored form?
4 x squared plus 11 x plus 6
(1 point)
Responses
Left parenthesis 2 x plus 3 right parenthesis left parenthesis 2x plus 2 right parenthesis
Image with alt text: Left parenthesis 2 x plus 3 right parenthesis left parenthesis 2x plus 2 right parenthesis
Left parenthesis 4 x plus 1 right parenthesis left parenthesis x plus 6 right parenthesis
Image with alt text: Left parenthesis 4 x plus 1 right parenthesis left parenthesis x plus 6 right parenthesis
Left parenthesis 2 x plus 1 right parenthesis left parenthesis 2 x plus 6 right parenthesis
Image with alt text: Left parenthesis 2 x plus 1 right parenthesis left parenthesis 2 x plus 6 right parenthesis
Left parenthesis 4 x plus 3 right parenthesis left parenthesis x plus 2 right parenthesis
Image with alt text: Left parenthesis 4 x plus 3 right parenthesis left parenthesis x plus 2 right parenthesis
The expression in factored form is:
(2x + 3)(2x + 2)
To find the expression in factored form, we need to factor the given quadratic expression. Let's use the quadratic factoring method.
The given expression is 4x^2 + 11x + 6.
Step 1: We need to identify two numbers whose product is equal to the product of the coefficient of the x^2 term (4) and the constant term (6) and whose sum is equal to the coefficient of the x term (11).
The factors of 4 are 1, 2, and 4, and the factors of 6 are 1, 2, 3, and 6. By testing various combinations, we find that 3 and 2 satisfy the conditions, as their product is 6 and their sum is 5 (which matches the coefficient of the x term 11 when multiplied by 4).
Step 2: Now, we rewrite the middle term (11x) using the two numbers found in step 1.
We replace the middle term 11x with these two terms: 3x and 8x (since 3x + 8x = 11x and 3x * 8x = 24x^2).
Our expression becomes: 4x^2 + 3x + 8x + 6.
Step 3: Now, we group the terms in pairs and factor out the common factors.
Grouping the terms, we have: (4x^2 + 3x) + (8x + 6).
Factoring out the common factor in the first group, we get: x(4x + 3).
Factoring out the common factor in the second group, we get: 2(4x + 3).
Step 4: Finally, we identify the common factor shared by both groups, which is (4x + 3).
The expression in factored form is: (4x + 3)(x + 2).
Therefore, the correct choice is: Left parenthesis 4 x plus 3 right parenthesis left parenthesis x plus 2 right parenthesis.
To express the expression 4x^2 + 11x + 6 in factored form, we need to factorize it.
First, we look for two binomials that multiply to give us the quadratic expression. Since the coefficient of the x^2 term is 4, the first term in each binomial should be 2x.
Next, we need to find factors of 6 (the constant term) that, when multiplied together, give us 6, and when added together, give us 11 (the coefficient of the x term). The factors are 2 and 3.
Using these factors, we can write the factored form as (2x + 3)(2x + 2).
Therefore, the expression in factored form is (2x + 3)(2x + 2).