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
The correct answer is: Left parenthesis 2 x plus 3 right parenthesis left parenthesis 2x plus 2 right parenthesis
The expression in factored form for 4x^2 + 11x + 6 is:
(2x + 3)(2x + 2)
To find the expression in factored form, we need to factorize the given quadratic expression: 4x^2 + 11x + 6.
Step 1: We need to find two numbers that multiply to give 4 * 6 = 24 and add up to give 11. The pair of numbers that satisfy this condition is 3 and 8, because 3 * 8 = 24 and 3 + 8 = 11.
Step 2: Now, we use these two numbers to factorize the quadratic expression. We replace the middle term (11x) with the sum of the two numbers we found in Step 1, which is 3x + 8x:
4x^2 + 3x + 8x + 6
Step 3: Now, we group the four terms by their common factors:
(4x^2 + 3x) + (8x + 6)
Step 4: Next, we factor out the greatest common factor (GCF) from each group:
x(4x + 3) + 2(4x + 3)
Step 5: Finally, we can see that we have a common binomial factor of (4x + 3) for both groups. We can factor it out:
(4x + 3)(x + 2)
So, the expression in factored form is (4x + 3)(x + 2).