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
The expression in factored form is:
(2x + 3)(2x + 2)
To find the factored form of the expression 4x^2 + 11x + 6, we need to break down the expression into two binomial factors.
First, we need to find two numbers that multiply to 4 * 6 = 24 and add up to 11. The numbers that satisfy these conditions are 3 and 8.
Next, we can rewrite the expression using these two numbers:
4x^2 + 3x + 8x + 6
Now, we can group the terms in pairs:
(4x^2 + 3x) + (8x + 6)
From each group, we can factor out the greatest common factor:
x(4x + 3) + 2(4x + 3)
Notice that we have a common binomial factor, (4x + 3), in both terms.
Now, we can factor out this common binomial factor:
(4x + 3)(x + 2)
Therefore, the factored form of the expression 4x^2 + 11x + 6 is (4x + 3)(x + 2).
So, the correct answer is:
Left parenthesis 4 x plus 3 right parenthesis left parenthesis x plus 2 right parenthesis
To determine the expression in factored form, you need to factor the given quadratic expression.
The given expression is 4x^2 + 11x + 6.
Step 1: Multiply the coefficient of the quadratic term (4) with the constant term (6). It gives us 24.
Step 2: Find two numbers whose product is 24 and sum is the coefficient of the linear term (11). In this case, the numbers are 3 and 8. (3 * 8 = 24, 3 + 8 = 11)
Step 3: Rewrite the middle term (11x) using the two numbers found in the previous step. It becomes 3x + 8x.
Now, let's factor the expression by grouping:
4x^2 + 3x + 8x + 6
Step 4: Group the terms:
(4x^2 + 3x) + (8x + 6)
Step 5: Factor out the common factors from each group:
x(4x + 3) + 2(4x + 3)
Step 6: Note that we now have a common factor (4x + 3). Factor it out:
(4x + 3)(x + 2)
Therefore, the expression in factored form is " (4x + 3)(x + 2)".