Sure, let's go through this problem step by step.
### Step 1: Rewrite the Expression in Standard Form
The given expression is:
[tex]\[ 22x - 8 + 6x^2 \][/tex]
The standard form for a quadratic expression is [tex]\( ax^2 + bx + c \)[/tex], where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are constants. To rewrite the expression in this form, we need to arrange the terms in descending order of their degree (powers of [tex]\( x \)[/tex]). So, we have:
[tex]\[ 6x^2 + 22x - 8 \][/tex]
Now, our expression is in the standard form, where:
[tex]\[
a = 6, \quad b = 22, \quad c = -8
\][/tex]
### Step 2: Factor the Quadratic Expression
Our next goal is to factor the quadratic expression [tex]\( 6x^2 + 22x - 8 \)[/tex].
The factors of the quadratic expression [tex]\( 6x^2 + 22x - 8 \)[/tex] are:
[tex]\[ (2)(x + 4)(3x - 1) \][/tex]
Let's verify the factors.
When we expand the factored form [tex]\( 2(x + 4)(3x - 1) \)[/tex], we get:
[tex]\[ 2(x + 4)(3x - 1) = 2 \cdot (3x^2 - x + 12x - 4) = 2(3x^2 + 11x - 4) = 6x^2 + 22x - 8 \][/tex]
Thus, the factors of the quadratic expression [tex]\( 6x^2 + 22x - 8 \)[/tex] are correctly given by:
[tex]\[ 2(x + 4)(3x - 1) \][/tex]
### Final Answer
- The expression in standard form is:
[tex]\[ 6x^2 + 22x - 8 \][/tex]
- The factors of the expression are:
[tex]\[ 2(x + 4)(3x - 1) \][/tex]
