At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
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]
### 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]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.