Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To factor the polynomial [tex]\( x^4 + 2x^3 - 7x^2 - 8x + 12 \)[/tex] with the given factor [tex]\((x - 2)\)[/tex]:
1. Polynomial Division:
We start by dividing the polynomial [tex]\( x^4 + 2x^3 - 7x^2 - 8x + 12 \)[/tex] by [tex]\( x - 2 \)[/tex].
The quotient from this division is [tex]\( x^3 + 4x^2 + x - 6 \)[/tex].
2. Factoring the Quotient Polynomial:
Now we need to factor [tex]\( x^3 + 4x^2 + x - 6 \)[/tex].
3. Finding the Factors:
After factoring [tex]\( x^3 + 4x^2 + x - 6 \)[/tex], we get the factors [tex]\( (x - 1) \)[/tex], [tex]\( (x + 2) \)[/tex], and [tex]\( (x + 3) \)[/tex].
So, the other factors of the polynomial [tex]\( x^4 + 2x^3 - 7x^2 - 8x + 12 \)[/tex] besides [tex]\( (x - 2) \)[/tex] are:
[Choose [tex]\( x + 2 \)[/tex]],
[Choose [tex]\( x + 3 \)[/tex]], and
[Choose [tex]\( x - 1 \)[/tex]].
1. Polynomial Division:
We start by dividing the polynomial [tex]\( x^4 + 2x^3 - 7x^2 - 8x + 12 \)[/tex] by [tex]\( x - 2 \)[/tex].
The quotient from this division is [tex]\( x^3 + 4x^2 + x - 6 \)[/tex].
2. Factoring the Quotient Polynomial:
Now we need to factor [tex]\( x^3 + 4x^2 + x - 6 \)[/tex].
3. Finding the Factors:
After factoring [tex]\( x^3 + 4x^2 + x - 6 \)[/tex], we get the factors [tex]\( (x - 1) \)[/tex], [tex]\( (x + 2) \)[/tex], and [tex]\( (x + 3) \)[/tex].
So, the other factors of the polynomial [tex]\( x^4 + 2x^3 - 7x^2 - 8x + 12 \)[/tex] besides [tex]\( (x - 2) \)[/tex] are:
[Choose [tex]\( x + 2 \)[/tex]],
[Choose [tex]\( x + 3 \)[/tex]], and
[Choose [tex]\( x - 1 \)[/tex]].
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.