Help me please
Is the given linear expression a factor of the polynomial? Show work.
f(x)=2x^3+x^2-5x+2; x+2
( 2 x ^ 3+ x ^ 2 - 5 x + 2 ) / ( x + 2 ) =
2 x ^ 2 - 3 x + 1
In google type .
calc 101
When you see list of results click on :
c a l c 1 0 1 . c o m
When page be open click on :
long division
In rectangle :
Divide
type :
2x^3+x^2-5x+2
In rectangle :
by
type :
x+2
Then click option :
DO IT!
i know how to divide polynomials using long division and also the synthetic way. But, I just don't understand what the question is trying to ask??
( 2 x ^ 3 + x ^ 2 - 5 x + 2 ) / ( x + 2 ) =
2 x ^ 2 - 3 x + 1
2 x ^ 2 - 3 x + 1 = ( x - 1 ) ( 2 x - 1 )
So :
2 x ^ 3 + x ^ 2 - 5 x + 2 =
( x + 2 ) ( x - 1 ) ( 2 x - 1 )
x + 2
is one of fators of :
2 x ^ 3 + x ^ 2 - 5 x + 2
oh okai thanks!!!
To check if the given linear expression, x + 2, is a factor of the polynomial f(x) = 2x^3 + x^2 - 5x + 2, you need to perform polynomial division.
Here are the steps to perform polynomial division:
1. Set up the division problem by arranging the polynomial f(x) and the linear expression x + 2 in long division format:
```
2x^2 - 3x + 1 (quotient)
x + 2 │ 2x^3 + x^2 - 5x + 2 (dividend)
- (2x^3 + 4x^2) (subtract)
----------------
-3x^2 - 5x + 2 (partial remainder)
```
2. Divide the first term of the dividend (2x^3) by the first term of the divisor (x). The result is 2x^2. Place this term above the line, on top of the division symbol, as the first term of the quotient.
```
2x^2 - 3x + 1 (quotient)
x + 2 │ 2x^3 + x^2 - 5x + 2 (dividend)
- (2x^3 + 4x^2) (subtract)
----------------
-3x^2 - 5x + 2 (partial remainder)
```
3. Multiply the divisor (x + 2) by the first term of the quotient (2x^2) to obtain the product 2x^3 + 4x^2. Write this product below the dividend.
4. Subtract the product (2x^3 + 4x^2) from the dividend (2x^3 + x^2 - 5x + 2). This will give you a new polynomial.
```
2x^2 - 3x + 1 (quotient)
x + 2 │ 2x^3 + x^2 - 5x + 2 (dividend)
- (2x^3 + 4x^2) (subtract)
----------------
-3x^2 - 5x + 2 (partial remainder)
- (-3x^2 - 6x) (subtract)
----------------
x + 2 (remainder)
```
5. Repeat steps 2-4 with the new polynomial (partial remainder) obtained from step 4.
In this case, the remainder is x + 2. If the remainder is zero, it means that the given linear expression is a factor of the polynomial. If the remainder is not zero, it means that the given linear expression is not a factor of the polynomial.
Therefore, since the remainder is not zero, x + 2 is not a factor of the polynomial f(x) = 2x^3 + x^2 - 5x + 2.