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.