Question

Consider the polynomial function P(x)=2x³+3x²-2x-3.Verify that P(−1) = 0. Since P(−1) = 0, what must one of the factors of P be?

Answer 1

To verify that P(-1) = 0, substitute -1 into the polynomial function P(x) = 2x³ + 3x² - 2x - 3. The factor of P(x) is (x + 1).

Step-by-step explanation:

To verify that P(-1) = 0, we substitute -1 into the polynomial function P(x) = 2x³ + 3x² - 2x - 3.

P(-1) = 2(-1)³ + 3(-1)² - 2(-1) - 3

Simplifying this expression, we get P(-1) = -2 + 3 + 2 - 3 = 0.

Since P(-1) = 0, it means that (x + 1) is one of the factors of the polynomial function P(x).

Answer 2

So (x+1) will be the one of factor of given polynomial

Step-by-step explanation:

We have given the equation
`2x^3+3x^2-2x-3`

First we have to find the value of
`p(-1)`

For finding
`p(-1)` we have to put x = -1 in the polynomial

So
`p(-1)=2* (-1)^3+3(1)^2-2* (-1)-3=-2+3+2-3=0`

As
`p(-1)` is zero so x = -1 will be the root of the given polynomial

So (x+1) will be the one of factor of given polynomial