Solved on Mar 01, 2024

Find the difference of two functions $p(x) = x^2 - 9x$ and $c(x) = -2x + 3$ as a simplified polynomial or rational function.

STEP 1

Assumptions
1. $p(x)$ is a polynomial given by $p(x) = x^2 - 9x$ .
2. $c(x)$ is a polynomial given by $c(x) = -2x + 3$ .
3. We need to find the product $(p-c)(x)$ , which means we need to subtract $c(x)$ from $p(x)$ and then simplify the result.

STEP 2

First, we write down the expressions for $p(x)$ and $c(x)$ .
$p(x) = x^2 - 9x$ $c(x) = -2x + 3$

STEP 3

The expression $(p-c)(x)$ means we need to subtract $c(x)$ from $p(x)$ . Let's set up the subtraction.
$(p-c)(x) = p(x) - c(x)$

STEP 4

Substitute the expressions for $p(x)$ and $c(x)$ into the subtraction.
$(p-c)(x) = (x^2 - 9x) - (-2x + 3)$

STEP 5

Distribute the negative sign through the second polynomial.
$(p-c)(x) = x^2 - 9x + 2x - 3$

STEP 6

Combine like terms.
$(p-c)(x) = x^2 - 7x - 3$
The result is a polynomial in simplest form.
The expression $(p-c)(x)$ is $x^2 - 7x - 3$ .

Was this helpful?

Find the difference of two functions $p(x) = x^2 - 9x$ and $c(x) = -2x + 3$ as a simplified polynomial or rational function.

STEP 1

Assumptions
1. $p(x)$ is a polynomial given by $p(x) = x^2 - 9x$ .
2. $c(x)$ is a polynomial given by $c(x) = -2x + 3$ .
3. We need to find the product $(p-c)(x)$ , which means we need to subtract $c(x)$ from $p(x)$ and then simplify the result.

STEP 2

First, we write down the expressions for $p(x)$ and $c(x)$ .
$p(x) = x^2 - 9x$ $c(x) = -2x + 3$

STEP 3

The expression $(p-c)(x)$ means we need to subtract $c(x)$ from $p(x)$ . Let's set up the subtraction.
$(p-c)(x) = p(x) - c(x)$

STEP 4

Substitute the expressions for $p(x)$ and $c(x)$ into the subtraction.
$(p-c)(x) = (x^2 - 9x) - (-2x + 3)$

STEP 5

Distribute the negative sign through the second polynomial.
$(p-c)(x) = x^2 - 9x + 2x - 3$

STEP 6

Combine like terms.
$(p-c)(x) = x^2 - 7x - 3$
The result is a polynomial in simplest form.
The expression $(p-c)(x)$ is $x^2 - 7x - 3$ .

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the difference of two functions p(x)=x2−9xp(x) = x^2 - 9xp(x)=x2−9x and c(x)=−2x+3c(x) = -2x + 3c(x)=−2x+3 as a simplified polynomial or rational function.

STEP 1

STEP 2

First, we write down the expressions for p(x) p(x) p(x) and c(x) c(x) c(x).p(x)=x2−9x p(x) = x^2 - 9x p(x)=x2−9x c(x)=−2x+3 c(x) = -2x + 3 c(x)=−2x+3

STEP 3

The expression (p−c)(x) (p-c)(x) (p−c)(x) means we need to subtract c(x) c(x) c(x) from p(x) p(x) p(x). Let's set up the subtraction.(p−c)(x)=p(x)−c(x) (p-c)(x) = p(x) - c(x) (p−c)(x)=p(x)−c(x)

STEP 4

Substitute the expressions for p(x) p(x) p(x) and c(x) c(x) c(x) into the subtraction.(p−c)(x)=(x2−9x)−(−2x+3) (p-c)(x) = (x^2 - 9x) - (-2x + 3) (p−c)(x)=(x2−9x)−(−2x+3)

STEP 5

Distribute the negative sign through the second polynomial.(p−c)(x)=x2−9x+2x−3 (p-c)(x) = x^2 - 9x + 2x - 3 (p−c)(x)=x2−9x+2x−3

STEP 6

Combine like terms.(p−c)(x)=x2−7x−3 (p-c)(x) = x^2 - 7x - 3 (p−c)(x)=x2−7x−3The result is a polynomial in simplest form.The expression (p−c)(x) (p-c)(x) (p−c)(x) is x2−7x−3 x^2 - 7x - 3 x2−7x−3.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the difference of two functions $p(x) = x^2 - 9x$ and $c(x) = -2x + 3$ as a simplified polynomial or rational function.

First, we write down the expressions for $p(x)$ and $c(x)$ .
$p(x) = x^2 - 9x$ $c(x) = -2x + 3$

The expression $(p-c)(x)$ means we need to subtract $c(x)$ from $p(x)$ . Let's set up the subtraction.
$(p-c)(x) = p(x) - c(x)$

Substitute the expressions for $p(x)$ and $c(x)$ into the subtraction.
$(p-c)(x) = (x^2 - 9x) - (-2x + 3)$

Distribute the negative sign through the second polynomial.
$(p-c)(x) = x^2 - 9x + 2x - 3$

Combine like terms.
$(p-c)(x) = x^2 - 7x - 3$
The result is a polynomial in simplest form.
The expression $(p-c)(x)$ is $x^2 - 7x - 3$ .