Math / Algebra

QuestionGiven that $f(x)=x^{2}-5 x-36$ and $g(x)=x-9$ , find $(f-g)(x)$ and express the result as a polynomial in simplest form.

Studdy Solution

STEP 1

1. We are given two functions, $f(x)$ and $g(x)$ .
2. We need to find the expression for $(f-g)(x)$ .
3. The result should be expressed as a polynomial in its simplest form.

STEP 2

1. Define the expression for $(f-g)(x)$ .
2. Substitute the given functions into the expression.
3. Simplify the resulting polynomial.

STEP 3

Define the expression for $(f-g)(x)$ :
$(f-g)(x) = f(x) - g(x)$

STEP 4

Substitute the given functions into the expression:
$f(x) = x^2 - 5x - 36$ $g(x) = x - 9$
So,
$(f-g)(x) = (x^2 - 5x - 36) - (x - 9)$

STEP 5

Simplify the expression by distributing the negative sign and combining like terms:
$(f-g)(x) = x^2 - 5x - 36 - x + 9$
Combine the $x$ terms and the constant terms:
$= x^2 - 6x - 27$
The polynomial in simplest form is:
$\boxed{x^2 - 6x - 27}$

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QuestionGiven that $f(x)=x^{2}-5 x-36$ and $g(x)=x-9$ , find $(f-g)(x)$ and express the result as a polynomial in simplest form.

Studdy Solution

STEP 1

1. We are given two functions, $f(x)$ and $g(x)$ .
2. We need to find the expression for $(f-g)(x)$ .
3. The result should be expressed as a polynomial in its simplest form.

STEP 2

1. Define the expression for $(f-g)(x)$ .
2. Substitute the given functions into the expression.
3. Simplify the resulting polynomial.

STEP 3

Define the expression for $(f-g)(x)$ :
$(f-g)(x) = f(x) - g(x)$

STEP 4

Substitute the given functions into the expression:
$f(x) = x^2 - 5x - 36$ $g(x) = x - 9$
So,
$(f-g)(x) = (x^2 - 5x - 36) - (x - 9)$

STEP 5

Simplify the expression by distributing the negative sign and combining like terms:
$(f-g)(x) = x^2 - 5x - 36 - x + 9$
Combine the $x$ terms and the constant terms:
$= x^2 - 6x - 27$
The polynomial in simplest form is:
$\boxed{x^2 - 6x - 27}$

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QuestionGiven that f(x)=x2−5x−36f(x)=x^{2}-5 x-36f(x)=x2−5x−36 and g(x)=x−9g(x)=x-9g(x)=x−9, find (f−g)(x)(f-g)(x)(f−g)(x) and express the result as a polynomial in simplest form.

Studdy Solution

STEP 1

1. We are given two functions, f(x) f(x) f(x) and g(x) g(x) g(x).2. We need to find the expression for (f−g)(x) (f-g)(x) (f−g)(x).3. The result should be expressed as a polynomial in its simplest form.

STEP 2

1. Define the expression for (f−g)(x) (f-g)(x) (f−g)(x).2. Substitute the given functions into the expression.3. Simplify the resulting polynomial.

STEP 3

Define the expression for (f−g)(x) (f-g)(x) (f−g)(x):(f−g)(x)=f(x)−g(x) (f-g)(x) = f(x) - g(x) (f−g)(x)=f(x)−g(x)

STEP 4

Substitute the given functions into the expression:f(x)=x2−5x−36 f(x) = x^2 - 5x - 36 f(x)=x2−5x−36 g(x)=x−9 g(x) = x - 9 g(x)=x−9So, (f−g)(x)=(x2−5x−36)−(x−9) (f-g)(x) = (x^2 - 5x - 36) - (x - 9) (f−g)(x)=(x2−5x−36)−(x−9)

STEP 5

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QuestionGiven that $f(x)=x^{2}-5 x-36$ and $g(x)=x-9$ , find $(f-g)(x)$ and express the result as a polynomial in simplest form.

1. We are given two functions, $f(x)$ and $g(x)$ .
2. We need to find the expression for $(f-g)(x)$ .
3. The result should be expressed as a polynomial in its simplest form.

1. Define the expression for $(f-g)(x)$ .
2. Substitute the given functions into the expression.
3. Simplify the resulting polynomial.

Define the expression for $(f-g)(x)$ :
$(f-g)(x) = f(x) - g(x)$

Substitute the given functions into the expression:
$f(x) = x^2 - 5x - 36$ $g(x) = x - 9$
So,
$(f-g)(x) = (x^2 - 5x - 36) - (x - 9)$