Math / Algebra

Questionc. Using the table, find a number a such that the remainder of the division $\frac{f(x)}{x-a}$ is equal to 4. Show or explain how you get your answer. \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline-4 & -11 \\ \hline-3 & 8 \\ \hline-2 & 13 \\ \hline-1 & 10 \\ \hline 0 & 5 \\ \hline 1 & 4 \\ \hline 2 & 13 \\ \hline 3 & 38 \\ \hline 4 & 85 \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? We need to find an $a$ value where, when $f(x)$ is divided by $x - a$ , the remainder is $4$ . Watch out! Remember the Remainder Theorem: when we divide a polynomial $f(x)$ by $x - a$ , the remainder is $f(a)$ .

STEP 2

1. Apply the Remainder Theorem

STEP 3

The Remainder Theorem tells us that if we divide a polynomial $f(x)$ by $x - a$ , the remainder is $f(a)$ .
So, we're looking for an $a$ value where $f(a) = 4$ .

STEP 4

Let's scan our awesome table for an $f(x)$ value equal to 4.
Boom! We see that when $x = 1$ , $f(1) = 4$ .

STEP 5

Since we're looking for $f(a) = 4$ , and we found $f(1) = 4$ , then our magical $a$ value is $1$ !

STEP 6

The value of $a$ that makes the remainder of $\frac{f(x)}{x - a}$ equal to $4$ is $a = 1$ .

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Studdy Solution

STEP 1

What is this asking? We need to find an $a$ value where, when $f(x)$ is divided by $x - a$ , the remainder is $4$ . Watch out! Remember the Remainder Theorem: when we divide a polynomial $f(x)$ by $x - a$ , the remainder is $f(a)$ .

STEP 2

1. Apply the Remainder Theorem

STEP 3

The Remainder Theorem tells us that if we divide a polynomial $f(x)$ by $x - a$ , the remainder is $f(a)$ .
So, we're looking for an $a$ value where $f(a) = 4$ .

STEP 4

Let's scan our awesome table for an $f(x)$ value equal to 4.
Boom! We see that when $x = 1$ , $f(1) = 4$ .

STEP 5

Since we're looking for $f(a) = 4$ , and we found $f(1) = 4$ , then our magical $a$ value is $1$ !

STEP 6

The value of $a$ that makes the remainder of $\frac{f(x)}{x - a}$ equal to $4$ is $a = 1$ .

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Studdy Solution

STEP 1

What is this asking? We need to find an aaa value where, when f(x)f(x)f(x) is divided by x−ax - ax−a, the remainder is 444. Watch out! Remember the Remainder Theorem: when we divide a polynomial f(x)f(x)f(x) by x−ax - ax−a, the remainder is f(a)f(a)f(a).

STEP 2

1. Apply the Remainder Theorem

STEP 3

The Remainder Theorem tells us that if we divide a polynomial f(x)f(x)f(x) by x−ax - ax−a, the remainder is f(a)f(a)f(a).So, we're looking for an aaa value where f(a)=4f(a) = 4f(a)=4.

STEP 4

Let's **scan** our awesome table for an f(x)f(x)f(x) value equal to **4**.Boom! We see that when x=1x = 1x=1, f(1)=4f(1) = 4f(1)=4.

STEP 5

Since we're looking for f(a)=4f(a) = 4f(a)=4, and we found f(1)=4f(1) = 4f(1)=4, then our **magical** aaa value is 111!

STEP 6

The value of aaa that makes the remainder of f(x)x−a\frac{f(x)}{x - a}x−af(x)​ equal to 444 is a=1a = 1a=1.

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What is this asking? We need to find an $a$ value where, when $f(x)$ is divided by $x - a$ , the remainder is $4$ . Watch out! Remember the Remainder Theorem: when we divide a polynomial $f(x)$ by $x - a$ , the remainder is $f(a)$ .

The Remainder Theorem tells us that if we divide a polynomial $f(x)$ by $x - a$ , the remainder is $f(a)$ .
So, we're looking for an $a$ value where $f(a) = 4$ .

Let's scan our awesome table for an $f(x)$ value equal to 4.
Boom! We see that when $x = 1$ , $f(1) = 4$ .

Since we're looking for $f(a) = 4$ , and we found $f(1) = 4$ , then our magical $a$ value is $1$ !

The value of $a$ that makes the remainder of $\frac{f(x)}{x - a}$ equal to $4$ is $a = 1$ .