Verified Answer :

Answer:

The polynomial (x -5) is not a factor of second polynomial \(3x^2 + 7x + 40\)

Step-by-step explanation:

Factor theorem states that if you divide a polynomial p(x) by a factor x -a of that polynomial, then you will get a zero remainder.

i.,e \(p(x) = (x-a)q(x)\)   which means that if x - a is a factor of p(x), then the remainder, when we do synthetic division by  x= a, will be zero.

Determine whether the first polynomial is a factor of the second polynomial.

Given the polynomial:  \(f(x)=3x^2 + 7x + 40\)

For  \(x-5\) to be a factor of \(f(x)=3x^2 + 7x + 40\), the factor theorems implies that x = 5 must be a zero of f(x).

Now, to test whether \(x-5\)  is a factor;

Set x -5 = 0

⇒x = 5

Then,

we will use synthetic division method to divide f(x) by x =5

you can see the figure as shown below in the attachment.

Since, the remainder is 150 which is not equal to zero, then Factor theorem says that (x-5) is not a  factor of \(3x^2 + 7x + 40\)



View image OrethaWilkison

Answer:

No, (x-5) is not a factor of \(3x^2+7x+40\)

Explanation:

Factor theorem states that if (x-a) is a factor of the function f(x) then f(a) = 0.

We can use this theorem to check whether a polynomial is a factor of other polynomial or not.

Further Explanation:

Here, we have to check if (x-5) is a factor of \(3x^2+7x+40\) or not.

For this we can use the above mentioned factor theorem.

In our case,

a = 5

and \(f(x)=3x^2+7x+40\)

So, we find f(5) and see if it is zero or not. If f(5) = 0 then (x-5) must be the factor the polynomial.

\(f(5)=[tex]3(5)^2+7(5)+40\\\\=75+35+40\\\\=150 eq0\)

Since, f(5) is not zero. Hence, from factor theorem, (x-5) is not a factor of \(3x^2+7x+40\)

Learn More:

https://brainly.com/question/12482195 (Answered by Kudzordzifrancis)

https://brainly.com/question/11378552 (Answered by Alinakincsem)

Keywords:

Factor theorem, Remainder theorem.

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