40.7k views
5 votes
Is (x + 2) a factor of x + 6x2 + 3x – 10?

2 Answers

3 votes

Answer:

Assuming that you actually mean that if
(x+2) is a factor of
x^(3)+6x^(2)+3x-10, the answer is yes.

Explanation:

We need to do long division of the polynomial to figure out if this is true. I would show it here, but it is extremely difficult to do so. (Maybe someone could help me.) When I factor it, it does not leave a remainder, so this is true.


x^(3)+6x^(2)+3x-10= (x+2)(x^2+4x-5)

Another way one could figure this out is by graphing the equation
x^(3)+6x^(2)+3x-10 on your graphing calculator or on just a graphing website, lake Desmos. The screenshot below shows the graph.

The polynomial will have a factor of
(x-c) if the point
(0,c) exists on the graph. The graph has the following three zeroes.


(0,-2),
(0, -5), and
(0,1)

As such, it has the three factors
(x-(-2)),
(x-(-5)), and
(x-1).

Since
(x-(-2)=(x+2), it is a factor of the polynomial.

Is (x + 2) a factor of x + 6x2 + 3x – 10?-example-1
User Zoltan Magyar
by
8.1k points
3 votes

Answer:

no

Explanation:

6x² + 4x - 10 in factored form is:

2(3x+5)(x-1)

User Roshiro
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories