Question

Is (x−5) a factor of the polynomial p(x)=−x​^2​​−3x+10?

Answer 1

To simply know if it's a factor, try factoring the polynomial.
Factor out -1
\(p(x)=-(x^2+3x-10)\)
What two numbers when added you get +3 and when multiplied you get -10?

Answer 2

im not sure what im supposed to do with this question. i dont understand :/

Answer 3

What are the factors of -10?

Answer 4

1 2 5 10

Answer 5

Good.
-5 * 2 =-10
but if -5+2 =-3
and we have +3 in our function
\(p(x)=-(x^2\color{red}{+3}x-10)\)

Answer 6

If we hanged the negative signs, maybe we could get +3
so if 5*-2=-10
and if 5+(-2)=+3
Yes, so the factors of
\(P(x)=-(x+5)(x-2)\) which can also be written like this if -1 is distributed to (x+5)

\(P(x)=(-x-5)(x-2)\)

Answer 7

Do you think (x-5) is a factor?

Answer 8

no

Answer 9

We have (x+5), it is not the same as (x-5)
So (x-5) is not a factor.

Answer 10

thank you

Answer 11

No problem