Question

Determine whether the given binomial is a factor of the polynomial
(x+5): p(x)=2x^2-6x-1

(X-6); P(x)= -2x^2+15x-18

(x+3); P(x)= 2x^2-x+7

Answer 1

in order to factor a binomial you have to know that the discriminant is a perfect square.

Answer 2

what is the discriminant of \(\large\color{black}{ p(x)=2x^2-6x-1 }\) ?

Answer 3

hey, do you know what a discriminant is and how to find it? you don't seem to understand what I said.... and if you don't get what I said, ask ...

Answer 4

you can divide (for example) \(\large\color{black}{ 2x^2-6x-1 }\) by \(\large\color{black}{ x+5 }\)

Answer 5

and see if you have a remainder then x+5 is NOT a factor, if no remainder, then x+5 is a factor.

Answer 6

I would like to verify your answers once you are done, please.

Answer 7

and my suggestion is just the discriminant for the 1st and 3rd, and polynomial or synthetic division for the second.

Answer 8

the easiest method is to use the factor theorem

if (x- a) is a factor then x = a is a zero

so find p(a)... so if p(a) = 0 then a is a zero and (x - a) is a factor

in the 1st question

(x +5) is a factor... so x = -5 is a factor

find p(-5) if its equal to zero then (x + 5) is a factor, otherwise it's not

hope it helps

Answer 9

so

\[p(-5) = 2 \times (-5)^2 -6 \times (-5) - 1\]

just calculate the value if it's zero, then (x + 5) is a factor