Use the Factor Theorem to determine whether the binomial x – 3 is a factor of the polynomial function ƒ(x) = –5x3 + 16x2 – 9.

Answer 1

Hi Aaliyah,

when you want to check any expression such as (X - a ) is a factor of a polynomial function

IT IS ENOUGH X - a = 0 -----> X = a then by replacing a in the function you can make a decision whether it is a factor or not. if f(a) is ZERO it means (X-a) is a factor of function

NOW X- 3 = 0 ----> X = 3 then find f(3)

ƒ(x) = –5x3 + 16x2 – 9

f( 3 ) = -5 (3)^3 + 16 (3)^2 -9

f( 3 ) = -5 * 27 + 16 * 9 - 9

f( 3 ) = -135 + 144 - 9 =0 SO (X - 3 ) is one of the factor of ƒ(x) = –5x3 + 16x2 – 9

I hope it is useful,

Minoo

Answer 2

yes it is. Using either synthetic division or long division,

the answer is -5x² + x + 3 with no remainder

Synthetic: Dividing the polynomial by x=3

3 | -5 16 0 -9

| __ -15__3__9_

-5 1 3 0

( I know this looks funny but the dashed line should be solid all the way across.)

Answer 3

The FACTOR THEOREM, applied to this particular problem, states that X - 3 is a factor of

Y = -5X^3 + 16X^2 - 9, if substituting 3 into "X" is equal to zero.

Y = (-5)(3)(3)(3) + 16(3)(3) - 9

= (-5)(27) + (16)(9) - 9

= - 135 + 144 - 9

= -144 + 144

= 0

Therefore, X - 3 IS A FACTOR OF -5X^3 + 16X^2 - 9.

Hope this is helpful Aaliyah A.