The correct statements about given synthetic division are C, D, and F
"It is a polynomial with degree 2."
"It is defined as a way of dividing one polynomial by another polynomial of first degree."
For given question,
We have been given a quadratic polynomial [tex]F(x)=4x^{2} -17x-15[/tex]
We can factorize above quadratic polynomial as,
[tex]F(x)\\=4x^{2} -17x-15\\=4x^{2} -20x+3x-15\\=4x(x-5)+3(x-5)\\=(x-5)(4x+3)[/tex]
This means the factors of [tex]4x^{2} -17x-15[/tex] are (x - 5) (4x + 3)
And the roots of the polynomial would be,
[tex]\Rightarrow F(x)=0\\\Rightarrow 4x^{2} -17x-15=0\\\Rightarrow (x-5)(4x+3)=0\\\Rightarrow x-5=0~~,~~4x+3=0\\\Rightarrow x=5~~,~~x=-\frac{3}{4}[/tex]
This means, the roots of [tex]4x^{2} -17x-15[/tex] are 5 and [tex]\frac{-3}{4}[/tex]
Therefore, the correct statements about given synthetic division are C, D, and F
Learn more about polynomial here:
https://brainly.com/question/11536910
#SPJ2
