According to the synthetic division below,
statement C. The number 5 is a root of F(x) = [tex]4x^{2} -17x-15[/tex]
statement D. [tex](4x^{2} - 17x -15)/(x-5) = (4x+3)[/tex]
statement E. [tex](x-5)[/tex] is a factor of [tex]4x^{2} -17x-15[/tex] are true.
Synthetic division is the method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division.
When coefficient of divisor is 5, (x-5) is the divisor of the polynomial.
As given the coefficients of dividends 4, -17, -15, the dividend polynomial becomes [tex]4x^{2} -17x-15[/tex].
The final value on the right is the coefficient of remainder. Since it is 0, (x-5) is a factor of [tex]4x^{2} -17x-15[/tex].
The final value on the left is the coefficient of quotient. Thus, (4x + 3) becomes the quotient.
This implies that statement C, D and E are true.
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