Answer:
[tex]\textsf{Quotient:}\quad x^3 - 3x^2 - 5x + 15[/tex]
[tex]\textsf{Divisor:}\quad (x+2)[/tex]
[tex]\textsf{Remainder:}\quad \sf zero[/tex]
[tex]\textsf{Product of 2 factors:}\quad (x+2)(x^3 - 3x^2 - 5x + 15)[/tex]
Step-by-step explanation:
Quotient
The quotient of polynomial division is the result obtained by the division.
In synthetic division, the bottom row (except the last number) provides the coefficients of the quotient, with the degree of the quotient being one less than that of the dividend.
Therefore, in this case, the quotient is:
[tex]x^3 - 3x^2 - 5x + 15[/tex]
[tex]\dotfill[/tex]
Divisor
The divisor is the expression that divides the dividend.
In synthetic division, the number we put in the division box (c) is the zero of the divisor polynomial, so (x - c) = 0.
In this case, c = -2, so the divisor is:
[tex]x - (-2)=x+2[/tex]
[tex]\dotfill[/tex]
Remainder
In synthetic division, the rightmost number of the bottom row represents the remainder. Therefore, in this case, the remainder is zero.
[tex]\dotfill[/tex]
Product of two factors
To find the product of two factors, multiply the divisor by the quotient obtained from synthetic division:
[tex](x+2)(x^3 - 3x^2 - 5x + 15)[/tex]
