Question

Based on the Synthetic Division below, state the quotient, divisor, remainder and product of 2 factors.Label and write each part as a polynomial expression
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Answer 1

Answer:

$\textsf{Quotient:}\quad x^3 - 3x^2 - 5x + 15$

$\textsf{Divisor:}\quad (x+2)$

$\textsf{Remainder:}\quad \sf zero$

$\textsf{Product of 2 factors:}\quad (x+2)(x^3 - 3x^2 - 5x + 15)$

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:

$x^3 - 3x^2 - 5x + 15$

$\dotfill$

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:

$x - (-2)=x+2$

$\dotfill$

Remainder

In synthetic division, the rightmost number of the bottom row represents the remainder. Therefore, in this case, the remainder is zero.

$\dotfill$

Product of two factors

To find the product of two factors, multiply the divisor by the quotient obtained from synthetic division:

$(x+2)(x^3 - 3x^2 - 5x + 15)$