Question

1. choose the best answer.

the denominators of any rational roots of a polynomial will be the factors of the ___ coefficient.
constant
synthetic
leading
remainder

1. choose the best answer.

it is often useful to find the ___ of a polynomial in order to find its roots.
factors
synthetic
remainder
constant

1. divide using synthetic division.

$\begin{array}{r}2vert 1 2 -5 -6\\ end{array}$
$x^3 + 4x^2 + 3x$
$x^2 + 4x + 3$
$x + 4x + 2x$
$-x^3 - 4x - 3$

Explanation:

For Q8: By the Rational Root Theorem, the denominators of possible rational roots of a polynomial are factors of the polynomial's constant term.
For Q9: Factoring a polynomial is a key step to find its roots, as roots correspond to the factors set equal to zero.
For Q10: Perform synthetic division step-by-step: bring down the leading coefficient, multiply by the divisor value, add to the next coefficient, repeat, then form the quotient polynomial.

Step1: Bring down the first coefficient

$1$

Step2: Multiply by 2, add to next coeff

$2 + (1\times2) = 4$

Step3: Multiply by 2, add to next coeff

$-5 + (4\times2) = 3$

Step4: Multiply by 2, add to last coeff

$-6 + (3\times2) = 0$

Step5: Form quotient polynomial

Quotient: $x^2 + 4x + 3$, remainder $0$

Answer:

Q8: constant
Q9: factors
Q10: