Question

1. choose where the graphs of the polynomial functions would cross the x-axis.

$f(x)=x^2 - 8x + 15$
$\circ$ $x=-15, -1$
$\circ$ $x=-3, -5$
$\circ$ $x=1, 15$
$\circ$ $x=5, 3$

1. select the correct equation represented by the synthetic division problem.

\\(\

$$\begin{array}{r|rrrr}-4 & 1 & 8 & 14 & -8 \\\\ & & -4 & -16 & 8 \\\\ \\hline & 1 & 4 & -2 & 0 \\\\ \\end{array}$$

\\)
$\circ$ $(x^3 + 8x^2 + 14x - 8) \div (x - 4) = x^2 + 4x - 2$
$\circ$ $(x^3 + 8x^2 + 14x - 8) \div (x + 4) = x^2 + 4x - 2$
$\circ$ $(x^3 - 8x^2 - 14x + 8) \div (x - 4) = -x^2 - 4x + 2$
$\circ$ $(-x^3 - 8x^2 + 14x + 8) \div (x + 4) = x^2 + 4x - 2$

Explanation:

Question 13

Step1: Set $f(x)=0$

$x^2 - 8x + 15 = 0$

Step2: Factor the quadratic

$(x-3)(x-5)=0$

Step3: Solve for $x$

$x-3=0 \implies x=3$; $x-5=0 \implies x=5$

Step1: Identify divisor from synthetic division

Divisor: $x - (-4) = x+4$

Step2: Identify dividend coefficients

Dividend: $x^3 + 8x^2 +14x -8$

Step3: Identify quotient from results

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

Step4: Match to division equation

$(x^3 +8x^2 +14x -8) \div (x+4) = x^2 +4x -2$

Answer:

$\boldsymbol{x=5,3}$ (matches option D)

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Question 14