Question

15 fill in the blank 3 points
the expression $\frac{x^2 - 7x + 15}{x - 4}$ can be written in the form $x - a + \frac{b}{x - c}$, where a, b, and c are integers. what are the values of a, b, and c?
a = type your answer...
b = type your answer...
c = type your answer...

Explanation:

Step1: Polynomial long division setup

Divide $x^2 -7x +15$ by $x-4$

Step2: Divide leading terms

$\frac{x^2}{x}=x$, so first term is $x$

Step3: Multiply divisor by $x$

$x(x-4)=x^2-4x$

Step4: Subtract from dividend

$(x^2-7x+15)-(x^2-4x)=-3x+15$

Step5: Divide new leading term

$\frac{-3x}{x}=-3$, add to quotient

Step6: Multiply divisor by $-3$

$-3(x-4)=-3x+12$

Step7: Subtract to find remainder

$(-3x+15)-(-3x+12)=3$

Step8: Rewrite the expression

$\frac{x^2-7x+15}{x-4}=x-3+\frac{3}{x-4}$

Answer:

$a=1$, $b=-3$, $c=3$