Question

Use synthetic division method for performing the following division. Write the result in the form
Dividend = Divisor x Quotient + Remainder.

$(y^2-11y+30)÷(y-5)$

• A. $(y-7)(y+1)+0$
• B. $(y+4)(y+6)+0$
• C. $\left(y\right)(y-5)+0$
• D. $(y-5)(y-6)+0$

Answer 1

Answer: (D)

$(y-5)(y-6)+0$

Given that,

Dividend= $y^2-11y+30$

Divisor= $y-5$

Now,

Dividend =$y^2-11y+30$

$=y^2-5y-6y+30$

$=y(y-5)-6(y-5)$

$=(y-5)(y-6)$

Now, dividing the dividend by the divisor

$\frac{(y-5)(y-6)}{(y-5)}$

$=(y-6)$

$\therefore$ Quotient $=y-6$

Remainder $=0$

$y^2-11y+30=(y-5)(y-6)+0$