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\(2q^{ $2$ }-qr $-3$ r^{ $2$ }\div $2$ q^{ $2$ } $-9$ qr+ $9$ r^{ $2$ }(\newline\)(q+r)(q+ $3$ r)(\newline\)( $9$ ) Cannot be simplified(\newline\)(a+r)(a $-3$ r)(\newline\)(a-r)(q+ $3$ r)

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Divide polynomials using long division

Full solution

Q. \(2q^{

2

}-qr

-3

r^{

2

}\div

2

q^{

2

}

-9

qr+

9

r^{

2

}(\newline\)(q+r)(q+

3

r)(\newline\)(

9

) Cannot be simplified(\newline\)(a+r)(a

-3

r)(\newline\)(a-r)(q+

3

r)

Check Common Factor: Check if the numerator and denominator have a common factor. $\newline$ $2q^2 - qr - 3r^2$ and $2q^2 - 9qr + 9r^2$
Factor Numerator: Factor both the numerator and the denominator. $\newline$ Numerator: $2q^2 - qr - 3r^2 = (2q + 3r)(q - r)$ $\newline$ Denominator: $2q^2 - 9qr + 9r^2 = (q - 3r)(2q - 3r)$

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