Question

find g(x),ig p(x)=x²+5x+13 wheb q(x(=(x+2) and r(x)=7​

Answer 1

Answer :-

Given :-

• p(x) = x² + 5x + 13
• q(x) = x + 2
• r(x) = 7

To Find :-

• g(x)

Solution :-

We know that,

→ p(x) = g(x) × q(x) + r(x)

Substituting the values in formula :-

→ x² + 5x + 13 = ( x + 2 ) × g(x) + 7

→ x² + 5x + 13 - 7 = ( x + 2 ) × g(x)

→ x² + 5x + 6 = ( x + 2 ) × g(x)

→ x² + 2x + 3x + 6 = ( x + 2 ) × g(x)

→ x ( x + 2 ) + 3 ( x + 2 ) = ( x + 2 ) × g(x)

→ ( x + 3 ) ( x + 2 ) = ( x + 2 ) × g(x)

→ ( x + 3 ) ( x + 2 ) / ( x + 2 ) = g(x)

→ g(x) = x + 3

Value of g(x) = x + 3