Howdy!The polynomials f(x) and g(x) are defined above. Which of the fo

1.	Howdy!The polynomials f(x) and g(x) are defined above. Which of the following polynomials is divisible by ?
Answer» <P> $\bigstar\:\:\underline{\sf Give :} \: \bigstar \\$ $f(x)=2x^3+6x^2+<klux>4X</klux>$ $g(x)=x^2+3x+2$ The polynomials f(x) and g(x) are defined above. $\bigstar\:\:\underline{\sf To find :} \: \bigstar \\$ the following polynomials is divisible by $2x+3$ $\bigstar\:\:\underline{\sf Solution :} \: \bigstar \\$ option a) => h(x)=f(x)+g(x)= 2x^3+6x^2+4x+x^2+3x+2 Now , divide 2x^3+7x^2+7x+2 ÷ 2x+3 We get , REMINDER : 1/2 1/2 ≠ 0 So , this is not the ANSWER Option B) => p(x)=f(x)+3g(x) = 2x^3+6x^2+ 4x +3(x^2+3x+2) = 2x^3+6x^2+4x+3x^2+9x+6 = 2x^3+9x^2+13x+6 ÷ 2x+3 We get , Reminder : 0 ∴ p(x) =f(x)+3g(x) is satisfying So , Answer is Option b