Question

Howdy!

$f(x)=2x^3+6x^2+4x$
$g(x)=x^2+3x+2$

The polynomials f(x) and g(x) are defined above.

Which of the following polynomials is divisible by $2x+3$?

$A)h(x) = f(x) + g(x)$
$B) p(x) = f(x) + 3g(x)$
$C) r(x) = 2f(x) + 3g(x)$
$D) s(x) = 3f(x) + 2g(x)$​

Answer 1

$\bigstar\:\:\underline{\sf Give :} \: \bigstar$

$f(x)=2x^3+6x^2+4x$

$g(x)=x^2+3x+2$

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

Answer 2

Answer:

$f(x)=2x^3+6x^2+4x$

$g(x)=x^2+3x+2$

The polynomials f(x) and g(x) are defined above.

Which of the following polynomials is divisible by $2x+3$?

$A)h(x) = f(x) + g(x)$

$B) p(x) = f(x) + 3g(x)$

$C) r(x) = 2f(x) + 3g(x)$

$D) s(x) = 3f(x) + 2g(x)$