Question

Check whether 7+3x is a factor of 3x3+7x​

Answer 1

Question :

Check whether 7+3x is a factor of 3x³ + 7x…

Solution :

Let f(x) =7+3x

g(x) =3x³ + 7x…..(1)

7x+3 will be a factor of 3x³ + 7x only if 7+3x divides 3x³ + 7x leaving no remainder .

Apply remainder theorem

f(x) = 0

7+3x = 0

⇒x =$\dfrac{-7}{3}$

Now to check whether (7 + 3x) the polynomial is a factor of 3x³ + 7x, we prove that, f($\dfrac{-7}{3}$) = 0, by using remainder theorem

put x =$\dfrac{-7}{3}$ in equation (1)

$f ( \frac{ - 7}{3} ) = 3 \times ( \frac{ - 7}{3} ) {}^{3} + 7 \times( \frac{ - 7}{3} )$

$= 3 \times \frac{ - 343}{27} - \frac{49}{3}$

$= \frac{ - 343}{9} - \frac{49}{3}$

$= \frac{ - 343 \times 3 - 49 \times 9}{27 }$

$= \frac{ - 1029 - 441}{27}$

$= \frac{ - 1470}{27}$

$= \frac{ - 490}{9}$

Hence, (7 + 3x) is not a factor

of (3x³ + 7x).

Answer 2

Helo mate here your ans

Solution: Apply remainder theorem

=>7 + 3x =0

=> 3x = - 7

=> x = - 7/3

Replace x by - 7/3 we get

=>3x3 + 7x

=>3(-7/3)3 + 7(-7/3)

=>3(-343/27) – 49/3

=> (-343/9) – 49/3

This value is not equal to 0

So that 7 + 3x is not a factor of expression 3x3 + 7x

Hope this ans help you...