Check whether $7+ 3x$ is a factor of $3x^2 + 7x$.
Given :
$P(x) = 3x^2+7x$, $7+ 3x$.
To do :
We have to check whether $7+ 3x$ is a factor of P(x).
Solution :
Factor Theorem:
The factor theorem states that if p(x) is a polynomial of degree n > or equal to 1 and ‘a’ is any real number, then $x-a$ is a factor of $p(x)$, if $p(a)=0$.
We have to equate $7+3x = 0$
$3x+7 = 0$
$3x = -7$
$x = \frac{-7}{3}$
Therefore,
$P( \frac{-7}{3}) = 3( \frac{-7}{3})^2+7( \frac{-7}{3})$
$= 3(\frac{49}{9}) - \frac{49}{3}$
$= \frac{49}{3}- \frac{49}{3}$
$= 0$
Therefore, $7+ 3x$ is a factor of $3x^2 + 7x$.
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