Question

Find the value of a for which the polynomial 3x3 + 14x2 + 9x + a is divisible by
3x + 5.
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Answer 1

here is your answer

hope it helps

Answer 2

Answer:

The value of a for which the polynomial $3x^{3} +14x^{2} +9x+a$ is divisible by $3x+5$ is -10

Step-by-step explanation:

Given the polynomial $3x^{3}+14x^{2} +9x+a$ is divisible by $3x+5$

We know from Factors theorem , if $x+a$ is a factor of the polynomial $f(x)$ then remainder will be $f(-a)$

 So $3x+5=0$

or $x=-\frac{5}{3}$

So we have to find  $f(-\frac{3}{5} )$

substituting $x=-\frac{3}{5}$  we get

 $3(-\frac{5}{3}) ^{3} +14(-\frac{5}{3} )^{2} +9(-\frac{5}{3} )+a=0$

or $-3\times\frac{125}{27} +14\times\frac{25}{9} -9\times\frac{5}{3} +a=0$

or $-\frac{125}{9} +\frac{350}{9} -15+a=0$

or $a=15+\frac{125}{9} -\frac{350}{9}$

or $a= 15+\frac{125-350}{9}$

or $a=15-\frac{225}{9}$

or $a=\frac{135-225}{9}$

or $a=-\frac{90}{9}$

or $a=-10$

The value of a for which the polynomial $3x^{3} +14x^{2} +9x+a$ is divisible by $3x+5$ is -10