Question

Find the value of A if polynomial
$3x {}^{3} + 14x {}^{2} + 9x + a$
can be divided by polynomial
$3x + 5$
​

Answer 1

To Find:-

• Value of a

Given:-

• Polynomial p(x)=3x³+14x²+9x+a is divisible by 3x+5

Solution:-

Hence,3x+5 is a factor of the polynomial 3x³+14x²+14x²+9x+a

Therefore, according to Remainder theorem

3x+5=0

and the value of x in the polynomial 3x³+14x²+9x+a also makes 0

first,to find value of x

that is

3x+5=0

3x=-5

x=-5/3

Substituting it in p(x)=3x³+14x²+9x+a

p(-5/3)=3(-5/3)³+14(-5/3)²+9(-5/3)+a=0

3(-125/27)+14(25/9)+ (-15)+a=0

(-125/9)+(350/9)+a=15

225/9+a=15

(225+9a)/9=15

225+9a=15×9=135

9a=135-225

9a=-90

a=-90÷9

a=-10

Therefore value of a= -10