Question

Find the value of a for which the polynomial 3xcube+14xsquare+9x+a is divisible by 3x+5

Answer 1

Answer:

10

Step-by-step explanation:

see the image for explanation

Answer 2

The value of 'a' is (- 10).

Step-by-step explanation:

Method 1.

∵ the given polynomial is divisible by (3x + 5), it is a factor of the polynomial.

Now, 3x³ + 14x² + 9x + a

= 3x³ + 5x² + 9x² + 15x - 6x - 10 + 10 + a

= x² (3x + 5) + 3x (3x + 5) - 2 (3x + 5) + 10 + a

= (3x + 5) (x² + 3x - 2) + (10 + a)

Thus the remainder must be zero

i.e., 10 + a = 0 or, a = - 10

Method 2.

∵ the given polynomial is divisible by (3x + 5), it has a zero (- 5/3), for which the polynomial values zero.

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

or, - 125/9 + 350/9 - 15 + a = 0

or, (- 125 + 350 - 135)/9 + a = 0

or, 90/9 + a = 0

or, 10 + a = 0

i.e., a = - 10