Question

If the polynomial 6x3 + 16x2 + px – 5 is exactly divisible by 3x + 5, then find the value of p.

Answer 1

Answer:

Step-by-step explanation:

3x +5 = 0

3x = -5

x = -5/3

Now,

6x^3+16x^2+px-5=0

(6*-5/3)^3 +(16*-5/3)^2+(-5/3)*p-5=0

-288.8 - 5p/3 - 5=0

-295.46p = 0

p=1/295.46

Answer 2

The value of P is equal to 7.

GIVEN: The polynomial 6x3 + 16x2 + px – 5 is exactly divisible by 3x + 5
TO FIND the value of p.
SOLUTION:

The polynomial is given in the question,

6x3 + 16x2 + px – 5

And the divisor given is 3x + 5

To find the value of x :

3x+5 = 0

3x = -5

x = -5/3

Putting the value of x = -5/3 in the given polynomial

6(-5/3)³ + 16(-5/3)² + p(-5/3) - 5 = 0

6(-125/27) + 16(25/9) -5p/3 - 5 = 0

-720/27 + 400/9 - 5p/3 - 5 = 0

-750  + 1200 -45p - 135 = 0

315 - 45p = 0

315 = 45p

p = 7

Therefore, the required value of p=7

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