Question

$for \: what \: value \: of \: m \: is \: the \: polynomial \:$
$x {}^{2} - 2mx {}^{2} + 16$
$divisible \: by \: (x + 2).$
​

Answer 1

Step-by-step explanation:

ANSWER:-

GIVEN:-

x+2= 0

x = -2

Placing value of x in the polynomial,

(-2)²-2(-2)²m + 16 =0

4 -8m +16 =0

-8m = -20

m = 20/8 = 5/2

So,

m = 5/2 is the answer.

Things to Note:-

• If we square a negative number it turns positive
• If we square a positive number it remains positive.
• Always convert the value of x into some number given in question
• Then place the value
• Equate the equation equal to zero to get the required answer.

Answer 2

→GIVEN←

A polynomial [say p(x)] = x² - 2mx² + 16 is divisible by (x + 2).

→TO FIND←

The value of m, for which p(x) is divisible by (x + 2).

→WE MUST KNOW←

If a polynomial is divisible by another polynomial, then the remainder(R) must be 0.

→SOLUTION←

Zero of (x + 2) :-

x + 2 = 0

⇒x = -2

Now,

p(-2) = 0    (from the acknowledgement)

⇒(-2)² - 2m(-2)² +16 = 0

⇒4 - 8m + 16 = 0

⇒20 - 8m = 0

⇒8m = 20

⇒m = 20/8

⇒m = 5/2

⇒m = 2.5

Therefore, the value of m must be 2.5 for which p(x) is divisible by (x + 2).