Question

P is an integer. If (P-7) is a multiple of 11, then the largest number that will always divide (P + 4)(P + 15) is

Answer 1

Step-by-step explanation:

Given :-

P is an integer.

(P-7) is a multiple of 11

To find:-

If (P-7) is a multiple of 11, then the largest number that will always divide (P + 4)(P + 15) is ----?

Solution:-

Given that

P is an integer

P-7 is a multiple of 11

=>P-7 = 11 X

=>P = 11X + 7 -----------(1)

Now Given that

(P + 4)(P + 15)

On Substituting the value of P in the above expression then

=>(11X+7+4)(11X+7+15)

=>(11X+11)(11X+22)

=>11(X+1) × 11(X+2)

=>11×11×(X+1)(X+2)

=> 121 (X+1)(X+2)

X+1 and X+2 are Consecutive integers and

X+1 is an odd number and X+2 is an even number

Product of an odd and an even is an even number

So It is divisible by 2

(X+1)(X+2) is divisible by 2

=> 121×2n ,n is an integer

=> 242n

(P+4)(P+15) is divided by 242

Answer:-

The largest number that will always divide

(P + 4)(P + 15) is 242

Used formulae:-

• The Product of an odd and an even is an even number
• The product of two consecutive integers is always divisible by 2