Question

Which expression is equivalent to n2 + 26n + 88 for all values of n?

(n + 8)(n + 11)

(n + 4)(n + 22)

(n + 4)(n + 24)

(n + 8)(n + 18)

Answer 1

Solutions

The expression equivalent to n^2 + 26n + 88 is

n^2 + 26n + 88
(n + 4)(n + 22)

Answer 2

Option B is correct.

The expression which is equivalent to
`n^2+26n+88` is;
`(n+22)(n+4)`

Step-by-step explanation:

Given the equation:
`n^2+26n+88` for all values of n.

The quadratic equation in this form;
`ax^2+bx+c =0`

First find two numbers that multiply to give ac and add to give b.

From the given equation;

a =1 , b = 26 and c =88

then,

the two number that multiply to give ac =88 is, 22 or 4

and they add up to give b=26 (i.e 22+4)

Now, rewrite the middle term i.e 26n with 22n and 4n , we have

`n^2+22n+4n+88=0`

Now, factor the first two terms and last two terms,

`n(n+22)+4(n+22)`

we see that
`(n+22)` is common to both terms so, we have;

`(n+22)(n+4)`

Therefore, the expression
`(n+22)(n+4)` is equivalent to
`n^2+26n+88`

Check:

(n+4)(n+22) =
`n\cdot n+ 22n+4n+88`=
`n^2+26n+88` [ True]