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

Answer:

Option B is correct.

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

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]