Question

What is the missing expression? x8 + 3x5 = x5(_____) x + 3 x 2 + 3 x 3 + 3

Answer 1

Question:

What is the missing expression? $x^8+3x^5=x^5$(______)

Option A: $x+3$

Option B: $x^2+3$

Option C: $x^3+3$

Answer:

Option C:

The missing expression is $(x^3+3)$.

Solution:

Given expression is $x^8+3x^5$.

Let us factor the given expression.

There are 2 terms in the expression.

Take out common terms in each of the expression.

$x^8+3x^5=x^5(x^{8-5}+3x^{5-5})$  (use radical rule)

              $=x^5(x^3+3x^0)$   (use radical rule)

              $=x^5(x^3+3)$

$x^8+3x^5=x^5(x^3+3)$

Hence the missing expression is $(x^3+3)$.