Answered

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What is the missing expression?

[tex]\[ x^8 + 3x^5 = x^5 \times \square \][/tex]

A. [tex]\( x + 3 \)[/tex]

B. [tex]\( x^2 + 3 \)[/tex]

C. [tex]\( x^3 - 3 \)[/tex]


Sagot :

Sure, let's solve the equation step by step to find the missing expression.

We start with the equation given:

[tex]\[ x^8 + 3 x^5 = x^5 \cdot \text{(missing expression)} \][/tex]

Our goal is to determine the missing expression on the right-hand side.

First, we can factor out [tex]\( x^5 \)[/tex] from the left-hand side of the equation:

[tex]\[ x^8 + 3 x^5 = x^5 (x^3) + x^5 (3) \][/tex]

When we factor [tex]\( x^5 \)[/tex] out of the terms on the left, the equation becomes:

[tex]\[ x^8 + 3 x^5 = x^5 (x^3 + 3) \][/tex]

So, the missing expression in the given equation is:

[tex]\[ \boxed{x^3 + 3} \][/tex]

Therefore, the complete equation is:

[tex]\[ x^8 + 3 x^5 = x^5 (x^3 + 3) \][/tex]

This verifies that our missing expression is indeed [tex]\( x^3 + 3 \)[/tex].