Question

question 5
factor
$x^2 + 25$
$(x+5)(x-5)$
$(x-5)^2$
$(x+5)^2$
this is prime and cant be factored

Explanation:

Step1: Recall factoring rules

The difference of squares formula is \(a^2 - b^2=(a + b)(a - b)\), and the perfect square formulas are \((a + b)^2=a^2 + 2ab + b^2\) and \((a - b)^2=a^2-2ab + b^2\). For the expression \(x^2+25\), we can rewrite it as \(x^2+5^2\).

Step2: Analyze each option

• Option 1: \((x + 5)(x - 5)=x^2-25\) (using difference of squares), which is not equal to \(x^2 + 25\).
• Option 2: \((x - 5)^2=x^2-10x + 25\) (using perfect square formula), which is not equal to \(x^2 + 25\).
• Option 3: \((x + 5)^2=x^2+10x + 25\) (using perfect square formula), which is not equal to \(x^2 + 25\).
• Option 4: Since \(x^2+25\) cannot be factored using real - number coefficients (it doesn't fit the difference of squares or perfect square trinomial formulas), it is a prime polynomial (in the context of factoring over the real numbers) and can't be factored.

Answer:

This is prime and can't be factored