Factor the following expression completely: x^2+15x+26-square

To factor the expression \(x^2 + 15x + 26\) completely, we need to find two numbers that multiply to 26 and add up to 15.<br /><br />Let's denote these two numbers as \(a\) and \(b\). We need:<br />\[ a \cdot b = 26 \]<br />\[ a + b = 15 \]<br /><br />By examining the pairs of factors of 26, we find:<br />- \(1 \cdot 26 = 26\) and \(1 + 26 = 27\)<br />- \(2 \cdot 13 = 26\) and \(2 + 13 = 15\)<br /><br />The pair \(2\) and \(13\) satisfies both conditions:<br />\[ 2 \cdot 13 = 26 \]<br />\[ 2 + 13 = 15 \]<br /><br />Thus, we can rewrite the quadratic expression as:<br />\[ x^2 + 15x + 26 = (x + 2)(x + 13) \]<br /><br />So, the completely factored form of the expression \(x^2 + 15x + 26\) is:<br />\[ (x + 2)(x + 13) \]