Factor completely. k^2+11k+10 square

To factor the quadratic expression \( k^2 + 11k + 10 \) completely, we need to find two numbers that multiply to the constant term (10) and add up to the coefficient of the linear term (11).<br /><br />Let's denote these two numbers as \( a \) and \( b \). We need:<br />\[ a \cdot b = 10 \]<br />\[ a + b = 11 \]<br /><br />By examining the pairs of factors of 10, we find:<br />- \( 1 \times 10 = 10 \)<br />- \( 2 \times 5 = 10 \)<br /><br />Now, let's check their sums:<br />- \( 1 + 10 = 11 \)<br />- \( 2 + 5 = 7 \)<br /><br />The pair that satisfies both conditions is \( 1 \) and \( 10 \).<br /><br />Thus, we can write the quadratic expression as:<br />\[ k^2 + 11k + 10 = (k + 1)(k + 10) \]<br /><br />So, the completely factored form of \( k^2 + 11k + 10 \) is:<br />\[ \boxed{(k + 1)(k + 10)} \]