Factoring Polynomials I Score: 7/8 Answered: 7/8 square Factor c^2+2c+1 square

To factor the polynomial \( c^2 + 2c + 1 \), we need to find two binomials that multiply together to give us the original quadratic expression.<br /><br />First, let's rewrite the quadratic expression in standard form:<br />\[ c^2 + 2c + 1 \]<br /><br />Next, we look for two numbers that multiply to the constant term (1) and add up to the coefficient of the linear term (2). <br /><br />The numbers that satisfy these conditions are 1 and 1 because:<br />\[ 1 \times 1 = 1 \]<br />\[ 1 + 1 = 2 \]<br /><br />So, we can write the quadratic expression as:<br />\[ c^2 + 2c + 1 = (c + 1)(c + 1) \]<br /><br />Therefore, the factored form of \( c^2 + 2c + 1 \) is:<br />\[ (c + 1)^2 \]<br /><br />So, the final answer is:<br />\[ c^2 + 2c + 1 = (c + 1)^2 \]