Question \( 3(1 \) point) Factor the expression below: \( 2 x^{2}+21 x+27 \)

To factor the expression \( 2x^2 + 21x + 27 \), we are looking for two numbers that multiply to the product of the coefficient of \( x^2 \) (which is 2) and the constant term (27), so \( 2 \times 27 = 54 \), and add up to the coefficient of \( x \) (which is 21). The numbers 18 and 3 will work since \( 18 \times 3 = 54 \) and \( 18 + 3 = 21 \). Next, we can rewrite the expression as \( 2x^2 + 18x + 3x + 27 \). Now, we can factor by grouping. From the first two terms, factor out \( 2x \), and from the last two terms, factor out 3: \( = 2x(x + 9) + 3(x + 9) \) Now, we can factor out the common binomial \( (x + 9) \): \( = (2x + 3)(x + 9) \) So, the expression \( 2x^2 + 21x + 27 \) factors to \( (2x + 3)(x + 9) \).