Factor the following trinomials completely.
$z^2-11z+30$

• A. $(z+5)(z-6)$
• B. $(z-3)(z-10)$
• C. $(z+5)(z+6)$
• D. $(z-5)(z-6)$

Answer: (D)

Verified step by step guidance

1. Identify the trinomial to factor: \(z^2 - 11z + 30\).
2. Look for two numbers that multiply to the constant term \$30\( and add up to the coefficient of the middle term, which is \)-11$.
3. List the factor pairs of \$30\(: \)(1, 30)\(, \)(2, 15)\(, \)(3, 10)\(, and \)(5, 6)\(, and consider their signs to sum to \)-11$.
4. Since the middle term is negative and the constant is positive, both numbers should be negative. Check which pair of negative numbers multiply to \$30\( and add to \)-11$.
5. Write the factored form using the two numbers found: \((z - a)(z - b)\), where \(a\) and \(b\) are the numbers identified in the previous step.