Question

4. Write each expression in factored form. If not possible, write "not possible."

a.x² - 144
b. x² + 16
c. 25-x²
d. b²-a²
b
e. 100+ y²
ไ

Answer 1

Each expression was factored where possible, using the difference of squares identity for a, c, and d, while b and e are sums of squares and cannot be factored over the real numbers.

Step-by-step explanation:

The student has asked to write each expression in factored form, and we will address each one step by step:

• a. x² - 144: This is a difference of squares and can be factored as (x + 12)(x - 12).
• b. x² + 16: This is a sum of squares which cannot be factored over the real numbers, so the answer is "not possible."
• c. 25 - x²: This is another difference of squares and can be factored as (5 + x)(5 - x).
• d. b² - a²: Again a difference of squares, and it factors to (b + a)(b - a).
• e. 100 + y²: Like part b, this is a sum of squares which also cannot be factored over the real numbers, so the answer is "not possible."

When factoring quadratic equations, always look for patterns like the difference of squares and utilize identities to simplify expressions where possible. If an expression cannot be factored using real numbers, such as sums of squares, then it is considered not factorable in the context given.