Question

Factor the polynomial or solve the equation as indicated.

a. Factor p² - 25
b. Solve p² -25=0

Answer 1

The polynomial p² - 25 can be factored as (p + 5)(p - 5), and the equation p² - 25 = 0 is solved by finding the roots p = 5 and p = -5.

Correct option is A

Step-by-step explanation:

To answer the student's question:

1. To factor the polynomial p² - 25, we recognize this as a difference of squares, which factors to (p + 5)(p - 5).
2. To solve the equation p² - 25 = 0, we can use the factored form (p + 5)(p - 5) = 0 and determine that p = 5 or p = -5 are the solutions.

The quadratic equation ax² + bx + c = 0 can be solved using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). However, since the polynomial in this case is already factored as a difference of squares, we do not need to use the quadratic formula.

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