Answer:
p(x) = (x+7)(x+5)(-x+1)(x-35).
Explanation:
To factor p(x), we can use the following steps:
Find the factors of 35 that add up to 4, which is the coefficient of the quadratic term (x^2). In this case, the factors of 35 that add up to 4 are 7 and 5.
Use these factors to rewrite the quadratic term as the product of two binomials. In this case, we can write the quadratic term as (x+7)(x+5).
Substitute this expression into the original polynomial to get p(x) = (x+7)(x+5) + 2x + 35.
To complete the factorization, we need to find two numbers that multiply to 35 and add up to 2. These numbers are -1 and -35.
Use these numbers to rewrite the remaining linear term as the product of two binomials. In this case, we can write the linear term as (-x+1)(x-35).
Substitute this expression into the polynomial to get p(x) = (x+7)(x+5) + (-x+1)(x-35).
Finally, we can factor p(x) as the product of two quadratics: p(x) = (x+7)(x+5)(-x+1)(x-35).