Question

Write the polynomial as a product: x² + 7x − ax − 7a

a) Factorize the given polynomial.
b) Express the polynomial as a product of its factors.
c) Explain the process of factoring and how it applies to this polynomial.
d) Provide a simplified form of the factored expression.

Answer 1

To factorize the given polynomial, use the grouping method. The factored expression is (x - a)(x + 7).

Step-by-step explanation:

To factorize the given polynomial, we can use the grouping method. Group the terms with similar variables together and find common factors.

x² + 7x - ax - 7a = x(x + 7) - a(x + 7) = (x - a)(x + 7)

The polynomial can be expressed as a product of its factors: (x - a)(x + 7).

The process of factoring involves finding common factors and separating the polynomial into two or more expressions. In this case, we found a common factor of (x + 7) and separated the polynomial into (x - a) and (x + 7).

The factored expression is (x - a)(x + 7).