Question

A rectangular garden has an area of 2a² + 3a - 5 m².

a) Write the area as the product of two binomials.

Answer 1

The area of the garden, given by the quadratic expression 2a² + 3a - 5, is expressed as the product of two binomials by factoring. An example product is (2a - 1)(a + 2.5).

Step-by-step explanation:

The question asks us to express the area of a rectangular garden, which is given as the quadratic expression 2a² + 3a - 5 square meters, as the product of two binomials. To do this, we will use factoring by grouping or applying the quadratic formula and finding factors that match.

Steps to Factor the Quadratic Expression:

1. Find two numbers that multiply to (2a²)(-5) = -10a² and add to 3a.
2. Once we have these numbers, split the middle term into two terms that add up to 3a using the numbers found.
3. Factor by grouping, rearranging the equation into two binomials.

An example of two numbers that work for this scenario might be 5a and -2a. Thus, we can write the expression as (2a² + 5a) - (2a + 5).

Further factoring by grouping, we get 2a(a + 2.5) - 2(a + 2.5), which can be expressed as the product of two binomials: (2a - 1)(a + 2.5).