Question

the table shows the product when multiplying two binomials. what is the relationship between the numbers in the factors and the terms in the product? the first term of the product is the in each binomial. the coefficient of the second term of the product is the in each binomial. the last term of the product is the in each binomial. binomials: (x - 3)(x - 5), (x + 2)(x - 5), (x + 3)(x + 4). products: x² - 8x + 15, x² - 3x - 10, x² + 7x + 12

Explanation:

Step1: Recall FOIL method

When multiplying two binomials \((a + b)(c + d)=ac+ad+bc+bd\). For binomials of the form \((x + m)(x + n)=x^{2}+(m + n)x+mn\).

Step2: Analyze the first - term of the product

The first term of the product of two binomials of the form \((x + m)(x + n)\) is \(x^{2}\), which is the product of the \(x\) terms in each binomial (\(x\times x=x^{2}\)).

Step3: Analyze the coefficient of the second - term of the product

The coefficient of the second - term of the product \(x^{2}+(m + n)x+mn\) is the sum of the second numbers in each binomial (\(m + n\)).

Step4: Analyze the last term of the product

The last term of the product \(x^{2}+(m + n)x+mn\) is the product of the second numbers in each binomial (\(m\times n\)).

Answer:

The first term of the product is the product of the \(x\) terms in each binomial. The coefficient of the second term of the product is the sum of the second numbers in each binomial. The last term of the product is the product of the second numbers in each binomial.