Question

Consider the polynomial 9x2 – 16. What is the value of ac? What is the value of b? What two numbers multiply to get ac and add to get b? The factored form of 9x2 – 16 is

Answer 1

The value of ac for the quadratic expression 9x^2 - 16 is -144. The value of b is 0, as it represents the coefficient of x, which is absent in the expression. Therefore, we do not need two numbers that multiply to ac and add to b; the expression is factored using the difference of squares as (3x + 4)(3x - 4).

Step-by-step explanation:

The polynomial 9x2 − 16 is a quadratic expression that can be factored using the difference of squares method. To answer the questions:

• The value of ac is the product of the coefficient of x2 and the constant term, which in this case is 9 × (− 16) = − 144.
• The value of b in the standard form ax2 + bx + c is the coefficient of x, which is 0 since there is no x term in the original expression.
• To factor, we need two numbers that multiply to ac (which is − 144) and add up to b (which is 0). However, this step is not applicable as the polynomial is already in the form a2 − b2 and will be factored as a difference of squares.
• The factored form of the polynomial is (3x + 4)(3x − 4).

Answer 2

9x² - 16 = (3x - 4) (3x + 4)
A C

The value of ac together is 16(9x²) or 144x²

The value of B is zero, since there is no B (b is x, (note not x², but only 1 x))


hope this helps