Question

Consider the polynomial 16x2 – 1. 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 16x2 – 1 is

Answer 1

ANSWER

The given expression is
$16 {x}^{2} - 1$


This expression can be rewritten as,

$16 {x}^{2} + 0x - 1$

By comparing to
$a{x}^{2} + bx + c$
$a=16,b=0,c=-1$
$ac = - 16$


Two numbers that we multiply to get
$- 16$
and add to get zero are
$- 4 \: and \: 4$




The factored form is


$16 {x}^{2} - 4x + 4x- 1$


$4x(4x - 1) +1( 4x- 1)$

$(4x + 1)(4x - 1)$



We factor further to get,

Answer 2

1. -16

2. 0

3. -4 and 4

4. (4x-1)(4x+1)