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

9514 1404 393

Step-by-step explanation:

a) ac is the product of the leading coefficient (16) and the constant (-1).

  ac = (16)(-1) = -16

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b) b is the coefficient of x. There is no x term, so ...

  b = 0

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c) Two factors that add to give zero must be opposites. That is, they must be the square root of the opposite of -16, and the opposite of that.

  the two numbers are -4 and 4

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d) The factored form for the two numbers p and q just found is ...

  ax^2 +bx +c = (ax +p)(ax +q)/a

  = (16x -4)(16x +4)/16

  = (4x -1)(4x +1) . . . . factored form of 16x^2 -1

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!