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

Consider the polynomial 16x2 – 1.

*) What is the value of ac?

–16

**) What is the value of b?

0

***) What two numbers multiply to get ac and add to get b?

–4 and 4

****) The factored form of 16x2 – 1 is

(4x– 1)(4x+ 1)

.

Explanation:

Edge 2021

Answer 2

9514 1404 393

Answer:

• ac = -16
• b = 0
• -4, 4
• (4x -1)(4x +1)

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