How do you list all possible roots and find all factors of $4x^2-9$ ?

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Answer 1 · 2016-09-28T00:50:47

Roots: $+-3/2$ Factors: $(2x+3)(2x-3)$

$f(x) = 4x^2-9$

The roots of $f(x)$ are the values of $x$ for which $f(x)=0$

Since $f(x)$ is of 2nd degree, we know that the number of roots is at most 2.

Notice that both $4x^2$ and $9$ are square values and remember that: $a^2-b^2 = (a+b)(a-b)$

In this example $a=2x$ and $b=3$

$:. f(x) = (2x+3)(2x-3)$

$f(x) = 0$ when either $(2x+3)=0$ or $(2x-3)=0$

Hence the roots of $f(x)$ are $+-3/2$

How do you list all possible roots and find all factors of 4x^2-94x^2-9?