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

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Answer 1 · 2016-09-28T00:50:47

Roots: $\pm \frac{3}{2}$ $+-3/2$ Factors: $(2 x + 3) (2 x - 3)$ $(2x+3)(2x-3)$

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

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

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

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

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

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

$f(x) = 0$ 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^2-94x2−94x^2-9?