How do you factor a perfect square trinomial $9 x^{2} - 12 x + 4$ $9x^2 − 12x + 4$ ?

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How do you factor a perfect square trinomial $9 x^{2} - 12 x + 4$ $9x^2 − 12x + 4$ ?

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Answer 1 · 2015-07-07T16:32:18

$9 x^{2} - 12 x + 4 = {(3 x - 2)}^{2}$ $9x^2-12x+4=(3x-2)^2$

Explanation:

If $A x^{2} + B x + C = {(a x + c)}^{2}$ $Ax^2+Bx+C = (ax+c)^2$ is a perfect square trinomial
then for some set ${a, c}$ ${a,c}$
$XXXX$ $color(white)("XXXX")$ $A = a^{2}$ $A=a^2$
$XXXX$ $color(white)("XXXX")$ $C = c^{2}$ $C=c^2$
and
$XXXX$ $color(white)("XXXX")$ $B = 2 a c$ $B = 2ac$

Given that $9 x^{2} - 12 x + 4$ $9x^2-12x+4$ is a perfect square trinomial
$XXXX$ $color(white)("XXXX")$ $A = 9 x^{2} \to a = 3 x$ $A=9x^2 rarr a=3x$
$XXXX$ $color(white)("XXXX")$ $C = 4 \to c = \pm 2$ $C=4 rarr c=+-2$

Since $B = - 12 x = 2 a c = 2 (3 x) c$ $B=-12x = 2ac = 2(3x)c$
$XXXX$ $color(white)("XXXX")$ $\to c = - 2$ $rarr c=-2$

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How do you factor a perfect square trinomial $9 x^{2} - 12 x + 4$ $9x^2 − 12x + 4$ ?

1 Answer

Explanation:

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How do you factor a perfect square trinomial $9 x^{2} - 12 x + 4$ $9x^2 − 12x + 4$ ?