Factor the expression 9X^2 + 24X + 16

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Let f(x) = 9x^2 + 24x + 16

We notice that the function is a complete square :

Then the function has two similar factors which are the square roots of first and last terms:

==> f(x)= (3x+4)^2

Let us check the answer:

==> f( x) = (3x)^2 + 2*3x*4 +...

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Let f(x) = 9x^2 + 24x + 16

We notice that the function is a complete square :

Then the function has two similar factors which are the square roots of first and last terms:

==> f(x)= (3x+4)^2

Let us check the answer:

==> f( x) = (3x)^2 + 2*3x*4 + 4^2

               = 9x^2 + 24x + 16

Also we can use the formula to find the roots and then factor:

The roots = (-b + sqrt( b^2 - 4ac) /2 =  - 4/3

==> the factor is ( x+ 4/3) ==>multiply by 3:==>  (3x + 4 )

Then the factor is ( 3x+4) * ( 3x+ 4) = ( 3x+ 4)^2

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