contestada

Replace * with a number in such a way that the trinomial could be rewritten in the form a(x+b)^2 or a(x−b)^2.

a) 3x^2+24x + *


Can you please explain the process to follow when you do this

Respuesta :

prozehus

Answer:

[tex]3x^{2} +24x+48[/tex]

Step-by-step explanation:

given [tex]3x^{2} +24x....[/tex] choose [tex]a(x+b)^{2}[/tex] (plus sign)

and  [tex]a(x+b)^{2}[/tex]  = [tex]a(x^{2} +2bx+b^{2}); common factor (3)[/tex]

[tex]3(x^{2} +8x+b^{2} )[/tex]; where if a=3, x=1 and 2bx=8 then  2.b.1=8 → b=8/2=4;

[tex]3(x^{2} +8x+b^{2} )=3(x^{2} +8x+4^{2})=3(x^{2} +8x+16)[/tex];

Finally [tex]\sqrt{x^{2} } =x;\sqrt{16}=4[/tex]; [tex]3(x+4)^{2} =3(x^{2} +8x+16)=3x^{2} +24x+48[/tex]

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