Question

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

Answer 1

Answer:

$3x^{2} +24x+48$

Step-by-step explanation:

given $3x^{2} +24x....$ choose $a(x+b)^{2}$ (plus sign)

and  $a(x+b)^{2}$  = $a(x^{2} +2bx+b^{2}); common factor (3)$

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

$3(x^{2} +8x+b^{2} )=3(x^{2} +8x+4^{2})=3(x^{2} +8x+16)$;

Finally $\sqrt{x^{2} } =x;\sqrt{16}=4$; $3(x+4)^{2} =3(x^{2} +8x+16)=3x^{2} +24x+48$