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

`3x^(2) +24x+48`

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;√(16)=4`;
`3(x+4)^(2) =3(x^(2) +8x+16)=3x^(2) +24x+48`