The factored form of given equation y = x^2 + 4x - 21 is (x + 7)(x – 3)
Solution:
Given, equation is [tex]y=x^{2}+4 x-21[/tex]
We have to factor the above equation
Now, take the expression [tex]\mathrm{x}^{2}+4 \mathrm{x}-21[/tex]
[tex]\rightarrow x^{2}+4 x-21[/tex]
"4x" can be splitted as (7 - 3)x
[tex]\rightarrow x^{2}+(7-3) x-21[/tex]
"21" can rewritten as [tex]7 \times 3[/tex]
[tex]\rightarrow x^{2}+7 x-3 x-7 \times 3[/tex]
Taking "x" as common from first two terms and "3" as common from next two terms
[tex]\rightarrow x(x+7)-3(x+7)[/tex]
Taking "x + 7" as common term,
[tex]\rightarrow(x+7)(x-3)[/tex]
Hence, the factored form of given equation is y = ( x + 7 )( x – 3 )
