The expression (x^2 + 6x) + 5 transforms into the form (x + 3 )^2 - 4.
Polynomials are those algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.
Given expression
[tex]\rm x^{2} +6x+5[/tex]
We can write terms as
[tex]\rm (x^{2} +6x)+5[/tex]
Any term that is added to an expression is also subtracted from the expression
[tex]\rm( x^{2} +2\times3\times x)+5[/tex]
2ab = 6x
b=3
So,
As b = 3 so [tex](b)^2[/tex] will be added and subtracted in the expression
[tex]\rm (x^{2} +6x)+5+3^{2} -3^{2}[/tex]
[tex]\rm (x^{2} +6x +3^{2})+5 -3^{2}\\\rm (x +3)^{2}+5 -3^{2}[/tex]
[tex]\rm (x +3)^{2}-4[/tex]
Thus, transforming the expression [tex]\rm (x^{2} +6x)+5[/tex] into the form [tex]\rm (x +3)^{2}-4[/tex].
Learn more about polynomials;
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