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find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. x^2+10x+n

Sagot :

From the problem, we have :

[tex]x^2+10x+n[/tex]

To make it a perfect square trinomial, we will use the formula :

[tex]n=(\frac{b}{2a})^2[/tex]

and we can factor the trinomial as :

[tex](x+\frac{b}{2a})^2^{}[/tex]

a = 1 and b = 10

so n will be :

[tex](\frac{b}{2a})^2=(\frac{10}{2\times1})^2=5^2=25[/tex]

The value of n is n = 25

and the factor of the trinomial will be (x + 5)^2

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