Question

Select the perfect square trinomial for each polynomial. (There are 2 correct answers)

Question 1 options:


x^2−10x−25


x^2−18x+81


x^2+2x+1


x^2+7x+49

Answer 1

x^2−18x+81

x^2+2x+1

Explanation:

we know that

A trinomial is a perfect square trinomial if it can be factored into a binomial multiplied to itself

so

`a^2\pm2ab+b^2=(a\pm b)(a\pm b)=(a\pm b)^2`

Verify each case

case a) x^2−10x−25

we know that

`(x-5)^2=x^2-10x+25`

therefore

Is not a perfect square trinomial

case b) x^2−18x+81

we know that

`(x-9)^2=x^2-18x+81`

therefore

Is a perfect square trinomial

case c) x^2+2x+1

we know that

`(x+1)^2=x^2+2x+1`

therefore

Is a perfect square trinomial

case d) x^2+7x+49

we know that

`(x+3.5)^2=x^2+7x+12.25`

therefore

Is not a perfect square trinomial