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Lapatulllka [165]
3 years ago
9

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

Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
3 0

Answer:

x^2−18x+81

x^2+2x+1

Step-by-step 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

<u><em>Verify each case</em></u>

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

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Step-by-step explanation:

Final result :

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "k2"   was replaced by   "k^2".

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  k2+k-42

The first term is,  k2  its coefficient is  1 .

The middle term is,  +k  its coefficient is  1 .

The last term, "the constant", is  -42

Step-1 : Multiply the coefficient of the first term by the constant   1 • -42 = -42

Step-2 : Find two factors of  -42  whose sum equals the coefficient of the middle term, which is   1 .

     -42    +    1    =    -41

     -21    +    2    =    -19

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     -6    +    7    =    1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  7

                    k2 - 6k + 7k - 42

Step-4 : Add up the first 2 terms, pulling out like factors :

                   k • (k-6)

             Add up the last 2 terms, pulling out common factors :

                   7 • (k-6)

Step-5 : Add up the four terms of step 4 :

                   (k+7)  •  (k-6)

            Which is the desired factorization

Final result :

 (k + 7) • (k - 6)

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