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What is the factored form of the following expressions?

d^2-19d+90

a. (d-9)(d+10)
b. (d-9)(d-10)
c. (d+9)(d-10)
d. (d+9)(d+10)

Respuesta :

Answer: The answer is (b) [tex](b-9)(b-10).[/tex]


Step-by-step explanation: Given equation to be factored is

[tex]d^2-19x+90.[/tex]

Since the given expression is quadratic, so we can factor it into two linear factors, by using the following factorisation rule.

[tex]x^2-(a+b)x+ab=(x-a)(x-b).[/tex]

So, we will solve the given equation in the following way.

[tex]x^2-19x+90\\\\=x^2-(9+10)x+90\\\\=x^2-9x-10x+90\\\\=x(x-9)-10(x-9)\\\\=(x-9)(x-10).[/tex]

Thus, the correct option is (b).



JonHenderson55

Answer:  The correct answer is:   [B]:

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                       →     [B]:   " (d − 9)(d − 10) " .

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Step-by-step explanation:

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To factor the following expression:

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           →   "  d² −  19d + 90 " ;

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What factors of:  " ⁺90 " ;  add up to: " -19 " ?

   From " ⁺90 " ; we can factor out a "10" ;

    Try "10" and "9" ;   →  10 + 9 =? -19?  ;  →  No!  { "10 + 9 = ⁺ 19" .}.

    Try "-10 and "-9" ;  →  -10 + (-9) =?  -19? ; →  -10 − 9 =?  - 19?  Yes!

So, the we have:  "-10" and "-9" ;

The expression:  " d² −  19d + 90 " ;

  →  factors into:  " (d − 10)(d − 9) " ;  which is the same as:

           ↔  " (d − 9)(d − 10) " ;

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           →  which corresponds to:

           →  Answer choice:  [B]: " (d − 9)(d − 10) " .

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Hope this helps!

     Best wishes to you!

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