Question

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)

Answer 1

Answer: The correct answer is: [B]:

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→ [B]: " (d − 9)(d − 10) " .

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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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Answer 2

Answer: The answer is (b)
`(b-9)(b-10).`

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

`d^2-19x+90.`

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

`x^2-(a+b)x+ab=(x-a)(x-b).`

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

`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).`

Thus, the correct option is (b).