How can I Factor X^2+x-2

Mathematics

1 answer:

AlekseyPX2 years ago

5 0

The factored form of the given expression x² + x - 2 is ( x - 1 )( x + 2 ).

<h3>What is the factored form of the given expression?</h3>

Given the expression;

x² + x - 2

Consider the standard form ax² + bx + c compared to the given expression;

a = 1
b = 1
c = -2

Now, we find a pair of integers whose product gives the value of c which is -2 and whose sum gives the value of b which is 1.

The integers are -1 and +2.

Check

-1 × 2 = -2

-1 + 2 = 1

Now, we write the factored form using these integers.

( x - 1 )( x + 2 )

Therefore, the factored form of the given expression x² + x - 2 is ( x - 1 )( x + 2 ).

Learn more about factorization here: brainly.com/question/3658321

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Paul is two years younger than Patricia. Daniel is 25% older than Patricia. Ten years ago, Daniel was 50% older than Patricia. H

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We have 3 people: Paul, Daniel and Patricia. Let each name denote that person’s current age in years. Remember that % is the symbol for 1/100.

PAUL: (#A) Paul = Patricia – 2
DANIEL:
(#B) Daniel = 125% * Patricia = 125 * (1/100) * Patricia = 1.25 * Patricia
(#C) Ten years ago, Daniel’s age at that time would have been Daniel’s current age – 10. IE “Daniel – 10”.
Ten years ago, Patricia’s age at that time would have been Patricia’s current age – 10. IE “Patricia – 10”.
Ten years ago, Daniel’s age at that time (IE Daniel – 10) was 50% greater than Patricia’s age at the time (Patricia – 10).
IE

Daniel – 10 = 150% * (Patricia – 10)
Daniel – 10 = 1.50 * (Patricia – 10)
Daniel – 10 = 1.50 * Patricia – 1.50 * 10
Daniel – 10 = 1.50 * Patricia – 15
Daniel = 1.50 * Patricia – 15 + 10
Daniel = 1.50 * Patricia – 5

So now we have 3 equations in 3 unknowns:
(A) Paul = Patricia – 2
(B) Daniel = 1.25 * Patricia
(C) Daniel = 1.50 * Patricia – 5

Solve equations B & C simultaneously
1.25 * Patricia = 1.50 * Patricia – 5
1.25 * Patricia – 1.50 * Patricia = – 5
– 0.25 * Patricia = – 5
Patricia = (– 5) / (– 0.25)
Patricia = + 20

So now we can write the 3 people’s ages:
(a) Patricia = 20
(b) Paul = Patricia – 2 = 20 – 2 = 18
(c) Daniel = 1.25 * Patricia = 1.25 * 20 = 25

<span>Finally, we check our solution against the original question. </span>
Paul is two years younger than Patricia. ……… 20 – 2 = 18 ✔
Daniel is 25% older than Patricia. ……… 25 = 125% * 20 ✔
Ten years ago, Daniel was 50% older than Patricia. 25 – 10 = 150% (20– 10) ✔

Hope that helped :)

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