Math  /  Algebra

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Write two numbers that multiply to the value on top and add to the value on bottom.

Studdy Solution

STEP 1

What is this asking? We need to find two numbers that multiply to -16 and add up to -6. Watch out! Don't forget about negative numbers!
One of our numbers will have to be positive, and the other will have to be negative to get a negative product.

STEP 2

1. Find Factor Pairs
2. Check the Sums

STEP 3

Let's **start** by finding all the pairs of numbers that multiply to -16.
Since we're looking for a negative product, one number must be positive and the other negative.
Let's **think**!
We have (1)16=16(-1) \cdot 16 = -16, 1(16)=161 \cdot (-16) = -16, (2)8=16(-2) \cdot 8 = -16, 2(8)=162 \cdot (-8) = -16, and (4)4=16(-4) \cdot 4 = -16.
That covers all the possibilities!

STEP 4

Now, let's **check** which of these pairs add up to -6.
We're looking for a negative sum, so the negative number must be larger in magnitude than the positive number.

STEP 5

Let's **add** them up! (1)+16=15(-1) + 16 = 15.
Nope, not this one. 1+(16)=151 + (-16) = -15.
Still not it! (2)+8=6(-2) + 8 = 6.
So close, but we need -6, not 6. 2+(8)=62 + (-8) = -6.
Bingo! We found our **winning pair**: 2 and -8.

STEP 6

Our two numbers are 2 and -8.
They multiply to (2)(8)=16(2) \cdot (-8) = -16 and add to 2+(8)=62 + (-8) = -6.
Perfect!

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