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dlinn [17]
3 years ago
15

Can someone help me with this question?

Mathematics
1 answer:
Anarel [89]3 years ago
3 0

Answer:

yea

Step-by-step explanation:

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Answer:

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When using the inspection method, the number you would add to (and subtract from) the constant term of the numerator so the poly
krok68 [10]

Question:

Consider the expression \frac{x^2 + x -10}{x + 3}

When using the inspection method the number you would add to (and subtract from) the constant term of the numerator so the polynomial in the numerator will have (x + 3) as a factor is?

Answer:

The constant to add is 4

Step-by-step explanation:

Given

\frac{x^2 + x -10}{x + 3}

First, we need to get an expression that has x + 3 has its factor.

Represent this expression with: (x + 3)(x + k)

Expand

x^2 + 3x + kx + 3k

Group like terms

x^2 + (3 + k)x + 3k

Compare the above expression to: x^2 + x - 10

(3 + k)x = x

3k = -10

However, we only consider solving (3 + k)x = x for k

(3 + k)x = x

3 + k = 1

Subtract 3 from both sides

3 - 3 + k = 1 - 3

k = 1 - 3

k= -2

Substitute -2 for k in (x + 3)(x + k)

(x + 3)(x + k) = (x + 3)(x -2)

(x + 3)(x + k) = x^2 + 3x - 2x - 6

(x + 3)(x + k) = x^2 + x - 6

So, the expression that has a factor of x + 3 is x^2 + x - 6

To get the constant term to add/subtract, we have:

Constant = (x^2 + x - 6) - (x^2 + x - 10)

Open brackets

Constant = x^2 + x - 6 - x^2 - x + 10

Collect Like Terms

Constant = x^2 - x^2+ x   - x - 6+ 10

Constant =  - 6+ 10

Constant =  4

6 0
3 years ago
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