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4 votes
Factorise : x² + 5x + 6 .​

User Shaobo Zi
by
7.5k points

2 Answers

5 votes

Answer: (x+2)(x+3)

Explanation:

To factorize an equation, you need to find the factors of the leading coefficient, and the constant. In this case, the leading coefficient is 1 (1x²) and the constant is 6. Let's find the factors of both:

Factors of 1 = 1

Factors of 6 = ±1, ±2, ±3, ±6 (± is positive and negative)

Now, we need to figure our the combination of factors that will add up to 5. There are only two that would work.

-1 and 6

2 and 3

Out of these, only 1 multiplies to 6, which is 2 and 3. (-1·6=-6)

Now we have our numbers (1, 1, 2, 3).

From there lets put them into factored form:

(1x+3)(1x+2) or (1x+2)(1x+3).

Now we can take away the 1's to simplify. And the final answer is (x+3)(x+2)

To check, we need to multiply:

x·x=x²

3·x=3x

x·2=2x

3·2=6

We now have the equation, x²+2x+3x+6

Now combine the like terms and we will get our origanal equation, x²+5x+6

Hope that helped a lot.

:)

User Mohit Gangrade
by
7.9k points
3 votes

Answer:

(x + 2) (x + 3)

Explanation:

x² + 5x + 6

x² + 3x + 2x + 6

x(x + 3) + 2(x + 3)

(x + 2) (x + 3)

User Catiana
by
7.7k points

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