x²+10x+24
(x+4)(x+6)
To factorize the expression x²+10x+24, we need to find two numbers that multiply to give 24 and add to give 10.
We can start by listing all of the factors of 24:
1 x 24 = 24
2 x 12 = 24
3 x 8 = 24
4 x 6 = 24
The pair of factors that add up to 10 is 4 and 6.
So, we can write x²+10x+24 as (x+4)(x+6).
To check if this is correct, we can use the distributive property:
(x+4)(x+6) = x(x+6) + 4(x+6) = x² + 6x + 4x + 24 = x²+10x+24
Therefore, our factorization is correct.
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