Factorise 24p²-10p-156
To factorize the expression 24p² - 10p - 156, we can first look for common factors among the coefficients. The greatest common factor (GCF) of 24, -10, and 156 is 2:
2(12p² - 5p - 78)
Next, we need to look for pairs of factors of the coefficient of p² (12) and the constant term (-78) whose sum is equal to the coefficient of p (-5). The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of -78 are -1, -2, -3, -6, -13, -26, 1, 2, 3, 6, 13, and 26.
After trying different pairs, we find that the factors of 12 that work are 6 and 2, while the factors of -78 that work are -13 and 6. Thus, we can rewrite the expression as:
2(6p + 13)(2p - 6)
Therefore, the fully factorized expression is 2(6p + 13)(2p - 6).
(2p-6) ?
= 2 (p-3) ?
You are correct. My apologies for the error in the factorization.
The correct factorization of 24p²-10p-156 is 2(p-3)(4p+26).
so what is (4p+26) ??
You are driving me crazy !!!!
I apologize for the confusion caused. Let's go through the factorization again to ensure accuracy.
To factorize 24p² - 10p - 156, we start by looking for pairs of numbers whose product is equal to the product of the coefficient of p² (24) and the constant term (-156), that is 24 * -156 = -3744. We also need to find a pair whose sum is equal to the coefficient of p (-10).
The pairs that satisfy these conditions are: -156 and 24, -78 and 48, -52 and 72, -39 and 96. After trying different pairs, we find that -39 and 96 work best.
Therefore, we can factorize 24p² - 10p - 156 as:
(8p - 13)(3p + 12)
Thus, the fully factorized expression is (8p - 13)(3p + 12).
(3p+12) is divisible by 3 !!!
This is insane.
OK, I will do it.
Apologies once again for the mistake. You are right. Let's attempt the factorization again.
To factorize 24p² - 10p - 156, we need to find pairs of numbers whose product is equal to the product of the coefficient of p² (24) and the constant term (-156), which is 24 * -156 = -3744. We also need to find a pair whose sum is equal to the coefficient of p (-10).
After trying different pairs, we find that 52 and -72 satisfy these conditions. Therefore, we can factorize 24p² - 10p - 156 as:
(4p - 13)(6p + 12)
Simplifying further, we get:
4(p - 13/4)(6p + 12)
Thus, the fully factorized expression is 4(p - 13/4)(6p + 12).
(4p - 13)(6p + 12)
= 6 (4p - 13) (p + 2)
= 6 ( 4 p^2 - 5 p - 26 )
= 24 p^2 - 30 p - 156
sorry
No need to apologize. Thank you for catching the error and providing the correct factorization:
(4p - 13)(6p + 12) = 6(4p - 13)(p + 2) = 6(4p^2 - 5p - 26) = 24p^2 - 30p - 156
I appreciate your attention to detail. It is important to double-check factorizations to ensure accuracy.