Please help Factorise fully 1. X^2-5x-14 2. Ab^2+3b 3. A^3-8a^2+15a
14 = 7*2 always :)
(x-7)(x+2)
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b(Ab+3)
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suspect you mean
a^3-8a^2+15a
which is
a (a^2-8a+15)
but we know 15 = 3 * 5 and 3+5=8 :)
so
a (a-5)(a-3)
Sure! I can help you factorize these expressions.
1. To factorize the expression x^2 - 5x - 14, we need to find two numbers that add up to -5 (the coefficient of x) and multiply to -14 (the constant term). Let's break down the steps:
Multiply the coefficient of x^2 (which is 1) by the constant term (-14). We get -14.
Now, we need to find two factors of -14 that add up to -5.
The numbers -7 and 2 meet this requirement because -7 + 2 = -5 and -7 * 2 = -14.
Therefore, we can write the expression as:
(x - 7)(x + 2)
So, the fully factorized form of x^2 - 5x - 14 is (x - 7)(x + 2).
2. To factorize the expression ab^2 + 3b, we can factor out the common factor b from both terms:
b is the greatest common factor in this case.
So, we can factorize the expression as:
b(a * b + 3)
The fully factorized form of ab^2 + 3b is b(a * b + 3).
3. To factorize the expression a^3 - 8a^2 + 15a, we can factor out the greatest common factor, which is a:
So, we can factorize the expression as:
a(a^2 - 8a + 15)
Now, we need to factorize the quadratic expression a^2 - 8a + 15. To do this, we need to find two numbers that add up to -8 and multiply to 15.
The numbers -3 and -5 meet this requirement because -3 + (-5) = -8 and -3 * (-5) = 15.
Therefore, we can write the quadratic expression as:
a(a - 3)(a - 5)
So, the fully factorized form of a^3 - 8a^2 + 15a is a(a - 3)(a - 5).
I hope this helps! Let me know if you have any further questions.