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Factorise the expression $$3x^2$$ - 6x - 9.
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(3x + 1)(x + 3)
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(3x - 1)(x - 3)
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(3x - 1)(x + 3)
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(3x + 3)(x - 3)
That's Correct!
It's Wrong!
The expression $$3x^2$$ - 6x - 9 can be factorized as (3x + 3)(x - 3).
To factorize this expression, we look for the greatest common factor (GCF) among the terms. The GCF of $$3x^2$$, -6x, and -9 is 3.
Now, we factor out the common factor of 3 from the expression:
3($$x^2$$ - 2x - 3)
Next, we need to factorize the quadratic expression inside the parentheses. We look for two numbers whose product is -2x and whose sum is -3. In this case, the numbers are -3 and 1.
We rewrite the expression using these numbers:
3($$x^2$$ - 3x + 1x - 3)
Now, we group the terms and factorize further:
3[($$x^2$$ - 3x) + (1x - 3)]
3[x(x - 3) + 1(x - 3)]
We can now factor out a common factor of (x - 3) from both terms:
3(x - 3)(x + 1)
So, the factorized form of the expression $$3x^2$$ - 6x - 9 is (3x + 3)(x - 3).
