How do you factor #y= 3x^3 + 9x^2 + 4x + 12# ?
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To factor the polynomial y = 3x^3 + 9x^2 + 4x + 12, you can use either synthetic division or polynomial long division to find one root, then use synthetic division or polynomial long division again to factor out the corresponding linear factor. This will leave you with a quadratic polynomial, which you can then factor using techniques like factoring by grouping, quadratic formula, or completing the square.
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To factor the polynomial ( y = 3x^3 + 9x^2 + 4x + 12 ), we can first look for any common factors among the terms. In this case, there isn't an obvious common factor among all terms.
Next, we can try to factor by grouping. To do this, we group the terms in pairs and look for common factors within each pair.
Grouping the terms: [ (3x^3 + 9x^2) + (4x + 12) ]
Factoring out the greatest common factor from each pair: [ 3x^2(x + 3) + 4(x + 3) ]
Now, we notice that both terms have a common factor of ( (x + 3) ).
Factoring out ( (x + 3) ): [ (x + 3)(3x^2 + 4) ]
So, the factored form of ( y = 3x^3 + 9x^2 + 4x + 12 ) is ( (x + 3)(3x^2 + 4) ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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