# How do you factor #3p^2 + 2p - 16 = 0#?

Find p' and q' by composing factor pairs of a.c = -48 -> (-4, 12)(-6, 8). This sum is 2 = b. Then p' = -6 and q' = 8.

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To factor the quadratic equation (3p^2 + 2p - 16 = 0), we can use the quadratic formula or factor by grouping. In this case, factoring by grouping is the most straightforward method. We split the middle term (2p) into two terms whose product is equal to the product of the leading coefficient (3) and the constant term (-16), which is (-48). We then factor by grouping the four terms and look for common factors.

Splitting (2p) into (8p) and (-6p), we rewrite the equation as (3p^2 + 8p - 6p - 16 = 0).

Now, we group the terms: ((3p^2 + 8p) + (-6p - 16) = 0).

Factoring out the greatest common factor from each pair: (p(3p + 8) - 2(3p + 8) = 0).

We notice that both pairs have a common factor of (3p + 8), so we can factor it out: ((3p + 8)(p - 2) = 0).

Setting each factor equal to zero and solving for (p), we get (3p + 8 = 0) and (p - 2 = 0).

Solving these equations, we find (p = -\frac{8}{3}) and (p = 2).

Therefore, the factored form of the quadratic equation (3p^2 + 2p - 16 = 0) is ((3p + 8)(p - 2) = 0).

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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.

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