How do you factor #F(x) = x^3 + x^2 + 4x + 4?

Answer 1
# x^3 + x^2 + 4x + 4#
We can make groups of two to factorise this expression: #(x^3+ x^2) + (4x +4)#
#x^2# is common to both the terms in the first group, and #4# is common to both the terms in the second group
We can write the expression as : #x^2(x+1) +4(x+1)# #=color(green)((x^2 +4 )(x+1)#
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Answer 2

To factor the polynomial (F(x) = x^3 + x^2 + 4x + 4), you can first look for any rational roots using the rational root theorem. The possible rational roots are the factors of the constant term (4) divided by the factors of the leading coefficient (1). In this case, the possible rational roots are ±1, ±2, and ±4.

Upon testing these possible roots using synthetic division or polynomial long division, you'll find that (x = -2) is a root. Therefore, (x + 2) is a factor.

Performing synthetic division or polynomial long division with (x = -2) will yield the quotient (x^2 + 3). You can further factor (x^2 + 3) using the quadratic formula or other methods.

So, the factored form of (F(x)) is ((x + 2)(x^2 + 3)).

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Answer from HIX Tutor

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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