How do you factor #2x^3 + 10x^2 + 4x + 20#?

Answer 1

#2(x+5)(x^2 + 2)#

There are 4 terms and there is a common factor of 2 in all of them. We can also group the term in pairs to create other common factors:

#(2x^3 + 10x^2) + (4x + 20)#

=#2x^2(x +5) + 4(x +5)" "# We now have a common bracket and a common factor of 2

=#2(x+5)(x^2 + 2)#

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Answer 2

Hazel Anglin

To factor the expression (2x^3 + 10x^2 + 4x + 20), you can first factor out the greatest common factor, which is (2):

[2(x^3 + 5x^2 + 2x + 10)]

Next, you can attempt to factor the expression within the parentheses using various methods such as grouping, trial and error, or synthetic division to find any rational roots. If any rational roots are found, you can use polynomial division to factor the expression further. If no rational roots are found, the expression may not factor easily using rational coefficients.

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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.