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How do you factor: #2x^2 + 7x +3#?

Answer 1

Julia Adams

#(x+3)(2x+1)#

#"using the a-c method of factorising"#

#"the factors of "2xx3=6# #"which sum to + 7 are + 6 and + 1"#

#"split the middle term using these factors"#

#rArr2x^2+6x+x+3larrcolor(blue)"factor by grouping"#

#=color(red)(2x)(x+3)color(red)(+1)(x+3)#

#"take out the common factor "(x+3)#

#=(x+3)(color(red)(2x+1))#

#rArr2x^2+7x+3=(x+3)(2x+1)#

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Answer 2

Eva Abramson

To factor the quadratic expression 2x^2 + 7x + 3, you need to find two numbers that multiply to give you the product of the coefficient of x^2 term (2) multiplied by the constant term (3), and add up to the coefficient of the x term (7).

The product of 2 and 3 is 6. The pairs of numbers that multiply to 6 are (1,6) and (-1,-6). Among these pairs, the pair that adds up to 7 is (1,6).

Now, split the middle term using these numbers:

2x^2 + 6x + x + 3

Now, factor by grouping:

2x(x + 3) + 1(x + 3)

Now, you can see that (x + 3) is common:

(x + 3)(2x + 1)

So, the factored form of 2x^2 + 7x + 3 is:

(x + 3)(2x + 1)

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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.