How do you factor completely 21x2+27x−30?

1 Answer
EZ as pi
May 1, 2016

Always look for a common factor in all the terms first.

Explanation:

3 is a factor of 21, 27 and 30. Taking it out gives

3(7x2+9x−10)

The quadratic trinomial inside the bracket seems not to factorise further, because there are no factor combinations of 7 and 10 which subtract to give 9. The only possibilities are 4, 9, 33 and 69. However, another approach would be to find the factors of 70, ( 7×10) and see if any of them differ by 9. Indeed 14 x 5 fits the bill.

Using the method of grouping gives the following:

3(7x2+9x−10) = 3(7x2+14x−5x−10)

(7x2+14x−5x−10)=(7x2+14x)+(−5x−10)

=7x(x+2)−5(x+2)=(x+2)(7x−5)

The final answer would be
3(7x2+9x−10)=3(x+2)(7x−5)

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