How do you factor #2x^2 + 21x + 10#?

1 Answer
Alan N.
Mar 3, 2017

#(2x+1)(x+10)#

Explanation:

To factorise #2x^2+21x+10# we need to find two integers #p# and #q# such that:

#(2x+p)(x+q) -= 2x^2+21x+10#

#2x^2+(p+2q)x +pq -= 2x^2+21x+10#

#:. pxxq = 10# and # 2q+p=21#

Considering factors of 10: #1xx10, 2xx5#

By inspection we see that #p=1# and #q=10# satisfy the conditions.

Hence: #2x^2+21x+10 = (2x+1)(x+10)#

Please note: After some practice, for simple quadratic functions that can be expressed as two linear factors, as in this example, you should be able to factorise the the function by inspection - without the need to express the logic above in written form. However, you will still perform the equivalent logic mentally.

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