How do you factor $2 x^{2} + 21 x + 10$ $2x^2 + 21x + 10$ ?

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How do you factor $2 x^{2} + 21 x + 10$ $2x^2 + 21x + 10$ ?

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Answer 1 · 2017-03-03T02:28:48

$(2 x + 1) (x + 10)$ $(2x+1)(x+10)$

Explanation:

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

$(2 x + p) (x + q) \equiv 2 x^{2} + 21 x + 10$ $(2x+p)(x+q) -= 2x^2+21x+10$

$2 x^{2} + (p + 2 q) x + p q \equiv 2 x^{2} + 21 x + 10$ $2x^2+(p+2q)x +pq -= 2x^2+21x+10$

$:. pxxq = 10$ 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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How do you factor $2 x^{2} + 21 x + 10$ $2x^2 + 21x + 10$ ?

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