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Factoring a hard trinomial

2,278 views · Published 1 May 2012 · 4:27 · Indexed 28 October 2026

Channel: Brian McLogan · 2012 · Education

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Learn how to factor higher order trinomials. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. To factor an algebraic expression means to break it up into expressions that can be multiplied together to get the original expression.

Given a higher order trinomials with consecutive positive integer exponents or in such a way that the exponent of the middle term is half the sum of the exponents of the first and last term, then we can try factoring the polynomial by determining two terms whose product is the product of the first and the last terms and whose sum is the middle term of the original polynomial. 

We can now replace the middle term by the two obtained terms and then complete the factoring by grouping.
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