Without actual division, show that (2x^2 − 7x−15) is a factor of (2x^3– 9x^2 –8x + 15)
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Let assume that
and
So,
can be further factorized using splitting of middle terms.
Now, in order to show that g(x) is a factor of f(x), we have to show that x - 5 and 2x + 3 is a factor of f(x), using factor theorem.
Factor theorem states that if a polynomial f(x) of degree greater than or equals to 1, then x - a is a factor of f(x) if f(a) = 0.
So, Consider,
Now, Consider
From equation (1) and (2), we concluded that
Basic Concept Used :-
Splitting of middle terms :-
In order to factorize ax² + bx + c we have to find numbers m and n such that m + n = b and mn = ac.
After finding m and n, we split the middle term i.e bx in the quadratic equation as mx + nx and get the required factors by grouping the terms.
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