factorise 2x²+5x/2+1/2
Answers
Answer:
Instead of using guess and check to factor this degree 2 polynomial expression, there is a neat trick that can be applied:
2x^2 −5x +2
Step 1: Multiply degree 2’s coefficient by the term with degree 0 (the constant term). Omit this coefficient from the expression - we will come back to this coefficient later so don't worry!
x^2 −5x +4
Step 2: (Factor this new, transformed expression)
(x−4)(x−1)
Step 3: Now, divide each constant term within each binomial by the original leading coefficient. In this case, it was 2.
(x − 4/2)(x − 1/2)
Step 4: In the first binomial, we are left with a constant term that is an integer- this is fine. However, for the second binomial, we must move the 2 to the front of the degree 1 term since the constant term is a fraction after division by the coefficient of 2.
(x−2)(2x−1)
Note: This trick can be very handy when factoring more complicated polynomials of degree 2. However, it may not be necessary for simpler expressions.
Answer:
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