how to factorise a quadratic polynomial with grouping method

Question

please tell me a gud way

Answer 1

First, look for a common factor in the terms. For example:

5x²-10x-15=0 has the common factor 5 so we can write:

5(x²-2x-3)=0.

So we need to look next at x²-2x-3. The x term is the negative sum of the zeroes and the constant is their product. So -3 has only two pairs of factors (-3,1) or (3,-1). The sum of the factors is either -2 or 2, so the corresponding negative sums are -(-2)=2 or -2. The x term is -2x so the zeroes must be 3 and -1.

5(x²-2x-3)=5(x-3)(x+1) is the factorisation. x²-2x-3 could be written x²-3x+x-3=x(x-3)+(x-3). This is how the quadratic can use grouping, because we have the common factor x-3, which means we can write the factors (x+1)(x-3).