Factorise
20x^2 -x -1
hmmm. can you factor x^2-x-20?
which two factors of 20 differ by 1?
To factorize the quadratic expression 20x^2 - x - 1, we are looking for two binomial expressions that, when multiplied, will give us this expression.
Step 1: Multiply the coefficient of the x^2 term (20) by the constant term (-1). 20 * (-1) = -20.
Step 2: Find two numbers that multiply to give -20 (the result from step 1) and add up to the coefficient of the x term (-1). In this case, the numbers are -5 and 4, since -5 * 4 = -20 and -5 + 4 = -1.
Step 3: Rewrite the middle term (-x) using the two numbers found in step 2: -5x + 4x.
Now, we can rewrite the original expression as follows:
20x^2 - x - 1
= 20x^2 - 5x + 4x - 1
Step 4: Group the terms and factor by grouping:
(20x^2 - 5x) + (4x - 1)
= 5x(4x - 1) + 1(4x - 1)
Step 5: Notice that we have a common binomial factor, (4x - 1). Factor out this binomial:
(4x - 1)(5x + 1)
So, the factored form of 20x^2 - x - 1 is (4x - 1)(5x + 1).