4x^2 - 13x + 3
How do you break this into groups?
So far I'm having trouble with this type of concept.
Please explain it, thanks!
4x^2 - 12x - 1x + 3
... 4 is to 12 as 1 is to 3
4x (x - 3) - 1 (x - 3)
(4x - 1) (x - 3)
try googling this
... "factoring polynomials british method"
To break the quadratic expression into groups, we need to identify two numbers that multiply together to give us the product of the coefficient of the squared term (in this case, 4) and the constant (in this case, 3). In this example, the product of 4 and 3 is 12.
Next, we need to find two numbers, when added or subtracted together, give us the coefficient of the middle term (in this case, -13). In other words, we need to find two numbers that add up to -13 or subtract to -13.
To find these two numbers, we need to factorize 12. The factors of 12 are 1, 2, 3, 4, 6, and 12. We then check each pair of factors to see if they add or subtract to -13.
In this case, the numbers -4 and -9 add up to -13, so we will break the middle term -13x into -4x and -9x.
Now we can rewrite the original expression:
4x^2 - 4x - 9x + 3
We can now group the terms:
(4x^2 - 4x) + (-9x + 3)
Now we can factor out the greatest common factor (GCF) from each group:
4x(x - 1) - 3(3x - 1)
So, the quadratic expression 4x^2 - 13x + 3 can be broken into groups as (4x(x - 1) - 3(3x - 1)).