Factorise
4x^2-7x+3=
and
6x^2+10x-5=
Thanks
Method would be good-as I am stuck.
1. (4x-3)(x-1)
2. Use the quadratic formula which you can find on youtube.
Thanks,can you tell me the answer to the second one.
Ans also I got this far for the first part's method
4x^2-7x+3=
4x^2-3x-4x+3=
x(4x-3)-1(4x+3)
but there is nothing similar-how did you get (4x-3) for both of them.
Can someone please help-I need to do this today.
All I need is the method and answer.
4x^2 - 7x + 3.
Use the AC Method:
A * C = 4 * 3 = 12 = -3 * -4,
4X^2 + (-3X + -4X) +3,
Group the 4 terms into 2 factorable pairs:
4x^2 -4x) + (-3x + 3),
Factor 4x from the 1st pair & -3 from
the 2nd pair:
4x(x - 1) + -3(x - 1),
Factor (x - 1) from each term:
(x - 1) (4x - 3).
To factorize the quadratic expressions 4x^2 - 7x + 3 and 6x^2 + 10x - 5, we can use the method of quadratic factorization. Here's how you can do it step by step:
Factorizing 4x^2 - 7x + 3:
Step 1: Multiply the coefficient of the leading term by the constant term: 4 * 3 = 12.
Step 2: Find two numbers whose product is equal to 12 and whose sum is equal to the coefficient of the linear term (-7). In this case, the numbers are -4 and -3 because (-4) * (-3) = 12, and (-4) + (-3) = -7.
Step 3: Rewrite the middle term (-7x) using the two numbers you found in the previous step. So, replace -7x with -4x - 3x.
4x^2 - 4x - 3x + 3
Step 4: Group the terms in pairs and factor out the greatest common factor from each pair.
4x(x - 1) - 3(x - 1)
Step 5: Notice that (x - 1) is a common factor in both terms. Factor it out.
(x - 1)(4x - 3)
Therefore, 4x^2 - 7x + 3 can be factorized as (x - 1)(4x - 3).
Factorizing 6x^2 + 10x - 5:
Step 1: Multiply the coefficient of the leading term by the constant term: 6 * (-5) = -30.
Step 2: Find two numbers whose product is equal to -30 and whose sum is equal to the coefficient of the linear term (10). In this case, the numbers are 15 and -2 because 15 * (-2) = -30, and 15 + (-2) = 10.
Step 3: Rewrite the middle term (10x) using the two numbers you found in the previous step. So, replace 10x with 15x - 2x.
6x^2 + 15x - 2x - 5
Step 4: Group the terms in pairs and factor out the greatest common factor from each pair.
3x(2x + 5) - 1(2x + 5)
Step 5: Notice that (2x + 5) is a common factor in both terms. Factor it out.
(3x - 1)(2x + 5)
Therefore, 6x^2 + 10x - 5 can be factorized as (3x - 1)(2x + 5).