Factor 3x^2 - 4x + 1
these aswell
x^2 - 16
x^2– 6x + 9
a^2- 2ab + b^ 2
x^2+ 6x -16
x^2– 6x -16
(3x +a )(x +a )
3a +a= -4, so what is a?
To factor the given expressions, we need to find two binomial factors that, when multiplied together, give us the original expression.
Let's start with the first expression: 3x^2 - 4x + 1
To factor this trinomial, we need to find two binomials in the form (ax + b)(cx + d)
Step 1: Multiply the coefficient of the x^2 term (3) by the constant term (1).
3 * 1 = 3
Step 2: Find two numbers whose product is equal to 3 and whose sum is equal to the coefficient of the x term (-4). In this case, the numbers are -3 and -1.
-3 * -1 = 3
-3 + (-1) = -4
Step 3: Rewrite the middle term (-4x) using the two numbers found in step 2.
3x^2 - 3x - x + 1
Step 4: Group the terms and factor them by grouping.
(3x^2 - 3x) + (-x + 1)
3x(x - 1) - 1(x - 1)
Step 5: Factor out the common binomial (x - 1).
(x - 1)(3x - 1)
Now, moving on to the next expressions:
1. x^2 - 16
This can be factored as (x + 4)(x - 4).
2. x^2 - 6x + 9
This is a perfect square trinomial and can be factored as (x - 3)^2.
3. a^2 - 2ab + b^2
This is a perfect square trinomial and can be factored as (a - b)^2.
4. x^2 + 6x - 16
This can be factored as (x + 8)(x - 2).
5. x^2 - 6x - 16
This can be factored as (x - 8)(x + 2).
Finally, you mentioned the equation 3a + a = -4. To find the value of a, we can combine like terms on the left side:
4a = -4
Divide both sides by 4:
a = -1
Therefore, a is equal to -1.