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What are the rules of factorization?
Do in this order. 1. All, find the gfc 2. Binomial, factor as difference of squares, sum of cubes, difference of cubes. 3. Trinomial, factor as a quadratic. 4. 4 or more terms, factor by grouping.
Factoring quadratic trinomials?
To factor quadratic trinomials, we find the two numbers which add to a certain number, and multiply to equal a certain number. Let me explain using the general form of a quadratic trinomial: ax2 + bx + c. If the quadratic trinomial is monic (coefficient on x2 is 1), then you simply find two numbers which add up to the coefficient of x (b) and multiply to give the constant (c). For example: The monic quadratic trinomial x2 - 5x + 6. Two numbers which add up to to give -5 and multiply to give 6 are -3 and -2. (-3 + -2 = -5; -3 x -2 = 6). Therefore the factors are (x - 3)(x-2). If the quadratic trinomial is non-monic (coefficient on x2 is greater than 1), then there's a slightly different method to go around solving them. I'll show this through the example: 2x2 + 5x - 3. We start off by changing the coefficient by multiplying it by the coefficient of x2 (in this case, 2). So the new coefficient will by -6. Then we split the equation into two factors (2x )(2x ) [They are blank because we don't know the numbers yet], and divide the factors by the coefficient of x2 (which is 2). So we have (2x )(2x ) divided by 2. Then we use the method of solving monic quadratics, and find two numbers which add to give +5, and multiply to give -6 (the new constant). In this case, the numbers are +6 and -1. (6 + -1 = 5; 6 x -1 = -6). So we put in our two numbers to get (2x + 6)(2x - 1) all over 2. Lastly, we make sure we factorise any of the factors [(2x + 6) can be factored as 2(x + 3)] to get 2(x+3)(2x-1) all over 2. And we just cancel out both twos on the numerator and denominator, and we are left with (x + 3)(2x - 1). One last example for non-monic quadratics: 4x2 + 7x - 2. First step: Multiply coefficient of x2 with constant to get new constant (4 x -2 = -8). Then we put the coefficient of x2 over the two factors we are yet to find. So we get (4x )(4x ) divided by 4. We then find the two numbers which add to give 7 and multiply to give -8, which are +8 and -1. We then have (4x + 8)(4x - 1) all over 4. Factorise whatever we can, to get 4(x+2)(4x-1) all over 4. Cancel out the 4s and we are left with (x + 2)(4x - 1).
In which situation would you factor out -1 from a trinomial?
You would factor out -1 (a) from a trinomial in an equation such as -a^2 +30a - 2a + 60 after the middle term has been separated. The final answer of this trinomial would then be (a-30) (a-30).
Factor Trinomial 3x2 plus 7x plus 2?
(3x+1)(x+2)
What is the factorization of this trinomial -3x2 10x-8?
-(3x - 4)(x - 2)
What are the factors of this quadratic trinomial 5x2-8x-4?
(5x+2) and (x-2)
How do you factor this quadratic trinomial 2x2 plus 4x2?
As written, that's 6x^2 which factors to 2 * 3 * x * x If you meant 2x^2 + 4x + 2, that's 2(x + 1)(x + 1)
What is the trinomial 3x squared plus 7x plus 2?
It is a quadratic expression and can be factored into: (3x+1)(x+2)
Can a trinomial have two identical factors?
Yes. Consider the trinomial x2 + 2x + 4. It can be factored as (x+2)(x+2), that is to say, it has two identical factors of (x+2).
How many terms are there in a quadratic trinomial?
Because the prefix "tri" means three, a trinomial has three terms: a squared variable, a normal variable, and a number without a variable. For example, 3x^2 + 5x +7 is a trinomial.
Can a trinomial be factored or is it a prime?
[ x3 + 3x2 + 2x ] is a trinomial. It's factors are [ x, (x + 1), (x + 2) ] .
What is the trinomial pf x2-12x plus 35?
If you mean x^2 -12x+35 then it is a quadratic expression which can be factored in the form of (x-7)(x-5)
Factor the trinomial negative x2 plus 7x plus 18?
-((x + 2)(x - 9))
Is this trinomial a trinomial square 49y2 - 35y plus 6?
Factors are (7y - 3)(7y - 2) so it's not a perfect square.
What is the factored quadratic trinomial of 2xsquared plus 4x plus 2?
It is: 2x2+4x+2 by dividing all terms by 2 it is then (x+1)(x+1) when factored
What is 6t squared plus 17t plus 12?
-4/3 and -3/2 To solve this, you must find the two factors that multiply to equal that trinomial (or use the quadratic equation) that trinomial can be rewritten as (3t + 4)(2t + 3) *check this first. It will prove that it is correct* Then, find the values of t when the equation equals 0 and you will see that the solutions are -4/3 and -3/2
How do you factor the trinomial completely 30x2-23x-14?
30x2-23x-14 = (6x-7)(5x+2) when factored with the help of the quadratic equation formula
