Previously we have discussed about is pi a rational number ? and now we are going to learn about factorizing the trinomial which falls under karnataka education board. A trinomial is of the form: ax2+ bx + c. To proceed further with factoring of a trinomial we are going to understand it with the help of an example. The factoring of a trinomial can be done by following certain steps or you can take help of online tutors.
Suppose we have a trinomial x2 + 4x +3. We split the middle term such that on multiplying the first and the last term we get 3x2 and on addition we get 4x.
We get x2 + 3 x + x +3. Now we take the first two terms and the last two terms and take common out of them. We get x(x+ 3) +1(x+3). Note that both the common terms in bracket should be the same. We get (x+3) and (x+1) as factors on factoring trinomials.(Know more about Trinomial in broad manner, here,)
Thus we can see that factoring a trinomial can be easily understood with the help of the above mentioned example. In similar way other types of trinomials can also be solved irrespective of the signs.
Let’s take another example. Suppose we have a trinomial of the form x2 -6x +9. To solve this trinomial we again take the product of the first and last terms on multiplication and get 9x2. Now we split the middle term such that we get 9x2 on multiplication and -6x on addition as follows: x2 – 3x -3x + 9. Now we take first two terms and last two terms and take common factors .We get x(x-3) – 3(x-3). So the factors are (x-3) and (x-3). Thus we have learnt about solving a trinomial with the method of factorization and if anyone want to know about Perfect Square Trinomials then they can refer to Internet and text books for understanding it more precisely. Read more maths topics of different grades such as Simplifying rational expressions in the next session here.
Suppose we have a trinomial x2 + 4x +3. We split the middle term such that on multiplying the first and the last term we get 3x2 and on addition we get 4x.
We get x2 + 3 x + x +3. Now we take the first two terms and the last two terms and take common out of them. We get x(x+ 3) +1(x+3). Note that both the common terms in bracket should be the same. We get (x+3) and (x+1) as factors on factoring trinomials.(Know more about Trinomial in broad manner, here,)
Thus we can see that factoring a trinomial can be easily understood with the help of the above mentioned example. In similar way other types of trinomials can also be solved irrespective of the signs.
Let’s take another example. Suppose we have a trinomial of the form x2 -6x +9. To solve this trinomial we again take the product of the first and last terms on multiplication and get 9x2. Now we split the middle term such that we get 9x2 on multiplication and -6x on addition as follows: x2 – 3x -3x + 9. Now we take first two terms and last two terms and take common factors .We get x(x-3) – 3(x-3). So the factors are (x-3) and (x-3). Thus we have learnt about solving a trinomial with the method of factorization and if anyone want to know about Perfect Square Trinomials then they can refer to Internet and text books for understanding it more precisely. Read more maths topics of different grades such as Simplifying rational expressions in the next session here.
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