Question

शो दैट द फैक्टर्स ऑफ़ एक्स स्क्वायर प्लस एक्स माइनस 4 एक्स माइनस 3 एंड एक्स प्लस 4 ​

Answer 1

Answer:

Step-by-step explanation:

(x+2)(x−3)=x2+(−3+2)x−6=x2−x−6

We have also shown how we can factorize a polynomial by finding a common factor among all terms. If we look at the example above we see a trinomial that does not have a common factor, but it could still be factorized by reversing the process.

We can factorize all trinomials of the form

x2+bx+c

by making them into a product of two binomials

x2+bx+c=(x+m)(x+n)

where

m+n=bandm⋅n=c

If we use the trinomial from the example above:

x2−x−6

We know that we have to find two factors of -6 whose sum is -1

It's a good idea to make a table to test all combinations

Factorof−6−1,61,−62,−3−2,3Sumoffactors5−5−11

We see that if m = 2 and n = -3 than we will get the correct factors.

x2−x−6=x2+(2−3)x+(2⋅−3)=(x+2)(x−3)

There is a pattern that could be good to know so that you don't have to try all different combinations of values for m and n.

If both b and c are positive then both m and n are positive.

If b is negative whereas c is positive then both m and n are negative

If c is negative then m and n do not have the same sign.

In the previous section we showed you some special patterns that could help you when you're simplifying polynomials. The same patterns can be used to help you when you're factorizing polynomials.

The difference of two squares pattern is the opposite to the sum and difference pattern

x2−y2=(x+y)(x−y)

If we use this as an example:

x2−25=x2−52=(x+5)(x−5)

The perfect square trinomial pattern is the opposite of the square of a binomial pattern

x2+2xy+y2=(x+y)2

x2−2xy+y2=(x−y)2

An example of this would be

x2+14x+49=x2+(2⋅x⋅7)+72=(x+7)2