Question

How to factor binomials?

Answer 1

Binomials are two-term expressions connected with a plus sign or minus sign, such as {ax+b}ax+b. The first term will always include a variable, while the second term may or may not. 1st: factoring is when you break a large number down into it's simplest divisible parts. Each one of these parts is called a "factor." So, for example, the number 6 can be evenly divided by four different numbers. 2nd: A binomial is simply the addition or subtraction of two numbers, at least one of which contains a variable. Sometimes these variables have exponents, like x^5 or 5y^6. 3rd :When first factoring binomials, it can help to reorder equations with ascending variable terms. This means you find the highest possible number that both parts of the binomial are divisible by. If you're struggling, simply factor both numbers on their own, then see what the highest matching number is.

Explanation:

Answer 2

Let us consider a binomial expression

For example,

x²+(a+b)x+ab

x²+ax+bx+ab

x(x+a)+b(x+a)

(x+a)(x+b)

Therefore, the above binomial expression has two factors (x+a) and (x+b).

Now by numericals

Consider, x²+12x+35

`{x}^(2) + 12x + 35\\Factors\:of\: 35\: is\: 5\: and\:7 \\ {x}^(2) + 5x + 7x + 35 \\ x(x + 5) +7(x + 5) \\ (x + 5)(x + 7)`

Here, (x+5) and (x+7) are the factors of the binomial expression x²+12x+35.