Question

Factorise the given expression by applying suitable identity : x2 + 10x + 16.
Also mention the identity used

Answer 1

Answer:

Mathematics NCERT Grade 8, Chapter 14: Factorisation- The chapter lays emphasis on the concept of how to express algebraic expressions as the products of their factors.

In the introduction part following topics are discussed:

1. Factors of natural numbers

2. Factors of algebraic expressions

An irreducible factor is a factor that cannot be expressed further as a product of factors.

The chapter gives detail about the following topics:

What is Factorisation?

When we factorise an algebraic expression, we write it as a product of factors. These factors may be numbers, algebraic variables or algebraic expressions.

After this, the Method of Common Factors is explained.

A systematic way of factorising an expression is the common factor method. It contains three steps.

Another section deals with a method called Factorising by regrouping terms. To practice questions based on this method, unsolved exercise 14.1 is given.

Now the question arises What is Regrouping?

Rearranging the expression allows us to form groups leading to factorisation. This is called regrouping.

Factorisation using identities and factors in the form of (x +a) (x+b) are explained.

Division of Algebraic Expressions: This section is divided into the following sub-sections:

a. Division of a monomial by another monomial

b. Division of a polynomial by a monomial

Division of algebraic expressions continued ( Polynomial ÷ Polynomial)

Division is the inverse of multiplication.

Can You Find the Error?

Important statements mentioned in the section:

Remember to make use of brackets, while substituting a negative value.

Remember, when you multiply the expression enclosed in a bracket by a constant (or a variable) outside, each term of the expression has to be multiplied by the constant (or the variable).

Coefficient 1 of a term is usually not shown. But while adding like terms, we include it in the sum.

Remember, when you square a monomial, the numerical coefficient and each factor has to be squared.

While dividing a polynomial by a monomial, we divide each term of the polynomial in the numerator by the monomial in the denominator.

All the topics are supplemented with examples and some short questions.

4 unsolved exercises are also given which contains questions in different patterns so that students can do enough practice of the same.

To make the content of the chapter- Factorisation more interesting some fun facts are also discussed in the chapter.

Recaptulisation of all important points is done at the end.

Answer 2

Answer:-

• x = -8 or x = -2

Question:-

• Factorise: x² + 10x + 16

step-by-step solution:-

⟹ x² + 10x + 16 = 0

⟹ x² + 8x + 2x + 16 = 0

⟹ x(x + 8) + 2(x + 8)

⟹ (x + 8) = 0 and (x + 2) = 0

⟹ x = - 8 and x = -2