Question

a²+4a+3
factorise the algebaric expression​

Answer 1

=> a²+4a+3

=> a²+3a+a+3{using splitting middle term}

=> a(a+3)+1(a+3)

=> (a+1)(a+3)

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Answer 2

Trying to factor by splitting the middle term

1.1 Factoring a2-4a+3

The first term is, a2 its coefficient is 1 .

The middle term is, -4a its coefficient is -4 .

The last term, "the constant", is +3

Step-1 : Multiply the coefficient of the first term by the constant 1 • 3 = 3

Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -4 .

-3 + -1 = -4 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and -1

a2 - 3a - 1a - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

a • (a-3)

Add up the last 2 terms, pulling out common factors :

1 • (a-3)

Step-5 : Add up the four terms of step 4 :

(a-1) • (a-3)

Which is the desired factorization

Equation at the end of step

1

:

(a - 1) • (a - 3) = 0

Step

2

:

Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : a-1 = 0

Add 1 to both sides of the equation :

a = 1

Solving a Single Variable Equation:

2.3 Solve : a-3 = 0

Add 3 to both sides of the equation :

a = 3

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