Question

(Class - 9)Factorise x²+12x+20​

Answer 1

Answer:

Factoring x2-12x+20

The first term is, x2 its coefficient is 1 .

The middle term is, -12x its coefficient is -12 .

The last term, "the constant", is +20

Step-1 : Multiply the coefficient of the first term by the constant 1 • 20 = 20

Step-2 : Find two factors of 20 whose sum equals the coefficient of the middle term, which is -12 .

-20 + -1 = -21

-10 + -2 = -12 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and -2

x2 - 10x - 2x - 20

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

x • (x-10)

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

2 • (x-10)

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

(x-2) • (x-10)

Which is the desired factorization

Equation at the end of step

1

:

(x - 2) • (x - 10) = 0

STEP

2

:

Theory - Roots of a product

Answer 2

Answer:

Factors of x² + 12x + 20 are (x + 10) (x + 2).

Step-by-step explanation:

Given :-

• x² + 12x + 20

To find :-

Factors.

Solution :-

Prime factorization :

2 | 20

2 | 10

5 | 5

1  | 1

∴ 20 = 2 × 2 × 5 = 10 × 2

Splitting middle term method :

x² + 12x + 20

10 × 2 = 20 & 10 + 2 = 12

x² + 10x + 2x + 20  

x(x + 10) + 2(x + 10)

(x + 10) (x + 2)

Hence,

Factors of x² + 12x + 20 are (x + 10) (x +2).