Question

What is the factored form of the expression?

21x^2 + 20x + 4

Answer 1

21x^2 + 20x + 4 = (3x + 2)(7x + 2).

Explanation:

Given the expression is 21x² +20x +4

We can solve the equation as follows:-

21x² +20x +4 = 0

Then a = 21, b = 20, c =4.

Using Quadratic formula, x = ( -b ± √(b² -4ac) )/2a

x = ( -20 ± √(400 - 4*21*4) )/2*21

x = ( -20 ± √(400 - 336) )/42

x = ( -20 ± √(64) )/42

x = ( -20 ± 8 )/42

x = -28/42 or x = -12/42

x = -2/3 or x = -2/7

(x + 2/3) = 0 or (x + 2/7) = 0

Now the factored form can be written as follows:-

(x + 2/3)(x + 2/7) = 0

(3x+2)(7x+2) = 0

Hence, the factored form is 21x^2 + 20x + 4 = (3x+2)(7x+2).