What is the completely factored form of 9x2 + 24x + 16? (3x + 8)(3x + 2) (3x + 4)(3x + 4) (9x + 8)(x + 2) (9x + 4)(x + 4)
Answers
Answer:
(3x+4)(3x+4) or (3x+4)2
Step-by-step explanation:
To factorize 9x2+ 24x +16, we first identify two factors in such a way that their product and sum is 144 and 24 respectively.
The factors are: 12 and 12.
The equation becomes: 9x2+12x+12x+16
=3x(3x+4)+ 4(3x+4)
= (3x+4)(3x+4) or (3x+4)2
Answer:
The complete factored form of 9x² + 24x + 16 is (3x+4)(3x+4)
Step-by-step explanation:
We can apply the product sum method to factor this equation
In an equation: ax² + bx + c The fisrt step is to find the pair of numbers that have the sum of the coefficient of term x (b) and the product of two numbers should be equal to the product of the coefficient of term x² and c (ac)
In this case, 9x² + 24x + 16 , the numbers should have a sum of of 24 and a product of 9×16 = 144
The two numbers are 12 and 12
Product of 12 × 12 = 144
And The sum of 12 + 12 = 24
The next step is to expand the equation by splitting the middle term using the two numbers:
9x² + 24x + 16
This will be 9x² + 12x + 12x 16
Next step is to factor the terms together
9x² + 12x + 12x 16 = (9x² + 12x) + (12x 16)
Simplify further by finding factors that can divide both terms in the bracket:
(9x² + 12x) + (12x 16)
3x( 3x + 4) + 4( 3x + 4)
(3x + 4)( 3x + 4)
Therefore 9x² + 24x + 16 factored completely = (3x + 4)(3x + 4)