The product of 6 and the square of a number is increased by 5 times the number, the result is 4.
Let's represent the number as y
The algebraic expression for the above sentence is written as:
(6 x y²) + 5y = 4
6y² + 5y = 4
The above expression can also be written as:
6y² + 5y - 4 = 0
We have to factorize the above expression to solve for y
6y² - 3y + 8y - 4 = 0
3y (2y - 1) + 4(2y + 1) = 0
(3y + 4)(2y - 1) = 0
Solving for y
3y + 4 = 0
3y = -4
Divide both sides by 3
3y/3 = -4/3
y = [tex]\frac{-4}{3}[/tex]
or
2y - 1 = 0
2y = 1
Divide both sides by 2
2y/2 = 1/2
y = [tex]\frac{1}{2}[/tex]
Therefore, the values that the number could be is given as [tex]\frac{-4}{3} or \frac{1}{2}[/tex]
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