What is the factorization of 3x2 – 8x + 5?

Mathematics

1 answer:

Tanzania [10]3 years ago

7 0

Answer:

$(x-1)(3x-5)$

Step-by-step explanation:

Factorize means convert and expression into multiple factors.

You have to find to factor that multiplied equals the original equation. Firts of all you split the expression of square X into 3X an X, so you guarantee that when you multiply 3X by X, the result is 3X^2.

After doing that, you need to think in numbers that equals the middle term (8X) and the constant (5).

-1 and -5 guarantee you that the multiplication of them results into +5, so you start with those numbers. Then you have to find where to put them in order to find the -8X.

-5 x X = -5X

-1 x 3X = -3X

And adding those two expresion you find the -8X that you need!

Please try to solve it multiplying term by term and check the final equation.

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Determine the equation of g(x) that results from translating the function f(x)=x^2+9 upward 10 units.

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The simple/ common sense method:
The typical lay out of a quadratic equation is ax^2+bx+c
'c' represents where the line crosses the 'y' axis.
The equation is only translated in the 'y' (upwards/downwards) direction, therefore only the 'c' component of the equation is going to change.
A translation upwards of 10 units means that the line will cross the 'y' axis 10 places higher.
9+10=19,
therefore c=19.
The new equation is: y=x^2+19 

The most complicated/thorough method:
This is useful for when the graph is translated both along the 'y' axis and 'x' axis.
ax^2+bx+c
a=1, b=0, c=9
Find the vertex (the highest of lowest point) of f(x).
Use the -b/2a formula to find the 'x' coordinate of your vertex..
x= -0/2*1, your x coordinate is therefore 0.
substitute your x coordinate into your equation to find your y coordinate..
y= 0^2+0+9
y=9.
Your coordinates of your vertex f(x) are therefore (0,9) 
The translation of upward 10 units means that the y coordinate of the vertex will increase by 10. The coordinates of the vertex g(x) are therefore:
(0, 19) 
substitute your vertex's y coordinate into f(x)
19=x^2+c
19=0+c
c=19
therefore g(x)=x^2+19

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