How do you factor r^2 + (6/4r) + (9/16)?

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How do you factor r^2 + (6/4r) + (9/16)?

How fractions get factored?

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Answer 1 · 2018-05-15T23:36:43

${(r + \frac{3}{4})}^{2}$ $(r+3/4)^2$

Explanation:

Start by finding two numbers (let's call them $a$ $a$ and $b$ $b$ ) such that:

$a \cdot b = \frac{9}{16}$ $a*b = 9/16$
$a + b = \frac{6}{4}$ $a+b=6/4$

This requires a bit of guess-and-checking but we can propose that a and b are equal and check if it works:

$a \cdot a = \frac{9}{16}$ $a*a=9/16$
gives $a = \frac{3}{4} and b = \frac{3}{4}$ $a=3/4 and b = 3/4$ which just happens to satisfy the second requirement as well
$\frac{3}{4} + \frac{3}{4} = \frac{6}{4}$ $3/4 + 3/4=6/4$
making the factored form equal to ${(r + \frac{3}{4})}^{2}$ $(r+3/4)^2$

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How do you factor r^2 + (6/4r) + (9/16)?

How fractions get factored?

1 Answer

Explanation:

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