Question

15(x-3)^2+5(x-3)-20÷5x-20
​

Answer 1

$\bf [15( {x - 3)}^{2} + 5(x - 3) - 20] \div (5x - 20 )\:$ is $\bf \red{3x - 5}$

Given:

• $15( {x - 3)}^{2} + 5(x - 3) - 20 \div 5x - 20 \:$

To find:

• Perform division and find result.

Solution:

Identity to be used:

$\bf ( {a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$

Step 1:

Apply identity in numerator and simplify.

$15( {x}^{2} - 6x + 9) + 5x - 15 - 20$

or

$15 {x}^{2} - 90x + 135 + 5x - 15 - 20$

or

$15{x}^{2} - 85x +100$

Step 2:

Perform division.

$5x - 20 \: ) \: 15 {x}^{2} - 85x + 100 \: (3x - 5 \\ 15 {x}^{2} - 60x \\( - ) \: \: ( + ) \: \: \: \: \\ - - - - - - \\ - 25x + 100 \\ - 25x + 100 \\ ( +) \: \: ( - ) \: \: \: \\ - - - - - - \\ 00 \\ - - - - - -$

Thus,

Quotient is 3x-5 and remainder is 0.

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