Question

Find and correct the errors in the following mathematical statements.....Factorisation..pls answer​

Answer 1

Solution:-

$\rm \implies \dfrac{8 {x}^{2} - 26x + 15}{2x - 5} = 4x - 10$

Using cross multiplication

$\rm \implies \: 8 {x}^{2} - 26x + 15 = (4x - 10)(2x - 5)$

$\rm \implies \: 8 {x}^{2} - 26x + 15$

$\rm \implies \: 8 {x}^{2} - 26x + 15 = 8 {x}^{2} - 20x - 20x + 50$

$\rm \implies8 {x}^{2} - 26x + 15 = 8 {x}^{2} - 40x + 50$

$\rm \implies \cancel{8 {x}^{2} } - 26x + 15 = \cancel{8 {x}^{2} } - 40x + 50$

$\rm \implies - 26x + 15 = - 40x + 50$

$\rm \implies40x - 26x = 50 - 15$

$\rm \rm \implies \: 14x = 35$

$\rm \implies \: x = \dfrac{35}{14}$

More information

=> Linear equation, statement that a first-degree polynomial—that is, the sum of a set of terms, each of which is the product of a constant and the first power of a variable—is equal to a constant.

Answer 2

Given statement is wrong correct statement is $:\implies\sf\dfrac{8x^{2} - 26x + 15}{2x - 5} = 4x - 10$

Let's start the factorisation of this statement :)

$\underline{\orange{\bf Given :-}}$

$:\implies\sf\dfrac{8x^{2} - 26x + 15}{2x - 5} = 4x - 10$

$\underline{\orange{\bf To \: Find :-}}$

$:\implies\sf Value \: of \: \boxed{\bf x}$

$\underline{\orange{\bf Solution :-}}$

$:\implies\sf\dfrac{8x^{2} - 26x + 15}{2x - 5} = 4x - 10$

$:\implies\sf 8x^{2} - 26x + 15 = (4x - 10)(2x - 5)$

$:\implies\sf 8x^{2} - 26x + 15 = 8x^{2} - 20x - 20x + 50$

$:\implies\sf\cancel{8x^{2}} - 26x \cancel{- 8x^{2}} + 20x + 20x = 50 - 15</p><p>$

$:\implies\sf - 26x + 40x = 50 - 15$

$:\implies\sf 14x = 35$

$:\implies\sf x = \dfrac{35}{14}$

$:\implies\underline{\boxed{\blue{\sf x = 2\dfrac{7}{14}}}}$

______________________________

Additional Information :-

1) + × + = +

☆ Example :-

• 5x × 2x = 10x²

2) + × - = -

☆ Example :-

• 5x × (- 2x) = - 10x²

3) - × - = +

☆ Example :-

• (- 5x) × (- 2x) = 10x²

______________________________