Question

factor the following completely​

Answer 1

Answer:

Solution :-

A.

1) x² - 25

➙ (x)² - (5)²

➙ (x + 5) (x - 5)

∴ The answer of this question is (x + 5) (x - 5)

Formula used :-

✻ a² - b²

→ (a + b) (a - b)

2. 2x² - 15x - 8 = 0

➻ 2x² - (16 - 1)x - 8 = 0

➻ 2x² - 16x + x - 8 = 0

➻ 2x(x - 8) + 1(x - 8) = 0

➻ (x - 8) (2x + 1) = 0

➻ (x - 8) = 0

➻ x - 8 = 0

➻ x = 8

Either,

➻ (2x + 1) = 0

➻ 2x + 1 = 0

➻ 2x = - 1

➻ x = - 1/2

∴ The answer of this question is x = 8, - 1/2

3. 3x² + 30x + 75 = 0

➪ 3(x² + 10x + 25) = 0

➪ 3{x² + (5 + 5)x + 25} = 0

➪ 3{x² + 5x + 5x + 25} = 0

➪ 3{x(x + 5) + 5(x + 5)} = 0

➪ 3{(x + 5) + (x + 5)} = 0

➪ (x + 5) (x + 5) = 0

➪ (x + 5) = 0

➪ x + 5 = 0

➪ x = - 5

Either,

➔ (x + 5) = 0

➔ x + 5 = 0

➔ x = - 5

∴ The answer of this question is x = - 5, - 5

4. x³ - 27

➜ (x)³ - (3)³

➜ (x - 3) {(x)² + x × 3 + (3)²}

➜ (x - 3) (x² + 3x + 9)

∴ The answer of this question is (x - 3) (x² + 3x + 9)

Formula used :-

❖ a³ - b³

➻ (a - b) (a² + ab + b²)

5. 5x³ - 5x² - 10x

➙ 5x(x² - x - 2)

➙ 5x{x² - (2 - 1)x - 2}

➙ 5x{x² - 2x + x - 2}

➙ 5x{x(x - 2) + 1(x - 2)}

➙ 5x{(x - 2) (x + 1)}

➙ 5x(x - 2) (x + 1)

∴ The answer of this question is 5x(x - 2) (x + 1)