Question

Factorise the Questions in the attachment.



☺ Solve it ☺


☺ Explanation Needed ☺​

Answer 1

Given :

• m² - 23m + 120
• m² - 25m + 100
• 3x² + 14x + 15
• 2x² + x - 45
• 20x² - 26x + 8
• 44x² - x - 3

Solution :

Note → x² + px + q

So, in order to factorize x² + px + q, we need to find two numbers a and b such that (a + b) = p and ab = q. Now, x² + px + q = x² + (a + b)x + ab = (x + a)(x + b)

• m² - 23m + 120
• 1 × 120 = 120
• Two numbers whose sum is 23 and product is 120
• Required numbers = 15 and 8

★ Split middle term ★

→ m² - 23m + 120

→ m² - (15 + 8)m + 120

→ m² - 15m - 8m + 120

→ m(m - 15) - 8(m - 15)

→ (m - 15)(m - 8)

• m² - 25m + 100

★ Split middle term ★

→ m² - (20 + 5)m + 100

→ m² - 20m - 5m + 100

→ m(m - 20) - 5(m - 20)

→ (m - 20)(m - 5)

• 3x² + 14x + 15

★ Split middle term ★

→ 3x² + (9 + 5)m + 15

→ 3x² + 9x + 5x + 15

→ 3x(x + 3) + 5(x + 3)

→ (x + 3)(3x + 5)

• 2x² + x - 45

★ Split middle term ★

→ 2x² + (10 - 9)x - 45

→ 2x² + 10x - 9x - 45

→ 2x(x + 5) - 9(x + 5)

→ (x + 5)(2x - 9)

• 20x² - 26x + 8

★ Split middle term ★

→ 20x² - (16 + 10)x + 8

→ 20x² - 16x - 10x + 8

→ 4x(5x - 4) - 2(5x - 4)

→ (5x - 4)(4x - 2)

• 44x² - x - 3

★ Split middle term ★

→ 44x² - (12 - 11)x - 3

→ 44x² - 12x + 11x - 3

→ 4x(11x - 3) + 1(11x - 3)

→ (11x - 3)(4x + 1)

Answer 2

(i) Let's factor  $\sf m^2-23m+120$

The middle number is -23 and the last number is 120.

Factoring means we want something like ⇒ $\sf{ (m+\_ )(m+\_ )}$

Which numbers go in the blanks?

We need two numbers that...

• Add together to get -23

• Multiply together to get 120

Can you think of the two numbers?

Try -8 and -15:

• $\sf {-8+-15 = -23}$

• $\sf {-8\times -15 = 120}$

Fill in the blanks in  $\sf{ (m+\_ )(m+\_ )}$ with -8 and -15 to get...

$\sf{ (m-8)(m-15)}$

∴ The answer is ⇒ $\sf{ (m-8)(m-15)}$.

$\rule{300}{1}$

(ii) Let's Factor $\sf {m^2-25m+100}$

The middle number is -25 and the last number is 100.

Factoring means we want something like ⇒ $\sf{ (m+\_ )(m+\_ )}$

Which numbers go in the blanks?

We need two numbers that...

• Add together to get -25

• Multiply together to get 100

Can you think of the two numbers?

Try -5 and -20:

• $\sf {-5+-20 = -25}$

• $\sf {-5\times -20 = 100}$

Fill in the blanks in  $\sf{ (m+\_ )(m+\_ )}$ with -5 and -20 to get...

$\sf{ (m-5)(m-20)}$

∴ The answer is ⇒ $\sf{ (m-5)(m-20)}$

$\rule{300}{1}$

(iii) Let's factor $\sf 3x^2+14x+15$

⇒ $\sf (3x+5)(x+3)$

∴The answer is ⇒ $\sf (3x+5)(x+3)$

$\rule{300}{1}$

(iv) Let's factor $\sf 2x^2+x-45$

⇒ $\sf (2x-9)(x+5)$

∴The answer is ⇒ $\sf (2x-9)(x+5)$

$\rule{300}{1}$

(v) Let's factor $\sf 20x^2-26x+8$

⇒ $\sf 2(5x-4)(2x-1)$

∴The answer is ⇒ $\sf 2(5x-4)(2x-1)$

$\rule{300}{1}$

(vi) Let's factor $\sf 44x^2-x-3$

⇒ $\sf (11x-3)(4x+1)$

∴The answer is ⇒ $\sf (11x-3)(4x+1)$

$\rule{300}{1}$