Question

3(x2 - 7x + 12) and 24(x2 – 9x + 20​

Answer 1

Here's your answer above in the picture

Answer 2

Correct Question:

Find H.C.F and L.C.M of 3(x² - 7x + 12) and 24(x² - 9x + 20)

Answer:

✰ H.C.F = 3 ( x - 4 )

✰ L.C.M = 24( x³ - 12x² + 47x - 60)

Step-by-step explanation:

➤ HCF is the highest common factor also known as G.C.D i.e, greatest common factor. To find the HCF of numbers express that numbers into their product of prime numbers and take out the greatest or highest common factor among them.

Finding H.C.F,

Take 3(x² - 7x + 12)

• 3(x² - 7x + 12)
• 3(x² - 3x - 4x + 12)
• 3[ ( x - 3 ) ( x - 4 ) ]

Now, take 24(x² – 9x + 20)

• 24(x² - 9x + 20)
• 24(x² - 5x - 4x + 20)
• 3 × 8 [ ( x - 5 ) ( x - 4 ) ]

H.C.F = 3 ( x - 4 ) [Common factor of both expression]

Now, find out the L.C.M

➤ L.C.M is the least common multiple. L.C.M and G.C.D are different.

• L.C.M = 3 ( x - 3 ) ( x - 4 ) × 8 ( x - 5 )

• LCM = 3 × 8 × ( x - 3 ) ( x - 4 ) ( x - 5 )

• 24( x² - 7x + 12 ) ( x - 5 )

• 24( x³ - 7x² + 12x - 5x² + 35x - 60)

• 24( x³ - 12x² + 47x - 60)

∴ L.C.M = 24( x³ - 12x² + 47x - 60)

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