factorise 4x2-10x+4
Answers
Answer:
Step-by-step explanation:
4x^2-10x+4
4x^2-8x-2x+4
4x(x-2) -2(x-2)
(4x-2)(x-2)
The expression 4x² - 10x + 4 can be factorised into 2 (x - 2) (2x - 1).
• The expression 4x² - 10x + 4 can be written as 4x² - 8x - 2x + 4, by splitting - 10x into - 8x and - 2x.
• ∴ 4x² - 8x - 2x + 4
= 4x (x - 2) - 2 (x - 2)
= (x - 2) (4x - 2)
= (x - 2) × 2 (2x - 1)
= 2 (x - 2) (2x - 1)
∴ 4x²- 10x + 4 = 2 (x - 2) (2x - 1)
• Steps to solve quadratic expressions of the form ax² + bx + c :
The expression 4x² - 10x + 4 is a quadratic expression of the form ax² + bx + c.
(i) Such expressions can be solved by splitting the middle term into two terms in a way that satisfies the following two conditions :
• The sum of the two terms should result into the middle term.
• The product of the two terms should equal the product of the first and the third term in the expression.
(ii) In the given expression, the middle term is - 10x, and the product of the first and the third term is 4x² × 4 = 16x².
(iii) Therefore, the expression can be written as 4x² - 8x - 2x + 4, by splitting - 10x into - 8x and - 2x, since - 8x - 2x = 10x and (- 8x) × (- 2x) = 16x².
(iv) The splitted expression can then be solved by taking out the common factor/s from the pair of 1st and 2nd terms, and then from the pair of 3rd and 4th terms, till no more common factor is left in any of the terms.