Question

Factorise the following 4m2 +17m+15

Answer 1

Please find the answer in the attachment.

Answer 2

m=$- \frac{5}{4} \: and \: - 3$

GIVEN:- 4m² +17m+15

TO FIND:- Factorise the given equation

SOLUTION:-

• In mathematics, Factorization or factoring includes writing a number or another mathematical element as a product of various factors, usually smaller or simpler element of the similar kind.

$4 {m}^{2} + 17m + 15$

Middle term splitting:-By taking LCM of 4 and 15 we get 60, We'll break the product of 60 in two numbers in a way in which the sum of both the numbers will be equal to 17. Thus, we get 12 and 5.

$= 4 {m}^{2} + 12m + 5m + 15 \\ = 4m(m + 3) + 5(m + 3) \\ = (4m + 5)(m + 3)$

Thus, (4m+5) and (m+3) are factors of the 4m² +17m+15

By solving both the linear factors

$4m + 5 = 0 \\ 4m = - 5 \\ m = \frac{ - 5}{4}$

$m + 3 = 0 \\ m = - 3$

Hence, by solving we get, m = $- \frac{5}{4} \: and \: - 3$

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