Question

2r²+15r+7 fully factorise the expression

Answer 1

2r² + 15r + 7

a = 2 ( factor of r²)
b = 15 ( factor of r)
C = 7


X = (-b ± √(b²-4ac) ) / 2a

X = -15 ± √(15² - 4×2×7) / 2(2)

X = ( -15 ± √ 225 - 56 ) / 4

X = ( -15 ± √ 169 ) / 4


X =( -15 ± 13 ) / 4


X₁ =( -15 - 13) / 4 = -28 / 4 = -7

X₂ = (-15 + 13) / 4 = -2/4 = -2

Answer 2

(2r + 1)(r + 7)

Explanation:

given

2r² + 15r + 7

Consider the factors of the product of the coefficient of the r² term and the constant term which sum to give the coefficient of the r- term.

product = 2 × 7 = 14 and sum = + 15

the factors are + 1 and + 14

use these factors to split the r- term

= 2r² + r + 14r + 7 ( factor the first/second and third/fourth terms )

= r(2r + 1) + 7(2r + 1) ← factor out (2r + 1) from each term

= (2r + 1)(r + 7) ← in factored form