Answer:
see explanation
Explanation:
the perimeter (P) is the sum of the 3 sides of the triangle.
P = 4x² + 1 + 26x + 6 + x² + 10x ← collect like terms
= 5x² + 36x + 7
to factor the expression, consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 5 × 7 = 35 and sum = 36
the factors are + 35 and + 1
use these factors to split the x- term
5x² + 35x + 1x + 7 ( factor the first/second and third/fourth terms )
= 5x(x + 7) + 1 (x + 7) ← factor out (x + 7) from each term
= (x + 7)(5x + 1) , then
P = (x + 7)(5x + 1) ← in factored form