5x^2 + 42x + 49?

5x^2+42x+49

5x^2+35x+7x+49

5x(x+7)+7(x+7)

(5x+7)(x+7)

5x^2+42x+49

by inspection, find a term which multiplies to 245x^2 and adds to 42x.

the two terms are 35x and 7x, because

35x x 7x = 245x^2

35x + 7x = 42x

now in the question rewrite 42x as 35x + 7x and then proceed as you would normally.

5x^2+35x+7x+49

take out the common factor 5x in the first half of the expression, and take out 7 in the second half of the expression

5x(x+7)+7(x+7)

(5x+7)(x+7)

therefore

5x^2 + 42x + 49 = (5x+7)(x+7)

it somewhat is a suitable sq. trinomial A^2 + 2AB + B^2 and that’s factored into (A+B)(A+B) or (A+B)^2. 9x^2+42x+forty 9 = (3x)^2 + 2(3x)(7) + 7^2 subsequently A = 3x and B = 7. for this reason, 9x^2+42x+forty 9 = (3x+7)^2

(5x+7) x (x+7)