Question

Perfect square trinomial factoring

x^2 + 12x + 36

answer and explain please

Answer 1

x^2 + 12x + 36


x^2 + 6x+6x + 36


(x^2 + 6x)+(6x + 36)


x(x+6)+6(x+6)


(x+6)(x+6)


(x+6)^2


So x^2 + 12x + 36 factors to (x+6)^2


In other words, x^2 + 12x + 36 = (x+6)^2

Answer 2

\[(x+a)(x+b)\]where a*b = 36 and a+b = 12
36 is a perfect square. 6^2 = 36. 6+6 = 12. Therefore, this is a perfect square\[(x+6)^2\]

Answer 3

Note: the numbers 6 and 6 both add to 12 and multiply to 36

Answer 4

what if the equation was not a perfect square. for example
x^2 - 10x +25

Answer 5

This is a perfect square since x^2-10x+25 = (x-5)^2

Answer 6

Same approach applies. \[(x+a)(x+b)\]where a*b = 25 and a+b=-10
Here, we can use -5 and -5. These add to -10 and multiply to 25. Again, we have a perfect square.

Answer 7

so the answer is (x + 5) (x - 15)?

Answer 8

so the answer is (x + 5) (x - 15)?