Which of the binomials below is a factor of this trinomial x^2-13+42

Question

asked Apr 27, 2021 149k views

2 Answers

Michael Reed · Answer 1 · 2021-04-30T13:10:18+0000

Answer:

$\boxed{ \bold{ \boxed{ \sf{(x - 7)(x - 6)}}}}$

Explanation:

$\sf{ {x}^(2) - 13x + 42 }$

Here, we have to find the two numbers that adds to 13 and multiplies to 42.

The numbers are 7 and 6

$\sf{ {x}^(2) - (7 + 6)x + 42}$

⇒
$\sf{ {x}^(2) - 7x - 6x + 42}$

Factor out x from the expression

⇒
$\sf{x(x - 7) - 6x + 42}$

Factor out 6 from the expression

⇒
$\sf{x(x - 7) - 6(x - 7)}$

Factor out x - 7 from the expression

⇒
$\sf{(x - 7)(x - 6)}$

Hope I helped!

Best regards!!