Question

Find the factors of x + 3x - 28

Answer 1

Answer:

(x-4)(x+7)

Step-by-step explanation:

Expression is

x^2+3x-28

middle term break ,

x^2+7x-4x-28

x(x+7)-4(x+7)

(x-4)(x+7)

Answer 2

Middle term split method: Let  $x^2+Sx+P$ be our quadratic equation.

                                             Here, 'S' is the sum of the factors and 'P' is the product of the factors of the equation.

• First, we will find two multiples of P and check whether their sum is S.
• Secondly, Keep in mind the signs of the multiples as it can make or break the solution.

Solution:

Our equation is  $x^2 + 3x - 28$.

Now using the steps given above we will find 2 multiples of -28 (keeping the signs in mind), whose sum will be +3.

• We can write : (7 x -4 = -28) because +7- 4 = +3
• Now we will replace '+3' with (+ 7 - 4) and make factors.

Solving further,

$x^2 + 7x -4x +28 = x(x+7) -4(x+7)$ $= (x+7)(x-4)$

Therefore, the factors of the equation are

x+7=0           ;    x-4=0

x= -7             ;    x=4

Answer :

x= -7 , 4