Question

Factorize the following quadratic expression by splitting the middle term:
x2 +3x -40​

Answer 1

Step-by-step explanation:

Given polynomial :  x² + 3x - 40  

Let p(x) = x² + 3x - 40

=> It is of the form ax² + bx + c  

By comparing, we get  

   a = 1, b = 3, c = -40  

where  

a - coefficient of x²  

b - coefficient of x  

c - constant term

By sum-product pattern,  

>> Find the product of quadratic term [ax²] and constant term [c]  

= x²  × (-40)  

= -40x²

>> find the factors of "-40x²" in pairs  

• (x) (-40x)
• (-x) (40x)
• (2x) (-20x)
• (-2x) (20x)
• (4x) (-10x)
• (-4x) (10x)
• (5x) (-8x)
• (-5x) (8x)

>> From the above, find the pair that adds to get linear term [bx]  

  -5x + 8x = 3x

>> Split the middle term 3x as -5x and 8x  

   x² + 3x - 40  

x² - 5x + 8x - 40

>> Find the common factor,  

x(x - 5) + 8(x - 5)

(x - 5) (x + 8)  

∴ x² + 3x - 40 = (x - 5) (x + 8)