3.1 Factorise completely

3.1.2 3x2 - 2x - 8​

3x² – 2x – 8

=> 3x² – 6x + 4x – 8

=> 3x( x – 2 ) + 4( x – 2 )

=> ( 3x + 4 ) ( x – 2 )

Therefore,

Either, 3x + 4 = 0

3x = - 4

x = - 4/3 (Ans)

And,

x – 2 = 0

x = 2 (Ans)

(x - 2)(3x + 4)

Step-by-step explanation:

Given

3x² - 2x - 8

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 8 = - 24 and sum = - 2

The factors are - 6 and + 4

Use these factors to split the x- term

3x² - 6x + 4x - 8 ( factor the first/second and third/fourth terms )

= 3x(x - 2) + 4(x - 2) ← factor out (x - 2) from each term

= (x - 2)(3x + 4)

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4