Q17: factor the expression. 3x *squared* −5x−12

(3x + 4)(x - 3)

Step-by-step explanation:

3x² - 5x - 12 = (3x + 4)(x - 3)

(x - 3)(3x + 4)

Step-by-step explanation:

Given

3x² - 5x - 12

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

product = 3 × - 12 = - 36 and sum = - 5

The factors are - 9 and + 4

Use these factors to split the x- term

3x² - 9x + 4x - 12 ( factor the first/second and third/fourth terms )

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

= (x - 3)(3x + 4) ← in factored form

i found two solutions,   n = 2 • ± √3 = ± 3.4641

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form