College Math Algbrea 2 Help please

Question

4x^2+27x-7=

 

Or is it prime?

Answer 1

ax² + bx + c = a(x - x₁)(x - x₂)
x₁ and x₂ are roots ob quadratic equation ax² + bx + c = 0
D = √(b² - 4ac)
x₁₂ = (- b ± √D) / 2a
If D > 0, quadratic equation has 2 real roots.
If D = 0,          ......            has 1 real root. 
If D < 0,      .....    does not have real roots and can not be factorized.
~~~~~~~~~~~~ 

4x² + 27x - 7 = 0
D = 27² + 112 = 841 = 29²

x₁ = (- 27 - 29) / 8 = - 7
x₂ = (- 27 + 29) / 8 = 1/4

4x² + 27x - 7 = 4(x - 1/4)(x + 7) = (4x - 1)(x + 7)

Answer 2

Hi again David;

4x²+27x-7

For the FOIL...

FIRST must be (4x)(x) or (2x)(2x)=4x²

OUTER and INNER must add-up to 27x

LAST must be (7)(1) or (1)(7) and one number must be negative.

(4x-1)(x+7)

Let's FOIL...

FIRST...(4x)(x)=4x²

OUTER...(4x)(7)=28x

INNER...(-1)(x)=-1x=-x

LAST...(-1)(7)=-7

4x²+28x-x-7

4x²+27x-7