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College Math Algbrea 2 Help please

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2 Answers

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
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)