How do you factor completely 14 plus 6x-x2?

Answer 1

35

Answer 2

x2 + 49 - 14x

= x2 - 14x + 49 (since -7 x -7 = 49, and -7 + -7 = -14 we have)

= (x - 7)(x - 7)

= (x - 7)2

or use the formula

(a - b) = (a2 - 2ab + b2)

x2 + 49 - 14x

= x2 - 14x + 49

= [x2 - 2(x)(7) + 72]

= (x - 7)2

Answer 3

10x**2-31x+14

Multiply first and last terms:

10*14=140

Find 2 Factors of 140 whose sum is -31

140=2*2*5*7

Factors:

4*35

10*14

7*20

2*70

5*28

None of these add up to -31

HOWEVER: I will continue this as if it was minus 14 instead of plus (so that I can show you how to do such a question)

Factor

4+-35=-31

rewrite:

10x**2-35x+4x-14

Factor sets of terms

10x**2-35x+4x-14=5x(2x-7)+2(2x-7)

Factor

5x(2x-7)+2(2x-7)=(5x+2)(2x-7)

Answer 4

5xx+14x-48

Steps

1. Multiply first and third terms:

5*-48=-240

2. Factor -240, find two factors that add up to the second term:

-240=2*2*2*2*3*5

-240=-2*120, 2*-120

-240=-3*80, 3*-80

-240=-5*48, 5*-48

-240=-4*60, 4*-60

-240=-6*40, 6*-40

-240=-15*16, 15*-16

-240=-8*30, 8*-30

-240=-12*20, 12*-20

-240=-24*10, 24*-10

3. Rewrite the polynomial:

5xx+14x-48

5xx+24x-10x-48

4. Factor pairs of terms (ie. first and second terms, third and fourth terms):

5xx+24x-10x-48

x(5x+24)-2(5x+24)

5. Combine like terms:

x(5x+24)-2(5x+24)

(x-2)(5x+24)

Answer 5

That doesn't factor neatly. Applying the quadratic formula, we find two real solutions: 3 plus or minus -1 times the square root of 23.

x = -1.7958315233127191

x = 7.7958315233127191

Answer 6

Do tou mean x2+14x+24?

If so then it is (x+2)(x+12) when factored

Answer 7

x2-49 = (x-7)(x+7) which is the difference of two squares

Answer 8

Complete the square or use the quadratic formula.

Answer 9

(7x - 12)(7x - 12) or (7x - 12)2