Find the length of chord QS

Given:

QW = 12 and WS = 4x + 1

PW = 14 and WR = 3x + 3

To find:

The length of the chord QS.

Solution:

If two chords intersect inside a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

Subtract 12 from both sides.

Subtract 42x from both sides.

Divide by 6 on both sides, we get

⇒ x = 5

QS = QW + WS

      = 43

The length of QS is 43.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."