Which first-degree polynomial is added to the polynomial 5x3 + 3x2 to

1.	Which first-degree polynomial is added to the polynomial 5x3 + 3x2 to get x2 – 1 as a factor.
Answer» p(x) = 5x³ +3x² + ax + b \(\therefore\) x²-1 is a factor then p(1), p(–1) will be zero. p(1) = 5 x 1 + 3 x 1 + a x 1 + b = 0 = 5x – 1 + 3 x 1 + ax – 1 + b = 0 a + b = –8 (1) = 5x – 1 + 3 x 1 + ax – 1 + b = 0 –a + b = 2 (2) Find the solutions of the equation b = –3, a = –5 added polynomial = –5x – 3

Which first-degree polynomial is added to the polynomial 5x3 + 3x2 to get x2 – 1 as a factor.

Answer»

p(x) = 5x³ +3x² + ax + b

\(\therefore\) x²-1 is a factor then p(1), p(–1) will be zero.

p(1) = 5 x 1 + 3 x 1 + a x 1 + b = 0

= 5x – 1 + 3 x 1 + ax – 1 + b = 0 a + b = –8 (1)

= 5x – 1 + 3 x 1 + ax – 1 + b = 0 –a + b = 2 (2)

Find the solutions of the equation

b = –3, a = –5 added polynomial = –5x – 3

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Which first-degree polynomial is added to the polynomial 5x3 + 3x2 to get x2 – 1 as a factor.

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