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Factorisation of Trinomials by Splitting Middle Term

Factorize x3+...

Question

Factorize $x^{3}$ + $2 x^{2}$ – 4x + 1 using synthetic division method.

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Solution

Consider p(x) = $x^{3}$ + $2 x^{2} - 4 x + 1$

By trial and error method we get x= 1 satisfies the equation.

Therefore (x – 1) is a factor of p(x)

p(x) = (x – 1) $(x^{2} + 3 x - 1)$

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Similar questions

Use synthetic division method for performing the following division. Write the result in the form
Dividend = Divisor x Quotient + Remainder.

(x^{3} + 2 x^{2} + x + 2) \div (x - 1)

Q. Find the quotient and remainder using synthetic division.

(8 x^{4} - 2 x^{2} + 6 x - 5) \div (4 x + 1)

f (x) = x^{3} + 2 x^{2} - 5 x - 6

using synthetic division and find zeros of it.

Q. Find the quotient when the polynomial

x^{3} + x^{2} + 1

x + 2

using synthetic division method.

Q. Use synthetic division and the remainder theorem to determine

f (1 / 2)

f (x) = - 3 x^{5} + x^{3} - 2 x^{2} + x - 3

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