Q. 6 C4.5( 4 Votes )

# Factorize the following polynomials:

p(x) = x^{3} — 3x^{2} + 9x — 27

Answer :

p(x) = x^{3} – 3x^{2} + 9x – 27

= x^{2} (x – 3) + 9 (x – 3)

= (x – 3) (x^{2} + 9)

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Prove that x — 2 is a factor of p(x) = x^{3} — 2x^{2}

Verify whether the given value of x is a solution of the quadratic equation or not:

Gujarat Board Mathematics

Factorize the following polynomials:

p(x) = x^{3} — 3x^{2} + 9x — 27

Factorize the following polynomials:

p(x) = 5x^{2} + 11x + 6

Examine the validity of the following statements:

(x — 3) is a factor of p(x) = x^{2} — 2x — 3

Verify whether the given value of x is a solution of the quadratic equation or not:

(3x — 8)(2x + 5) = 0, x = –

Gujarat Board MathematicsFind k, if one of the roots of x^{2} + 3(k + 2)x — 9 = 0 is —3.

Factorize the following polynomials:

p(x) = x^{3} —x^{2}—x + 1

Find k, if one of the roots of x^{2} — kx + 6 = 0 is 3.