Q. 4 B4.7( 3 Votes )

# Let us calculate the value of k for which g(x) will be a factor of the following polynomials f(x).

f(x) = kx^{2} – 3x + k and g(x) = x – 1

Answer :

Formula used.

If f(x) is a polynomial with degree n

Then (x – a) is a factor of f(x) if f(a) = 0

1^{st} we find out zero of polynomial g(x)

x – 1 = 0

x = 1

if x – 1 is factor of f(x) = kx^{2} – 3x + k

then f(1) = 0 ;

f(1) = k(1)^{2} – 3(1) + k = 0

= k – 3 + k

2k – 3 = 0

k =

Conclusion.

∴ if (x – 1) is factor of f(x) then k = –

Rate this question :

Let us calculate and write, which of the following polynomials will have a factor (x + 1)?

x^{4} + x^{3} – x^{2} + 4x + 5

If (x + 1) and (x + 2) are two factors of the polynomial x^{3} + 3x^{2} + 2ax + b, then let us calculate and write the values of a and b.

Let us calculate and write, which of the following polynomials will have a factor (x + 1)?

x^{4} + x^{2} + x + 1

By using Factor Theorem, let us write whether g(x) is a factor of the following polynomials f(x).

f(x) = 2x^{3} + 7x^{2} – 24x – 45 and g(x) = x – 3

By using Factor Theorem, let us write whether g(x) is a factor of the following polynomials f(x).

f(x) = 2x^{3} + 9x^{2} – 11x – 30 and g(x) = x + 5

Let us factorise the following algebraic expressions:

3a (3a + 2c) – 4b (b + c)

West Bengal MathematicsBy using Factor Theorem, let us write whether g(x) is a factor of the following polynomials f(x).

f(x) = 3x^{3} + x^{2} – 20x + 12 and g(x) = 3x – 2

Let us calculate and write, which of the following polynomials will have a factor (x + 1)?

3 + 3x – 5x^{3} – 5x^{4}