Advertisements
Advertisements
Question
Show that (x – 2) is a factor of 3x2 – x – 10 Hence factorise 3x2 – x – 10.
Advertisements
Solution
Let x – 2 = 0, then x = 2
Substituting the value of x in f(x),
f(x) = 3x2 – x – 10
= 3(2)2 – 2 – 10
= 12 – 2 – 10
= 0
∵ Remainder is zero
∴ x – 2 is a factor of f(x)
Dividing 3x2 – x – 10 by x – 2, we get
`x - 2")"overline(3x^2 - x - 10)("3x + 5`
3x2 – 6x
– +
5x – 10
5x – 10
– +
x
∴ 3x2 – x – 10 = (x – 2)(3x + 5).
APPEARS IN
RELATED QUESTIONS
Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.
Prove by factor theorem that
(x-2) is a factor of 2x3- 7x -2
Prove by factor theorem that
(2x+1) is a factor of 4x3 + 12x2 + 7x +1
Prove that (x - y) is a factor of yz( y2 - z2) + zx( z2 - x2) + xy ( x2 - y2)
Prove that (5x - 4) is a factor of the polynomial f(x) = 5x3 - 4x2 - 5x +4. Hence factorize It completely.
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
Show that (x – 1) is a factor of x3 – 5x2 – x + 5 Hence factorise x3 – 5x2 – x + 5.
Show that (x – 3) is a factor of x3 – 7x2 + 15x – 9. Hence factorise x3 – 7x2 + 15 x – 9
If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 – 2x + a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.
Find the value of 'a' if x – a is a factor of the polynomial 3x3 + x2 – ax – 81.
