Advertisements
Advertisements
प्रश्न
Show that x – 2 is a factor of 5x2 + 15x – 50.
Advertisements
उत्तर
(x – a) is a factor of a polynomial f(x) if the remainder, when f(x) is divided by (x – a), is 0, i.e., if f(a) = 0.
f(x) = 5x2 + 15x – 50
f(2) = 5(2)2 + 15(2) – 50
= 20 + 30 – 50
= 0
Hence, x – 2 is a factor of 5x2 + 15x – 50
APPEARS IN
संबंधित प्रश्न
Show that 3x + 2 is a factor of 3x2 – x – 2.
Find the value of ‘a’, if (x – a) is a factor of x3 – ax2 + x + 2.
Using the factor Theorem, show that:
2x + 7 is a factor 2x3 + 5x2 − 11x – 14. Hence, factorise the given expression completely.
If x - 2 and `x - 1/2` both are the factors of the polynomial nx2 − 5x + m, then show that m = n = 2
Prove by factor theorem that
(2x - 1) is a factor of 6x3 - x2 - 5x +2
Prove that (x - y) is a factor of yz( y2 - z2) + zx( z2 - x2) + xy ( x2 - y2)
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation, (K + 2)x2 – Kx + 6 = 0. Also, find the other root of the equation.
If both (x − 2) and `(x - 1/2)` is the factors of ax2 + 5x + b, then show that a = b
Which of the following is a factor of (x – 2)2 – (x2 – 4)?
