Advertisements
Advertisements
Question
Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem
Advertisements
Solution
Let the area of a rectangle be p(x)
p(x) = x2 – 2x – 8
When x + 2 is the side of the rectangle
p(–2) = (–2)2 – 2(–2) – 8
= 4 + 4 – 8
= 8 – 8
= 0
When x – 4 is the side of the rectangle.
P(4) = (4)2 – 2(4) – 8
= 16 – 8 – 8
= 16 – 16
= 0
(x + 2) and (x – 4) are the sides of a rectangle
APPEARS IN
RELATED QUESTIONS
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
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.
Find the value of k, if 3x – 4 is a factor of expression 3x2 + 2x − k.
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
Find the value of ‘a’, if (x – a) is a factor of x3 – ax2 + x + 2.
(3x + 5) is a factor of the polynomial (a – 1)x3 + (a + 1)x2 – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely.
Prove that (5x - 4) is a factor of the polynomial f(x) = 5x3 - 4x2 - 5x +4. Hence factorize It completely.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = 2x3 + 4x + 6 and g(x) = x + 1
Show that 2x + 7 is a factor of 2x3 + 5x2 - 11 x - 14. Hence factorise the given expression completely, using the factor theorem.
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.
