Advertisements
Advertisements
Question
Show that 2x + 7 is a factor of 2x3 + 5x2 - 11 x - 14. Hence factorise the given expression completely, using the factor theorem.
Advertisements
Solution
If 2x + 7 in factor of 2x3 + 5x2 - 11 x - 14 then on putting 2x + 7 = 0
x = `-(7)/(2)`
`f(-7/2)` = 0
= `2(-7/2)^3 + 5(-7/2)^2 -11(7/2)-14`
= `(-343)/(4) + (245)/(4) + (77)/(4) -14`
= `(-399)/(4) + (245 + 154)/(4)`
= `(-399 + 399)/(4)` = 0
Hence 2x + 7 is one factor.
Now 2x3 + 5x2 - 11x - 14
= x2 (2x + 7) -x (2x + 7) -2 (2x + 7)
= (2x + 7) (x2 - x - 2)
= (2x + 7) (x2 + x - 2x - 2)
= (2x + 7) [x (x + 1) -2 (x + 1)]
= (2x + 7) (x - 2) (x + 1).
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.
Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
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
The expression 2x3 + ax2 + bx - 2 leaves the remainder 7 and 0 when divided by (2x - 3) and (x + 2) respectively calculate the value of a and b. With these value of a and b factorise the expression completely.
By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x2 + 5x – 3.
Show that 2x + 7 is a factor of 2x3 + 5x2 – 11x – 14. Hence factorise the given expression completely, using the factor theorem.
If (3x – 2) is a factor of 3x3 – kx2 + 21x – 10, find the value of k.
If x – 2 is a factor of x3 – kx – 12, then the value of k is ______.
Is (x – 2) a factor of x3 – 4x2 – 11x + 30?
