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) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = 2x3 − x2 − 45, q(x) = x − 3
Show that (x - 1) is a factor of x3 - 7x2 + 14x - 8. Hence, completely factorise the above expression.
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
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 ax3 + 3x2 + bx – 3 has a factor (2x + 3) and leaves remainder – 3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.
If (x – 1) divides the polynomial kx3 – 2x2 + 25x – 26 without remainder, then find the value of k
If x – 3 is a factor of p(x), then the remainder is
Factors of 3x3 – 2x2 – 8x are ______.
Is (x – 2) a factor of x3 – 4x2 – 11x + 30?
