Using factor theorem- show that-x-5 is a factor of 2 x3-9 x2-11 x-30

Let: fx=2x3+9x2 11x 30 Here, nbsp; x+5=0 #8658;x= 5 By the factor theorem, (x nbsp;+ 5) is a factor of nbsp;the given polynomial nbsp;if nbsp;f nb ...

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Standard IX

Mathematics

Polynomials

Using factor ...

Question

Using factor theorem, show that:
(x + 5) is a factor of (2x³ + 9x² − 11x − 30)

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Solution

Let:
$f (x) = 2 x^{3} + 9 x^{2} - 11 x - 30$
Here,
$x + 5 = 0 \Rightarrow x = - 5$
By the factor theorem, (x + 5) is a factor of the given polynomial if f ( $-$ 5) = 0.
Thus, we have:
$f (- 5) = [2 \times {(- 5)}^{3} + 9 \times {(- 5)}^{2} - 11 \times (- 5) - 30] = (- 250 + 225 + 55 - 30) = 0$
Hence, (x + 5) is a factor of the given polynomial.

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Q. If

(x + 5)

is a factor

(2 x^{3} + 9 x^{2} - 11 x + a)

. Find

30 - a

Q. Show that:
(i) x + 3 is a factor of

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.

(ii) 2x – 3 is a factor of

x + 2 x^{3} - 9 x^{2} + 12

Question 16
Show that:
(i) x + 3 is a factor of $69 + 11 x - x^{2} + x^{3}$ .

(ii) 2x – 3 is a factor of $x + 2 x^{3} - 9 x^{2} + 12$ .

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Using factor theorem, show that: (x + 5) is a factor of (2x3 + 9x2 − 11x − 30)

Let: fx=2x3+9x2-11x-30 Here, x+5=0⇒x=-5 By the factor theorem, (x + 5) is a factor of the given polynomial if f (-5) = 0. Thus, we have: f-5=2×-53+9×-52-11×-5-30 =-250+225+55-30 =0 Hence, (x + 5) is a factor of the given polynomial.

Using factor theorem, show that:
(x + 5) is a factor of (2x³ + 9x² − 11x − 30)