Using factor theorem- show that gx is a factor of px- when px-2-2x2-5x-2- gx-x-2

ANSWER: Let: f(x)=2√(2)x^2+5x+√(2), g(x)=x+√(2) By the factor theorem, (x+ √(2) )will be a factor of the given polynomial if f( √(2) ) = 0 Thus, we have: f( √ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Factor Theorem

Using factor ...

Question

Using factor theorem, show that g(x) is a factor of p(x), when
$p (x) = 2 \sqrt{2} x^{2} + 5 x + \sqrt{2}, g (x) = x + \sqrt{2}$

Open in App

Solution

ANSWER:
Let:
$f (x) = 2 \sqrt{2} x^{2} + 5 x + \sqrt{2}, g (x) = x + \sqrt{2}$
By the factor theorem, ( $x + \sqrt{2}$ )will be a factor of the given polynomial if $f (- \sqrt{2}) = 0$
Thus, we have:
$f (- \sqrt{2}) = 2 \sqrt{2} (- \sqrt{2})^{2} + 5 \times (- \sqrt{2}) + \sqrt{2}$
= $5 \sqrt{2} - 5 \sqrt{2}$
=0
Hence, $x + \sqrt{2}$ is a factor of the given polynomial.

Suggest Corrections

Similar questions

Q. Using factor theorem, show that g(x) is a factor of p(x), when

p (x) = 2 \sqrt{2} x^{2} + 5 x + \sqrt{2}, g (x) = x + \sqrt{2}

Using factor theorem, show that g(x) is a factor of p(x), when
$p (x) = 2 x^{4} + 9 x^{3} + 6 x^{2} - 11 x - 6, g (x) = x - 1$

Using factor theorem, show that g(x) is a factor of p(x), when
$p (x) = x^{3} - 8, g (x) = - 2$

Q. Use the factor theorem to determine whether g(x) is a factor of p(x) in the following case.

p (x) = 3 x^{3} + 3 x^{2} + 3 x + 1; g (x) = x + 2

Q. Question 2
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:

(i) p (x) = 2 x^{3} + x^{2} - 2 x - 1, g (x) = x + 1

(i i) p (x) = x^{3} + 3 x^{2} + 3 x + 1, g (x) = x + 2

(i i i) p (x) = x^{3} - 4 x^{2} + x + 6, g (x) = x - 3

Join BYJU'S Learning Program

Using factor theorem, show that g(x) is a factor of p(x), when p(x)=2√2x2+5x+√2,g(x)=x+√2

ANSWER: Let: f(x)=2√2x2+5x+√2,g(x)=x+√2 By the factor theorem, (x+√2 )will be a factor of the given polynomial if f(−√2)=0 Thus, we have: f(−√2)=2√2(−√2)2+5×(−√2)+√2 = 5√2−5√2 =0 Hence, x+√2 is a factor of the given polynomial.

Using factor theorem, show that g(x) is a factor of p(x), when
$p (x) = 2 \sqrt{2} x^{2} + 5 x + \sqrt{2}, g (x) = x + \sqrt{2}$