Question

please answer accurately on page not keyboard.. Using factor theorem, proof that g(x) is a factor of p(x)​

Answer 1

Solution :

• p(x) = 2√2x² + 5x + √2

• g(x) = x + √2

Let's find the zero of the g(x)

→ g(x) = 0

→ x + √2 = 0

→ x = 0 - √2

→ x = -√2

Now,

p(x) = 2√2x² + 5x + √2

When x = -√2

→ p(-√2) = 2√2(-√2)² + 5(-√2) + √2

→ p(-√2) = 2√2(2) + -5√2 + √2

→ p(-√2) = 4√2 - 5√2 + √2

Put the value of √2 = 1.414

→4(1.414) - 5(1.414) + (1.414)

→ 5.656 - 7.07 + 1.414

→ 7.07 - 7.07

→ 0

$\therefore$ (x+√2) is factor of the polynomial 2√2x² + 5x + √2

Here, I've attached the picture too for your ease as mentioned in the question.

Answer 2

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QUESTION :

please answer accurately on page not keyboard.. Using factor theorem, proof that g(x) is a factor of p(x)

SOLUTION :

The entire solution is in the attachment as you wanted...