Question

if x+a is a factor of x4 -a2x2+3x- 6a
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Answer 1

$\huge\bold{\underline {Question}}$

Show that if (x+a) is a factor of x⁴-a²x²+3x-6a.

$\huge\bold{\underline {Solution}}$

If x+a=0

Then, x=-a

Let, f(x) be the polynomial x⁴-a²x²+3x-6a.

∴ f(x)=x⁴-a²x²+3x-6a

⇒f(-a)=(-a)⁴-a²(-a)²+3(-a)-6a

⇒f(-a)=a⁴-a⁴-3a-6a

⇒f(-a)=-9a

BTP,

f(x)=0

⇒-9a=0

⇒a=0

Since, the remainder is equal to 0, so (x+a) is a factor of polynomial f(x).

$\small\bold{ \sf{\boxed{PROVED}}}$

Answer 2

$\huge{ \underline{ \bold{ᴀɴsᴡᴇʀ....{ \heartsuit}}}}$

If x+a=0

Then, x=-a

Let, f(x) be the polynomial x⁴-a²x²+3x-6a.

∴ f(x)=x⁴-a²x²+3x-6a

⇒f(-a)=(-a)⁴-a²(-a)²+3(-a)-6a

⇒f(-a)=a⁴-a⁴-3a-6a

⇒f(-a)=-9a

BTP,

f(x)=0

⇒-9a=0

⇒a=0

Since, the remainder is equal to 0, so (x+a) is a factor of polynomial f(x).