Question

Factorise the polynomial X^3+13X^2+32X-36 if one of it's zero is -9
and first prove that -9 is the zero of polynomial.​

Answer 1

$\large{\underline{\purple{\rm{Given\:Polynomial:}}}}$

P(x)=x³+13x²+32x-36

one of its zero is -9

zero of polynomial written as x+9

$\large{\underline{\red{\rm{To\: Find:}}}}$

Factorise the given polynomial

Proved that -9 is zero of this polynomial

$\large{\underline{\orange{\rm{Solution:}}}}$

Given , the zero of polynomial we put the in the given polynomial to prove that -9 is the zero polynomial

=>P(x)=x³+13x²+32x-36

=>P(-9)=(-9)³+13×(-9)²+32×(-9)-36

=>P(-9)=-729+13×81-32×9-36

=>P(-9)=1053-729-288-36

=>P(-9)=1053-1053

=>P(-9)=0

Now we have to divide P(x) by x+9

x+9)x³+13x²+32x-36(x²+4x-4

x³+9x²

- -

4x²+32x-36

4x²+36x

- +

-4x-36

-4x-36

+ +

× ×

Now, we have to factorise here with help of divisor and quotient

=>(x+9)(x²+4x-4)

By quardric equation to solve

=>X²+4x-4

By quardric equation

a=1 b=4 c=-4

D=b²-4ac

D=4²-4*1*(-4)

D=16+16=32

X=-b+-√D/2

X=-4-√32/2=>4-4√2/2=>4(1-√2)/2=>2-2√2 X=2+2√2

=>(x+9)(x+2-2√2)(x+2+2√2)

Hence,

The required answer is (x+9)(x+2-2√2)(x-2+2√2)

Answer 2

Answer:

GivenPolynomial:

P(x)=x³+13x²+32x-36

one of its zero is -9

zero of polynomial written as x+9

\large{\underline{\red{\rm{To\: Find:}}}}

ToFind:

Factorise the given polynomial

Proved that -9 is zero of this polynomial

\large{\underline{\orange{\rm{Solution:}}}}

Solution:

Given , the zero of polynomial we put the in the given polynomial to prove that -9 is the zero polynomial

=>P(x)=x³+13x²+32x-36

=>P(-9)=(-9)³+13×(-9)²+32×(-9)-36

=>P(-9)=-729+13×81-32×9-36

=>P(-9)=1053-729-288-36

=>P(-9)=1053-1053

=>P(-9)=0

Now we have to divide P(x) by x+9

x+9)x³+13x²+32x-36(x²+4x-4

x³+9x²

- -

4x²+32x-36

4x²+36x

- +

-4x-36

-4x-36

+ +

× ×

Now, we have to factorise here with help of divisor and quotient

=>(x+9)(x²+4x-4)

By quardric equation to solve

=>X²+4x-4

By quardric equation

a=1 b=4 c=-4

D=b²-4ac

D=4²-4*1*(-4)

D=16+16=32

X=-b+-√D/2

X=-4-√32/2=>4-4√2/2=>4(1-√2)/2=>2-2√2 X=2+2√2

=>(x+9)(x+2-2√2)(x+2+2√2)

Hence,

The required answer is (x+9)(x+2-2√2)(x-2+2√2)