Question

How to factorise 3 x cube + 5 x square - 11 X + 3

Answer 1

Step-by-step explanation:

Given -

• p(x) = 3x³ + 5x² - 11x + 3

To Find -

• Zeroes

Now,

3x³ + 5x² - 11x + 3

» 3x³ - 3x² + 8x² - 8x - 3x + 3

» 3x²(x - 1)+ 8x(x - 1)- 3(x - 1)

» (x - 1) (3x² + 8x - 3)

» (x - 1) (3x² - x + 9x - 3)

» (x - 1) [x(3x - 1) + 3(3x - 1)]

» (x - 1) [(x + 3)(3x - 1)]

» (x - 1)(x + 3)(3x - 1)

Zeroes are -

x - 1 = 0, x + 3 = 0, and 3x - 1 = 0

• x = 1, -3, 1/3

Verification :-

• α + β + γ = -b/a

» -3 + 1 + 1/3 = -5/3

» -9 + 3 + 1/3 = -5/3

» -5/3 = -5/3

LHS = RHS

And

• αβ + βγ + γα = c/a

» -3×1 + 1×1/3 + 1/3×-3 = -11/3

» -3 + 1/3 - 1 = -11/3

» -9 + 1 - 3/3 = -11/3

» -11/3 = -11/3

LHS = RHS

And

• αβγ = -d/a

» -3 × 1 × 1/3 = -3/3

» -1 = -1

LHS = RHS

Hence,

Verified..

Answer 2

$\large{\boxed{\underline{\underline{\bf{\red{Answer:-}}}}}}$

$\large\underline\mathrm{The \: value \: of \: x \: is \: 1, \: -3, \: 1/3.}$

$\large\underline\mathrm{Given:-}$

• p(x) = 3x³ + 5x² - 11x + 3

$\large\underline\mathrm{To \: find}$

• zeroes

$\large\underline\mathrm{Solution}$

$\implies$ 3x³ + 5x² - 11x + 3

$\implies$ 3x³ - 3x² + 8x² - 11x + 3

$\implies$ 3x²(x - 1) + 8x(x - 1) - 3(x - 1)

$\implies$(x - 1)(3x² + 8x - 3)

$\implies$ (x - 1)(3x² - x + 9x - 3)

$\implies$ (x - 1)[x(3x - 1) + 3(3x - 1)]

$\implies$ (x - 1)[(x + 3)(3x - 1)]

$\implies$ (x - 1)(x + 3)(3x - 1)

$\implies$ x - = 0

$\implies$ x = 1

$\implies$ x + 3 = 0

$\implies$ x = -3

$\implies$ 3x - 1 = 0

$\implies$ 3x = 1

$\implies$ x = 1/3

$\large\underline\mathrm{hence}$

$\large\underline\mathrm{The \: value \: of \: x \: is \: 1, \: -3, \: 1/3.}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$