Question

Factorise by splitting the middle term.

$x^{2} - 20x { }^{2} + 64$
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Answer 1

$\textsf{\large{\underline{Solution}:}}$

We have to factorise the given polynomial.

$\rm = {x}^{2} - 20x + 64$

By splitting the middle term, we get:

$\rm = {x}^{2} - (16 + 4)x + 64$

$\rm = {x}^{2} -16x - 4x+ 64$

$\rm = x(x - 16) - 4(x - 16)$

$\rm = (x - 4)(x - 16)$

★ Therefore, the factorised form of the polynomial is (x - 4)(x - 16).

$\textsf{\large{\underline{Answer}:}}$

• Factorised form » (x - 4)(x - 16).

$\textsf{\large{\underline{Learn More}:}}$

1. Relationship between zeros and coefficients (Quadratic Polynomial)

Let f(x) = ax² + bx + c and let α and β be the zeros of f(x).

Therefore:

$\rm:\longmapsto\alpha+\beta=\dfrac{-b}{a}$

$\rm:\longmapsto\alpha\beta=\dfrac{c}{a}$

2. Relationship between zeros and coefficients (Cubic Polynomial)

Let f(x) = ax³ + bx² + cx + d and let α, β and γ be the zeros of f(x).

Therefore:

$\rm:\longmapsto\alpha+\beta+\gamma=\dfrac{-b}{a}$

$\rm:\longmapsto \alpha\beta+\beta\gamma+\alpha\gamma=\dfrac{c}{a}$

$\rm:\longmapsto \alpha\beta\gamma=\dfrac{-d}{a}$

Answer 2

Answer:

Step-by-step explanation:

Factors are :- -16 & -4

So...

x² - 16x - 4x + 64

= x(x-16) -4(x-16)

= (x-4)(x-16)

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