Question

factories
x²-4
x²-6
4x²-36
2x²-16​

Answer 1

$●\large\sf \bf \underline\purple{ your\: \: answer \: !!}$

1. Factorize:-

4x² - 9y²z⁴

→ -9y²z⁴ + 4x²

→ (3yz² + 2x) (-3yz²+2x)

2. Factorize:-

x²-8x+16

Solving by splitting the middle term:-

We need two numbers:-

=> Add together to get -8

=> Multiply together -16

we get:-

(-4) + (-4) = -8

(-4) × (-4) = -16

Filling them in:

\implies \sf (x-4) (x-4)⟹(x−4)(x−4)

3. 4a² - 36a

→ 4a² - 36a

→ 4a(a - 9)

4. 27x³ - y³

→ (3x - y)(9x² + 3xy + y²)

5. 6x² + x - 2

→ (3x + 2)(2x - 1)

Note down:-

The factorization is a method to find factors of the given polynomial.

They are generally written as products of other factors.

To factories, a quadratic polynomial splitting the middle term is widely used.

While identities and simplification can also be used in factorization.

To factorize a quadratic equation splitting the middle term is much preferred.

We search for a set of number which will add together to the middle term. And also the same set of numbers should give a product as the last term.

If p(a) = 0, p(b) = 0, then 'a,' and 'b' are factors. Now, you need to find what all possible values 'a' and 'b' could take where constant term = a.b (375000 in this question.)

Answer 2

Answer:

For factoring polynomials, "factoring" (or "factoring completely") is always done using some set of numbers as possible coefficient cannot be factored over the real numbers, but over the complex numbers it factors as