Question

complete factor
1.4x²-9y²z⁴

2.x²-8×+16

3.4a²-36a

4.27x³-y³

5.6x²+x-2​

Answer 1

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:

$\implies \sf (x-4) (x-4)$

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

Step-by-step explanation:

Answer ( 1 )

.

→ 4x² - 9y²z⁴

→ -9y²z⁴ + 4x²

→ (3yz² + 2x) (-3yz²+2x)

Answer ( 2 )

2.x²-8×+16

→ x² - 4x - 4x + 16

→ x( x - 4 ) - 4 ( x - 4 )

→ ( x - 4 ) ( x - 4 )

Answer ( 3 )

3.4a²-36a

→ 4 a ( a - 9 )

→ ( 4 a )( a - 9)

Answer ( 4 )

4.27x³-y³

→ (3x - y)(9x² + 3xy + y²)

Answer ( 5 )

5.6x²+x-2

→ 6x² + 4 x - 3x - 2

→ 2x ( 3x + 2 ) - 1 ( 3x + 2 )

→ ( 2x - 1 ) ( 3x + 2 )