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Mariulka [41]
3 years ago
9

What is factorisation ​

Mathematics
1 answer:
liubo4ka [24]3 years ago
6 0

Factorization is a method of writing numbers as the product of their factors or divisors.

<em><u>Solution:</u></em>

<em><u>Factorisation:</u></em>

Factorization is a method of writing numbers as the product of their factors or divisors.

In other words we can say, Finding what to multiply together to get an expression.

It is like "splitting" an expression into a multiplication of simpler expressions.

<em><u>Methods of factorisation:</u></em>

  • Factoring out the GCF
  • The sum-product pattern
  • The grouping method
  • The perfect square trinomial pattern
  • The difference of squares pattern

<em><u>Factoring out the GCF:</u></em>

This methods means that factoring out common factors

For example:

12x^2 + 3x = 3x(4x + 1)

This can be used when each term in given expression shares a common factor

<em><u>The sum-product pattern</u></em>

A quadratic equation may be expressed as a product of two binomials

For example:

x^2 + 7x + 12 = (x + 3)(x + 4)

This method can be used for quadratic equations of form ax^2 + bx + c = 0

<em><u>The grouping method</u></em>

If the polynomial is of the form  ax^2 + bx + c and there are factors of ac that add up to b , we can use this method

For example:

2x^2 + 7x + 3\\\\2x^2 + 6x + 1x + 3\\\\2x(x + 3) + 1(x + 3)\\\\(x + 3)(2x + 1)

<em><u>The perfect square trinomial pattern</u></em>

If the first and last terms are perfect squares and the middle term is twice the product of their square roots , we can use this method

For example:

x^2 + 10x + 25\\\\(x + 5)^2

<em><u>The difference of squares pattern</u></em>

If the expression represents a difference of squares, we can use this method

Because a^2 - b^2 = (a + b)(a - b)

For example:

x^2 - 25\\\\x^2 - 5^2\\\\(x + 5)(x - 5)

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Find the dimensions of a rectangle with a perimeter of 52cm if it’s length is 4cm more than its width
Zina [86]
So the perimeter(P) of a rectangle would be:
P= 2L+2W
L being the length and W being the width.
The problem says the length is 4cm more than the width, so L= 4+W.
So if we substitute L with 4+W, we get:
P= 2(4+W) + 2W
Use the Distributive Property
P= 8+2W+2W
Combine like terms
P=8+4W
Since we're given the perimeter, we could replace P with 52. So:
52=8+4W
Subtract 8 to both sides
44=4W
Divide 4 to both sides
11=W
Therefore, the width is 11cm
And since the length is 4cm more than the width, we could add 4cm to 11cm to find that the length is 15cm
Thus, the dimensions of the rectangle are 15cm by 11cm
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3 years ago
A.45<br> B.30<br> C.90<br> D.180<br> E.40<br> F.55<br> G.130<br> H.50
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Answer:

m<4=40

Step-by-step explanation:

Supplementary angles form 180 degrees

m<3 is vertical to the 50 degree angle which is equal.

so. m<3=50

m<5=90

90+50=140

180-140=40

m<4=40

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Bills plant grew at the rate of 1 1/2. How tall would the plant be after 3 weeks
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Answer:

9/2 or 4 1/2

Step-by-step explanation:

you do 1 1/2 times 3

3/2 times 3 equals

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Alexa worked 30 hours last week and earned $450. Her pay has now been increased by 20%. Which equation describes her new rate of
vesna_86 [32]

Answer:

p=18h

or

p=\dfrac{450}{30}\cdot 1.2\cdot h

Step-by-step explanation:

If Alexa worked 30 hours last week and earned $450, then her hourly payment is

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Her payment has now been increased by 20%, so her hourly payment becomes

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If she worked h hours, then she earned \$18h. If her new payment is p, then

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or

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3 years ago
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