This is for my friend, lolzsecondacc1.

Can you please help me give the Complete solution <br><br>(nonsence report )

Tasya [4]

$\huge \boxed{\mathfrak{Question} \downarrow}$

Factorise the polynomials.

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

__________________

${x}^{2} + 4x + 4$

Factor the expression by grouping. First, the expression needs to be rewritten as x²+ax+bx+4. To find a and b, set up a system to be solved.

$a+b=4 \\ ab=1\times 4=4$

As ab is positive, a and b have the same sign. As a+b is positive, a and b are both positive. List all such integer pairs that give product 4.

$1,4 \\ 2,2$

Calculate the sum for each pair.

$1+4=5 \\ 2+2=4$

The solution is the pair that gives sum 4.

$a=2 \\ b=2$

Rewrite x² + 4x + 4 as (x² + 2x) + (2x + 4)

$\left(x^{2}+2x\right)+\left(2x+4\right)$

Take out the common factors.

$x\left(x+2\right)+2\left(x+2\right)$

Factor out common term x+2 by using distributive property.

$\left(x+2\right)\left(x+2\right)$

Rewrite as a binomial square.

$b. \: \: \boxed{ \boxed{{(x + 2)}^{2} }}$

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$x ^ { 2 } - 8 x + 16$

Factor the expression by grouping. First, the expression needs to be rewritten as x²+ax+bx+16. To find a and b, set up a system to be solved.

$a+b=-8 \\ ab=1\times 16=16$

As ab is positive, a and b have the same sign. As a+b is negative, a and b are both negative. List all such integer pairs that give product 16.

$-1,-16 \\ -2,-8 \\ -4,-4$

Calculate the sum for each pair.

$-1-16=-17 \\ -2-8=-10 \\ -4-4=-8$

The solution is the pair that gives sum -8.

$a=-4 \\ b=-4$

Rewrite x²-8x+16 as $\left(x^{2}-4x\right)+\left(-4x+16\right)$ .

$\left(x^{2}-4x\right)+\left(-4x+16\right)$

Take out the common factors.

$x\left(x-4\right)-4\left(x-4\right)$

Factor out common term x-4 by using distributive property.

$\left(x-4\right)\left(x-4\right)$

Rewrite as a binomial square.

$d. \: \: \boxed{\boxed{\left(x-4\right)^{2} }}$

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$4 x ^ { 2 } + 12 x y + 9 y ^ { 2 }$

Use the perfect square formula, $a^{2}+2ab+b^{2}=\left(a+b\right)^{2}$ , where a=2x and b=3y.

$e. \: \: \boxed{ \boxed{\left(2x+3y\right)^{2} }}$

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$x ^ { 4 } - 2 x ^ { 2 } + 1$

To factor the expression, solve the equation where it equals to 0.

$x^{4}-2x^{2}+1=0$

By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term 1 and q divides the leading coefficient 1. List all candidates p/q.

$± \: 1$

Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

$x=1$

By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x⁴-2x²+1 by x-1 to get x³+x²-x-1. To factor the result, solve the equation where it equals to 0.

$x^{3}+x^{2}-x-1=0$

By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term -1 and q divides the leading coefficient 1. List all candidates p/q.

$± \: \: 1$

Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

$x=1$

By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x³+x²-x-1 by x-1 to get x²+2x+1. To factor the result, solve the equation where it equals to 0.

$x^{2}+2x+1=0$

All equations of the form ax²+bx+c=0 can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$ . Substitute 1 for a, 2 for b and 1 for c in the quadratic formula.

$x=\frac{-2±\sqrt{2^{2}-4\times 1\times 1}}{2} \\$

Do the calculations.

$x=\frac{-2±0}{2} \\$

Solutions are the same.

$x=-1$

Rewrite the factored expression using the obtained roots.

$\left(x-1\right)^{2}\left(x+1\right)^{2} \\ = a. \: \: \boxed{ \boxed{\left(x^{2}-1\right)^{2}}}$

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<em>Refer to the attached picture too.</em>

7 0

3 years ago

☑️ANSWER NEEDED QUICK,BRAINLIEST TO THE CORRECT ANSWER〰️

zubka84 [21]

Yes, because 2 is less than 3.
2(4)-6<3
8-6<3
2<3

4 0

3 years ago

Jack's bank account had a balance of -$25.48 last week. His paycheck of $393.69 was deposited this week. If there have been no

larisa [96]

Answer:

B

Step-by-step explanation:

because -25.48 - 393.69 is?

B) jacks current account balance is 368.21

6 0

3 years ago

Hi po pahelp ito pls pls pls pls pls pls pls

kodGreya [7K]

conversion of temperature

buying groceries

checking weight

measuring length

8 0

3 years ago

5 types of kitchen accidents and how to prevent them

Shalnov [3]

Answer:

Cutting any kind of fruit or vegetable. Prevent this by wearing gloves in the kitchen.
Forgotten kitchen spills are a major tripping hazard. Prevent this by not spilling anything, or if when you do, clean it up right away.
Washing dishes can result in knicks of plates and bowls, even even washing a knife improperly can harm you. Prevent this by being extra cautious when washing anything.
Unstable cutting boards are asking for improper cuts. Prevent this by only cutting on a surface that is level, sturdy, and reliable.
Skin contact with Chile Powder, or any kind of harmful cleaning substance.

Thanks so much for letting me help!!

8 0

4 years ago

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