Mathematics, 17.09.2021 09:20 aliozochika

Help me with solution please =(

Answers: 1

Show answers

Answers

Answer from: benwill0702

Step-by-step explanation:

please mark me as brainlest and follow me

Answer from: lilay30

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

Factorise the polynomials.

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

1. b² + 8b + 7

$\sf \: b ^ { 2 } + 8 b + 7$

Factor the expression by grouping. First, the expression needs to be rewritten as b²+pb+qb+7. To find p and q, set up a system to be solved.

$\sf \: p+q=8 \\ \sf pq=1\times 7=7$

As pq is positive, p and q have the same sign. As p+q is positive, p and q are both positive. The only such pair is the system solution.

$\sf \: p=1 \\ \sf \: q=7$

Rewrite $\sf\:b^{2}+8b+7 \: as \: \left(b^{2}+b\right)+\left(7b+7\right)$ .

$\sf \: \left(b^{2}+b\right)+\left(7b+7\right)$

Take out the common factors.

$\sf \: b\left(b+1\right)+7\left(b+1\right)$

Factor out common term b+1 by using distributive property.

$\boxed{\boxed{ \bf \: \left(b+1\right)\left(b+7\right) }}$

__________________

2. 4x² + 4x + 1

$\sf \: 4 x ^ { 2 } + 4 x + 1$

Factor the expression by grouping. First, the expression needs to be rewritten as 4x²+ax+bx+1. To find a and b, set up a system to be solved.

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

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.

$\sf \: 1,4 \\ \sf 2,2$

Calculate the sum for each pair.

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

The solution is the pair that gives sum 4.

$\sf \: a=2 \\ \sf b=2$

Rewrite $\sf4x^{2}+4x+1 as \left(4x^{2}+2x\right)+\left(2x+1\right)$ .

$\sf \: \left(4x^{2}+2x\right)+\left(2x+1\right)$

Factor out 2x in 4x² + 2x.

$\sf \: 2x\left(2x+1\right)+2x+1$

Factor out common term 2x+1 by using distributive property.

$\sf\left(2x+1\right)\left(2x+1\right)$

Rewrite as a binomial square.

$\boxed{ \boxed{\bf\left(2x+1\right)^{2}} }$

__________________

3. 5n² + 10n + 20

$\sf \: 5 n ^ { 2 } + 10 n + 20$

Factor out 5. Polynomial n² + 2n+4 is not factored as it does not have any rational roots.

$\boxed{\boxed{\bf5\left(n^{2}+2n+4\right)} }$

__________________

4. m³ - 729

$\sf \: m ^ { 3 } - 729$

Rewrite m³-729 as m³ - 9³. The difference of cubes can be factored using the rule: $a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right)$ . Polynomial m²+9m+81 is not factored as it does not have any rational roots.

$\boxed{ \boxed{ \bf \: \left(m-9\right)\left(m^{2}+9m+81\right) }}$

__________________

5. x² - 81

$\sf \: x ^ { 2 } - 81$

Rewrite x²-81 as x² - 9². The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .

$\boxed{ \boxed{ \bf\left(x-9\right)\left(x+9\right) }}$

__________________

6. 15x² - 17x - 4

$\sf \: 15 x ^ { 2 } - 17 x - 4$

Factor the expression by grouping. First, the expression needs to be rewritten as 15x²+ax+bx-4. To find a and b, set up a system to be solved.

$\sf \: a+b=-17 \\ \sf \: ab=15\left(-4\right)=-60$

As ab is negative, a and b have the opposite signs. As a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -60.

$\sf \: 1,-60 \\ \sf 2,-30 \\ \sf3,-20 \\ \sf4,-15 \\ \sf5,-12 \\ \sf 6,-10$

Calculate the sum for each pair.

$\sf \: 1-60=-59 \\ \sf 2-30=-28 \\ \sf3-20=-17 \\ \sf4-15=-11 \\ \sf5-12=-7 \\ \sf6-10=-4$

The solution is the pair that gives sum -17.

$\sf \: a=-20 \\ \sf \: b=3$

Rewrite $\sf15x^{2}-17x-4$ as $\sf \left(15x^{2}-20x\right)+\left(3x-4\right)$ .

$\sf\left(15x^{2}-20x\right)+\left(3x-4\right)$

Factor out 5x in 15x²-20x.

$\sf \: 5x\left(3x-4\right)+3x-4$

Factor out common term 3x-4 by using distributive property.

$\boxed{\boxed{ \bf\left(3x-4\right)\left(5x+1\right) }}$

Answer from: Quest

answer: the correct one is a

step-by-step explanation:

Answer from: Quest

$\frac{a^{2} }{4}$

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. a vending machine will only accept coins weighing between 5.48 g and 5.82 g. what percentage of legal quarters will be rejected? round your answer to two decimal places.

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

Mozart lenses inc. recently introduced seelites, a thinner lens for eyelasses. of a sample of 800 eyeglass wearers, 246 said they would purchases their next pair of eyeglasses with the new lenses. lenses inc. estimates that the number of people who purchase eyeglasses in a year is 1,700,000. most eyeglasses wearer buy one new pair of eyeglasses a year. what is the annual sales potential for the new lenses.

Answers: 1

Answer

Mathematics, 21.06.2019 20:10

Ascientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live for one week without producing any additional offspring. each replicated organism also replicates at the same rate. at hour one, there is one organism. at hour two, there are five more organisms. how many total organisms are there at hour seven? 2,801 19,531 19,607 97.655

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Solve each quadratic equation by factoring and using the zero product property. [tex]x^2+6x+8=0[/tex]

Answers: 2

Answer

You know the right answer?

Help me with solution please =(
...

Questions