Mathematics, 21.01.2021 05:00 chimmyy14

Factor 3a^3 + 18a² + 8a + 48 completely.

Answers: 3

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Answers

Answer from: Yeetadab1974

(3a2 + 8) • (a - 6)

Step-by-step explanation:

STEP 1:

Equation at the end of step 1

(((3 • (a3)) - (2•32a2)) + 8a) - 48

STEP 2:

Equation at the end of step 2:

((3a3 - (2•32a2)) + 8a) - 48

STEP 3:

Checking for a perfect cube

3.1 3a3-18a2+8a-48 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 3a3-18a2+8a-48

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: 8a-48

Group 2: -18a2+3a3

Pull out from each group separately :

Group 1: (a-6) • (8)

Group 2: (a-6) • (3a2)

Add up the two groups :

(a-6) • (3a2+8)

Which is the desired factorization

Polynomial Roots Calculator :

3.3 Find roots (zeroes) of : F(a) = 3a2+8

Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0

It would only find Rational Roots that is numbers a which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 3 and the Trailing Constant is 8.

The factor(s) are:

of the Leading Coefficient : 1,3

of the Trailing Constant : 1 ,2 ,4 ,8

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

Answer from: Quest

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

Bwill make the inequalities y < 2x + 1 and y> -x- 2 true. o a. region b o b. region c o c. r

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Factor 3a^3 + 18a² + 8a + 48 completely....