(18x^4 + 21x^3) ÷ 3x^2=___
Answers
Dont forget to mark me brainliest
STEP 1
Equation at the end of step 1
STEP 2
Equation at the end of step 2
STEP 3
Equation at the end of step 3
STEP 4
Equation at the end of step 4
STEP 5
18x4 + 21x3 + 9x2
Simplify —————————————————
3x2 + 2
STEP 6
Pulling out like terms
6.1 Pull out like factors :
18x4 + 21x3 + 9x2 = 3x2 • (6x2 + 7x + 3)
Trying to factor by splitting the middle term
6.2 Factoring 6x2 + 7x + 3
The first term is, 6x2 its coefficient is 6 .
The middle term is, +7x its coefficient is 7 .
The last term, "the constant", is +3
Step-1 : Multiply the coefficient of the first term by the constant 6 • 3 = 18
Step-2 : Find two factors of 18 whose sum equals the coefficient of the middle term, which is 7 .
-18 + -1 = -19
-9 + -2 = -11
-6 + -3 = -9
-3 + -6 = -9
-2 + -9 = -11
-1 + -18 = -19
1 + 18 = 19
2 + 9 = 11
3 + 6 = 9
6 + 3 = 9
9 + 2 = 11
18 + 1 = 19
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Polynomial Roots Calculator :
6.3 Find roots (zeroes) of : F(x) = 3x2+2
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x 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 2.
The factor(s) are:
of the Leading Coefficient : 1,3
of the Trailing Constant : 1 ,2
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 5.00
-1 3 -0.33 2.33
-2 1 -2.00 14.00
-2 3 -0.67 3.33
1 1 1.00 5.00
1 3 0.33 2.33
2 1 2.00 14.00
2 3 0.67 3.33
Polynomial Roots Calculator found no rational roots
Polynomial Long Division :
6.4 Polynomial Long Division
Dividing : 6x2+7x+3
("Dividend")
By : 3x2+2 ("Divisor")
dividend 6x2 + 7x + 3
- divisor * 2x0 6x2 + 4
remainder 7x - 1
Quotient : 2
Remainder : 7x-1
Final result :
3x2 • (6x2 + 7x + 3)
————————————————————
3x2 + 2
See results of polynomial long division:
1. In step #06.04