(4x^4+13x^3+6x^2+11x+19) divided by (4x+5)?

Question

I need to know the andwer in the form of
Q(x) + R(x)/4x+5

I have tried, but my pencil is wearing down..
confused about the answer form
Help me solve?

I believe the form is the terms
and the remainder

no fractions?

Answer 1

Hi Dear Franklin ;

4x^4 +13x^3 + 6x^2 + 11x +19 ÷ 4x+5

▪Step1
(4x+5 ) ( x ^ 3) = 4 x^4 + 5x^3 ; { let R1 = x ^3}
4x^4 +13x^3 + 6x^2 + 11x +19 - ( 4 x^4 + 5x^3 ) =
4x^4 +13x^3 + 6x^2 + 11x +19 - 4 x^4 - 5x^3 = 8 x^3 + 6x^2 + 11x + 19 {remainder}

▪Step 2
8 x^3 + 6x^2 + 11x + 19 ÷ 4x+5
(4x+5) * (2x^2) = 8 x^3 + 6x^2 ; { let R2 =2x^2 }
8 x^3 + 6x^2 + 11x + 19 - ( 8 x^3 + 6x^2) =
8 x^3 + 6x^2 + 11x + 19 - 8 x^3 - 6x^2 = - 4x^2 + 11x + 19 {remainder}

▪Step 3
- 4x^2 + 11x + 19 ÷ 4x+5
(4x+5)(-x ) = - 4x^2 - 5x ; { let R3 = -x }
- 4x^2 + 11x + 19 - ( - 4x^2 - 5x ) =
- 4x^2 + 11x + 19 + 4x^2+ 5x = 16x + 19 {remainder}


▪Step 4
16x + 19 ÷ 4x+5
(4x+5)( 4 ) = 16x + 20 ; { let R4 = 4 }
16x + 19 - ( 16x + 20 ) =
16x + 19 - 16x - 20 = -1 {remainder}

▪Step 5
Sum R1 , R2 , R3 , R4
R1 + R2 + R3 + R4
x^3 + 2x^2 - x + 4
(4x^4+13x^3+6x^2+11x+19) ÷ (4x+5) = R1 + R2 + R3 + R4
So;
(4x^4+13x^3+6x^2+11x+19) ÷ (4x+5) = x^3 + 2x^2 - x + 4

Q(x) = x^3 + 2x^2 - x + 4
R(x) = -1

Good Luck

Answer 2

Q(x) is the quotient, which is a polynomial, and R(x) is the remainder, which will be a constant, since the divisor, 4x+5, only has degree one.

First, divide the leading terms of both polynomials: 4x^4 / 4x = x^3, so x^3 is the leading term of your quotient.

Now, subtract x^3(4x+5):
(4x^4+13x^3+6x^2+11x+19) - x^3(4x+5) =
(4x^4+13x^3+6x^2+11x+19) - 4x^4 - 5x^3 =
8x^3+6x^2+11x+19.

Now divide leading terms again: 8x^3/4x = 2x^2, so that is the next term in your quotient.

Subtract, again:
8x^3+6x^2+11x+19 - 2x^2(4x+5) =
8x^3+6x^2+11x+19 - 8x^3 - 10x^2 =
-4x^2+11x+19

Divide leading terms again: -4x^2/4x = -x, which is the 3rd term in your quotient.

Subtract:
-4x^2+11x+19 - (-x)(4x+5) =
-4x^2+11x+19 + 4x^2 + 5x =
16x + 19.

Divide leading terms once more: 16x/4x = 4, so 4 is the last term in your quotient.

16x+19 - 4(4x+5) = 16x+19-16x-20 = -1, so the remainder R(x) is -1.

Your quotient is
Q(x) = x^3 + 2x^2 - x + 4.

Answer 3

4x+5)4x^4 + 13x^3 +6x^2 +11x +19 (x^3+2x^2-x+4
4x^4 + 5x^3
8x^3 +6x^2
8x^3 +10x^2
-4x^2 +11x
-4x^2 -5x
16x +19
16x +20
-1
Q=x^3+2x^2-x+4
the answer=x^3+2x^2-x+4+[-1/(4x+5)]

Answer 4

4x^4+13x^3+6x^2+11x+19

= x^3(4x+5) - 5x^3 + 13x^3 + 6x^2 + 11x + 19 ( make 4x divide 4x^4 keeping 4x+5 and subtract 5x^3 to cancell out)
= x^3(4x+5) +8x^3 + 6x^2 +11x+19
= x^3(4x+5)+ 2x^2(4x+5) - 10x^2+6x^2+ 11x+19
= (x^3+2x^2)(4x+5) - 4x^2 + 11x +19
= (x^3+2x^2)(4x+5) -x(4x+5)+5x+11x+19
= (x^3+2x^2-x)(4x+5) + 16x+19
= (x^3+2x^2-x)(4x+5) + 4(4x+5) -20 +19
= (x^3+2x^2-x+4)(4x+5)-1

Q(x) = x^3+2x^2-x+4
R(x) = -1

Answer 5

the first term is x^3. Then there's fractions involved, and I don't do fractions.

Answer 6

Use a calculator dumb ****