Add Polynomials
Find the sum in standard form:
(8x-2)+(-3x^2-7)
-3x^2+8x-9
Find the difference in standard form:
(3x^2+1)-(4+2x^2)
x^2-3
Rewrite in standard form:
(2x+6)(x+9)
2x^2+24x+54
Find the quotient: (if possible, write in factored form)
(2x^3+13x^2+26x+24)/(x+4)
2x^2 +5x+6
A student simplified (3x2+4x−5)−(2x2−3x+7) and got 5x2+x−2. What mistake did they make?
The mistake is in distributing the negative sign. The correct solution is:
(3x2+4x−5)−2x2+3x−7=x2+7x−12
Find the sum in standard form:
(3x^3+8x^2+7)+(3x^2+11)
3x^3+11x^2+18
(x^2+3x+3)-(7x^2-x-1)
-6x^2+4x+4
Rewrite in standard form:
-4x(12x^3-8x^2+7x+3)
-48x^4+32x^3-28x^2-12x
Find the quotient: (if possible, write in factored form)
(x ^ 3 +6x^ 2 +11x+6 )/(x+3)
x ^2 +3x+2
or
(x+1)(x+2)
I am a polynomial with exactly three terms. My leading coefficient is 2, my degree is 3, and my constant term is -4. What could I be?
Many answers - Mr. J will verify
Example:
2x^3+x-4
Find the sum in standard form:
(8x^3-6x^2+9x+12)+(-8x^3+6x^2-9x-12)
0
(7x^4+70x^2-19x-41)-(16x^4-8x^3+37x^2-19x-82)
-9x^4+8x^3+33x^2+41
Rewrite in standard form:
(3x-5)(x^2+x+5)
3x^3-2x^2+10x-25
Find the quotient (in factored form if possible):
(x^ 3 +9x^ 2 +26x+24)/(x+3)
x ^2 +6x+8
or
(x+4)(x+2)
Is (x-2) a factor of f(x)=4x3+3x2-2x+5? Explain or show how you know.
No, because f(2)=45. If x-2 is a factor, then f(2) should equal 0.
(3x^4+8x^3-12x^2+27)+(-6x^4+13x^3+18x-30)
-3x^4+21x^3-12x^2+18x-3
Find the difference in standard form:
(14x^4+11x^2-9x^5)-(-14+5x^5-11x^2)
-14x^5+14x^4+22x^2+14
Rewrite in standard form:
(-3x+5)(4x^3-2x^2-7x-5)
-12x^4+26x^3+11x^2-20x-25
Use synthetic division to find the result when
x^4−14x^3+27x^2−18x+9
is divided by
x-2
. If there is a remainder, express the result in the form
q(x)+(b(x))/(r(x)
.
2x ^ 3 −10x^ 2 +7x−4+ 1/(x−2
A student tried to multiply (x+3)(x2−2x+4) and got: x3−2x2+4x+3. What mistake did they make? What is the correct product?
The mistake is that the student only distributed the x and did not distribute the 2. The correct product is x3+x2-2x+12.
Find the sum in standard form:
(9x^2-13x^5-10+6x^3+4x)+(5x^3-8x^2+14x^5+24-4x^4)
x^5-4x^4+11x^3+x^2+4x+14
Find the difference in standard form:
(4x^2+7x^3)-(-6x^2-7x^3-4x)-(10x+9x^2)
14x^3+x^2-14x
Rewrite in standard form:
(3x^2-x-7)(2x^2+x+2)
6x^4+x^3-9x^2-9x-14
Use synthetic division to find the result when
x^4−6x^2−x−19
is divided by
x-3
. If there is a remainder, express the result in the form
q(x)+(b(x))/(r(x)
.
x^3 +3x^ 2 +3x+8+5/( x−3
Write a polynomial equation that meets these conditions:
A degree of 4
Three terms
A negative leading coefficient
A constant term of 7
Many answers. Example-: -x4+x3+x+7