adding and subtracting polynomials
how do you add and subtract polynomials?
To add polynomials, add like terms. You can use a vertical or a horizontal format. To subtract a polynomial, add its opposite. To find the opposite of a polynomial,multiply each of its terms by −1.
How do you solve multiplying polynomial equations?
By multiplying two binomials using the FOIL Method, find the sum of the products
What does factor form mean?
An equation is considered to be in factored form when the product of the factors is equal to 0. Match each factored form of the equation with its equivalent standard form and nonstandard form.
How do you do zero- product property?
When one side of an equation is a polynomial in factored form and the other side is 0, use the Zero-Product Property to solve the polynomial equation. The solutions of a polynomial equation are also called roots.
What is the equation for difference of two squares
a2 − b2= (a + b)(a − b)
(5y + 4) + (−2y + 6)
=3y+10
(m – 3)(m − 7)
=m2 - 10m + 21
x(x + 2)
= (x − 3)(x + 8)
Equation for zero-product property
If a and b are real numbers and ab = 0, then a = 0 or b = 0.
x2 − 9 = x2 − 32
= (x + 3)(x − 3)
(a2 − 3ab + 2b2)+ (−4a2 + 5ab − b2)
= -3a2 + 2ab + b2
(x + 5)(x2 − 3x − 2).
= x3 + 2x2 − 17x − 10.
5x2+ 15x + 10 = 5(x2 + 3x + 2)
= 5(x + 1)(x + 2)
2x(x − 4) = 0
x = 0 or x = 4
x2 − 25 = x2 − 52
= (x + 5)(x − 5)
(4x2 − 3x + 5) − (3x2− x − 8) = 4x2− 3x + 5 − 3x2 + x + 8
=x2− 2x + 13
(2x + 1)(3x − 5) = 2x(3x) + 2x(−5) + 1(3x) + 1(−5)
= 6x2 − 7x − 5
4x2 + 13x + 3
= (x + 3)(4x + 1).
(x − 3)(x − 9) = 0
x = 3 or x = 9
4z2− 1 = (2z)2 − 12
(2z + 1)(2z − 1).
(3x2 + x − 6) +(x2+ 4x + 10) = (3x2 + x2) + (x + 4x)+(−6 + 10)
=4x2+ 5x + 4
x2 − 2x − 35 when x = 18.
= 253
3x2 − 7x + 2
= (x − 2)(3x − 1)
(x − 1)2 = 0
x = 1 or x = 1
x2+ 6x + 9 = x2+ 2(x)(3) + 32
= (x + 3)2