Adding/ Subtracting
(2x^2+3x-1)+(x^2+2x+5)
3x^2+5x+4
2x(x^2+2x+3)
2x^3+4x^2+6x
What is the factored form of this expression? How do you know?
x^2-7x+12
The product of -4 and -3 is 12, and the sum is -7.
(x-4)(x-3)
According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example:
c^6*c^4
add
(3x^2-2x-5)+(2x^2+x-10)
5x^2-x-15
(3x-5)(3x-5)
9x^2-30x+25
Factor the difference of squares:
x^2-64
(x+8)(x-8)
According to exponent rules, when we raise the power to a power we _______ the exponents.
Example:
(d^2)^5
multiply
(3x^2-2x^3+4x)+(2x^3-2x+5)
3x^2+2x+5
(2x+3)(3x-2)
6x^2+5x-6
Factor:
3x^2+9x-30
Had to factor the GCF first, then X-method
3(x+5)(x-2)
Classify the following by terms (monomial, binomial, trinomial, other)
2p^4+p^3
1
-5n^4+10n-10
-8n^4+5n^3-2n^2-8n
2p^4+p^3 - binomial
1 - monomial
-5n^4+10n-10 - trinomial
-8n^4+5n^3-2n^2-8n - other (aka polynomial)
(3x^5-2x^4-5)-(2x^4+x^2-10)
3x^5-4x^4-x^2+5
(2x+1)(x^2-4x+5)
2x^3-7x^2+6x+5
What are the factors of
3x^2-5x-12
(3x+4)(x-3)
Classify the polynomial by degree and terms. Is it in standard form? What is the degree? What is the leading coefficient? How many terms does it have?
-4x^3+3x^2-1
Cubic trinomial
Yes it is in standard form (highest to lowest exponent)
degree is 3 (highest exponent)
leading coefficient is -4 (number at front)
has 3 terms
(3ab-2a^2+5b)-(4a^2-2ab+2)
-6a^2+5ab+5b-2
Multiply the polynomials (x+3)(2x−4). What is the product in the form
ax^2+bx+c
Find the coefficients:
a=_____
b=____
c=____
a= 2
b= 2
c= -12
The following polynomial is a perfect square trinomial. What is the value of k?
f(x)=x^2+kx+81
if it is a perfect square, then both factors are the same. we know that 9 times 9 is 81. So, if we add 9 + 9, we get 18.
k = 18
On a windy morning, a hot air balloon starts ascending and flying away from the top of a hill. The altitude, h(x), in feet of the balloon x hours after starting its ascent can be modeled by the function:
h(x)=-16x^2+56x+96
If factoring to find the roots, what would be the greatest common factor to pull out to begin?
It just wants the GCF.
GCF = 8