5.1 & 5.2
How many terms does a binomial have?
A binomial has 2 terms (Ex. 6x+7)
What is the number one think to look for when factoring polynomials?
The GCF
What is the first step to take when factoring? (Hint:think fo the values a,b,and c)
If a = 1, there will be two numbers with a product of “c” and a sum of “b”.
If a≠1, what's the first step you have to take to factor the quadratic?
Multiply the a and c values together, but keep the b value the same
Factor.
36w2-49
(6w-7)(6w+7)
Expand and simplify
(7g-3h)(7g+3h)
49g2 _ 9h2
4n2p3+10n4p2-12n3p2
2n2p2(2p+5n-6n)
Determine the value of b so that x2+bx+8 can be factored.
4 and 2
or
8 and 1
The height, h, in metres, of a toy rocket at any time, t, in seconds, during its flight can be estimated using the formula h=-5t2+23t+10. Write the formula in factored form and determine when the rocket will fall to the ground.
h=-(5t+2)(t-5)
The rocket will fall to the ground at 5s.
Determine two values of k so that the trinomial can be factored as a difference of squares.
m2-kn2
Answers will vary. Ex. 4, 9, 16...
Expand and simplify
(6x-5)2- 4x(9x-15)
25
Solve:
16v2-12v-12v+9
(4v-3)2
Factor
3x2+24x+45
3(x+5)(x+3)
Find two values of n so that each trinomial can be factored over the integers.
3y2+ny+25
28, 20
Factor the following
w2+25
Not factorable because addition isn't a difference of squares
Expand and simplify
-5(3x-1)(5x-2)+6(6x+3)(5x-2)
105x2+73x-46
Factor the following binomial:
3x(y+2)-6x2(y+2)
(y+2)(3x)(1-2x)
Determine two values of c so that x2-3x-c can be factored.
1) -5 and 2
2) -7 and 4
Explain how to solve the following quadratic:
5h2-14h-3
(5h+1)(h-3)
Factor.
9a2b2-24abcd+16c2d2
(3ab-4cd)2
Expand and simplify
A scuba diver is drifting in a current of 0.3 m/s. If she swims with the current at an additional speed of v metres per second, the distance, d, in metres, that she travels before running out of air can be modelled by the relation d=3000(v+0.3)(1.0-v).
a) Expand this relation.
b) If she swims at 0.2 m/s, how far can she swim before running out of air?
a) 2100v - 3000v2 + 900
b) 1200m
A rectangle has an area of x2+3x-10
a) determine possible expressions for the length and width
b) What would the length and width be if x=10
a) (x-2)(x+5)
b) Length= 8cm
Width = 15cm
The height of a ball thrown from the top of a building can be approximated by the formula h=-5t2+15t+20, where t is the time, in seconds, and h is the height, in metres.
a) Write the formula in factored form
a) h=-5(t+1)(t-4)
Factor the following:
2(x+a)22+3(x+a)+1
a) (2x+2a+1)(x+a+1)
Is x2-1 the same as (x-1)2? Explain using words.
No. The quadratic (x-1)2=(x-1)(x-1), while x2-1= (x-1)(x+1). The two factored expressions are not equivalent.