aa section 11-2
TRANSCRIPT
Section 11-2Polynomials and Geometry
Sunday, March 1, 2009
Warm-up
A box is 21 mm long, 13 mm wide, and 9 mm high. Find the volume and surface area.
Sunday, March 1, 2009
Warm-up
A box is 21 mm long, 13 mm wide, and 9 mm high. Find the volume and surface area.
V = lwh
Sunday, March 1, 2009
Warm-up
A box is 21 mm long, 13 mm wide, and 9 mm high. Find the volume and surface area.
V = lwh = 21(13)(9)
Sunday, March 1, 2009
Warm-up
A box is 21 mm long, 13 mm wide, and 9 mm high. Find the volume and surface area.
V = lwh = 21(13)(9) = 2457 mm3
Sunday, March 1, 2009
Warm-up
A box is 21 mm long, 13 mm wide, and 9 mm high. Find the volume and surface area.
V = lwh = 21(13)(9) = 2457 mm3
SA = 2lw + 2lh + 2hw
Sunday, March 1, 2009
Warm-up
A box is 21 mm long, 13 mm wide, and 9 mm high. Find the volume and surface area.
V = lwh = 21(13)(9) = 2457 mm3
SA = 2lw + 2lh + 2hw= 2(21)(13) + 2(21)(9) + 2(13)(9)
Sunday, March 1, 2009
Warm-up
A box is 21 mm long, 13 mm wide, and 9 mm high. Find the volume and surface area.
V = lwh = 21(13)(9) = 2457 mm3
SA = 2lw + 2lh + 2hw= 2(21)(13) + 2(21)(9) + 2(13)(9)
= 546 + 378 + 234
Sunday, March 1, 2009
Warm-up
A box is 21 mm long, 13 mm wide, and 9 mm high. Find the volume and surface area.
V = lwh = 21(13)(9) = 2457 mm3
SA = 2lw + 2lh + 2hw= 2(21)(13) + 2(21)(9) + 2(13)(9)
= 546 + 378 + 234= 1158 mm2
Sunday, March 1, 2009
3x
3x + 3
3x2 + 3x + 3
Anything else:
Sunday, March 1, 2009
3x
3x + 3
3x2 + 3x + 3
Anything else:
Monomial
Sunday, March 1, 2009
3x
3x + 3
3x2 + 3x + 3
Anything else:
Monomial (One term)
Sunday, March 1, 2009
3x
3x + 3
3x2 + 3x + 3
Anything else:
Monomial (One term)
Binomial
Sunday, March 1, 2009
3x
3x + 3
3x2 + 3x + 3
Anything else:
Monomial (One term)
Binomial (Two terms)
Sunday, March 1, 2009
3x
3x + 3
3x2 + 3x + 3
Anything else:
Monomial (One term)
Binomial (Two terms)
Trinomial
Sunday, March 1, 2009
3x
3x + 3
3x2 + 3x + 3
Anything else:
Monomial (One term)
Binomial (Two terms)
Trinomial (Three terms)
Sunday, March 1, 2009
3x
3x + 3
3x2 + 3x + 3
Anything else:
Monomial (One term)
Binomial (Two terms)
Trinomial (Three terms)
Polynomial
Sunday, March 1, 2009
3x
3x + 3
3x2 + 3x + 3
Anything else:
Monomial (One term)
Binomial (Two terms)
Trinomial (Three terms)
Polynomial (Many terms)
Sunday, March 1, 2009
x4 + 3x2y3 + y4
Sunday, March 1, 2009
x4 + 3x2y3 + y4
x4
Sunday, March 1, 2009
x4 + 3x2y3 + y4
x4 3x2y3
Sunday, March 1, 2009
x4 + 3x2y3 + y4
x4 3x2y3 y4
Sunday, March 1, 2009
x4 + 3x2y3 + y4
x4 3x2y3 y4
4 x’s
Sunday, March 1, 2009
x4 + 3x2y3 + y4
x4 3x2y3 y4
4 x’s 2 x’s3 y’s
Sunday, March 1, 2009
x4 + 3x2y3 + y4
x4 3x2y3 y4
4 x’s 2 x’s3 y’s
4 y’s
Sunday, March 1, 2009
x4 + 3x2y3 + y4
x4 3x2y3 y4
4 x’s 2 x’s3 y’s
4 y’s
Sunday, March 1, 2009
x4 + 3x2y3 + y4
x4 3x2y3 y4
4 x’s 2 x’s3 y’s
4 y’s
This has 5 variables
Sunday, March 1, 2009
x4 + 3x2y3 + y4
x4 3x2y3 y4
4 x’s 2 x’s3 y’s
4 y’s
This has 5 variables
The degree of this polynomial is 5.
Sunday, March 1, 2009
Degree of a polynomial in several variables
Sunday, March 1, 2009
Degree of a polynomial in several variables
The largest sum of the exponents of the variables in the terms.
Sunday, March 1, 2009
Example 1
Find a polynomial for A (the area of a triangle) in terms of x, y, and z.
x y
z + 3
Sunday, March 1, 2009
Example 1
Find a polynomial for A (the area of a triangle) in terms of x, y, and z.
x y
z + 3
Sunday, March 1, 2009
Example 1
Find a polynomial for A (the area of a triangle) in terms of x, y, and z.
x y
z + 3 b =
Sunday, March 1, 2009
Example 1
Find a polynomial for A (the area of a triangle) in terms of x, y, and z.
x y
z + 3 b = x + y
Sunday, March 1, 2009
Example 1
Find a polynomial for A (the area of a triangle) in terms of x, y, and z.
x y
z + 3 b = x + yh =
Sunday, March 1, 2009
Example 1
Find a polynomial for A (the area of a triangle) in terms of x, y, and z.
x y
z + 3 b = x + yh = z + 3
Sunday, March 1, 2009
Example 1
Find a polynomial for A (the area of a triangle) in terms of x, y, and z.
x y
z + 3 b = x + yh = z + 3
Sunday, March 1, 2009
Example 1
Find a polynomial for A (the area of a triangle) in terms of x, y, and z.
x y
z + 3 b = x + yh = z + 3
Sunday, March 1, 2009
Example 1
Find a polynomial for A (the area of a triangle) in terms of x, y, and z.
x y
z + 3 b = x + yh = z + 3
Sunday, March 1, 2009
Example 2
Expand and simplify.
a. (2x - 1)(3x2 - 5x + 4)
b. (y2 + 2y - 5)(4y2 - 6y -1)
Sunday, March 1, 2009
Example 2
Expand and simplify.
a. (2x - 1)(3x2 - 5x + 4)
= 6x3
b. (y2 + 2y - 5)(4y2 - 6y -1)
Sunday, March 1, 2009
Example 2
Expand and simplify.
a. (2x - 1)(3x2 - 5x + 4)
= 6x3 - 10x2
b. (y2 + 2y - 5)(4y2 - 6y -1)
Sunday, March 1, 2009
Example 2
Expand and simplify.
a. (2x - 1)(3x2 - 5x + 4)
= 6x3 - 10x2 + 8x
b. (y2 + 2y - 5)(4y2 - 6y -1)
Sunday, March 1, 2009
Example 2
Expand and simplify.
a. (2x - 1)(3x2 - 5x + 4)
= 6x3 - 10x2 + 8x - 3x2
b. (y2 + 2y - 5)(4y2 - 6y -1)
Sunday, March 1, 2009
Example 2
Expand and simplify.
a. (2x - 1)(3x2 - 5x + 4)
= 6x3 - 10x2 + 8x - 3x2 + 5x
b. (y2 + 2y - 5)(4y2 - 6y -1)
Sunday, March 1, 2009
Example 2
Expand and simplify.
a. (2x - 1)(3x2 - 5x + 4)
= 6x3 - 10x2 + 8x - 3x2 + 5x - 4
b. (y2 + 2y - 5)(4y2 - 6y -1)
Sunday, March 1, 2009
Example 2
Expand and simplify.
a. (2x - 1)(3x2 - 5x + 4)
= 6x3 - 10x2 + 8x - 3x2 + 5x - 4= 6x3
b. (y2 + 2y - 5)(4y2 - 6y -1)
Sunday, March 1, 2009
Example 2
Expand and simplify.
a. (2x - 1)(3x2 - 5x + 4)
= 6x3 - 10x2 + 8x - 3x2 + 5x - 4= 6x3 - 13x2
b. (y2 + 2y - 5)(4y2 - 6y -1)
Sunday, March 1, 2009
Example 2
Expand and simplify.
a. (2x - 1)(3x2 - 5x + 4)
= 6x3 - 10x2 + 8x - 3x2 + 5x - 4= 6x3 - 13x2 + 13x
b. (y2 + 2y - 5)(4y2 - 6y -1)
Sunday, March 1, 2009
Example 2
Expand and simplify.
a. (2x - 1)(3x2 - 5x + 4)
= 6x3 - 10x2 + 8x - 3x2 + 5x - 4= 6x3 - 13x2 + 13x - 4
b. (y2 + 2y - 5)(4y2 - 6y -1)
Sunday, March 1, 2009
Example 2
Expand and simplify.
a. (2x - 1)(3x2 - 5x + 4)
= 6x3 - 10x2 + 8x - 3x2 + 5x - 4= 6x3 - 13x2 + 13x - 4
b. (y2 + 2y - 5)(4y2 - 6y -1)
= 4y4 + 2y3 - 33y2 + 28y + 5
Sunday, March 1, 2009
Extended distribution:
Sunday, March 1, 2009
Extended distribution:
Multiply each term in the first polynomial by each term in the second polynomial.
Sunday, March 1, 2009
Example 3
A piece of cardboard is used to make an open box. It is 16.5 in by 23.5 in, with corners x in by x in cut from each corner. Let V(x) be the volume of the box. Find a polynomial to represent the volume.
Sunday, March 1, 2009
Sunday, March 1, 2009
Sunday, March 1, 2009
Sunday, March 1, 2009
Sunday, March 1, 2009
16.5 - 2x
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2x
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2xx
x
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2xx
x
V = lwh
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2xx
x
V = lwh = (16.5 - 2x)
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2xx
x
V = lwh = (16.5 - 2x)(23.5 - 2x)
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2xx
x
V = lwh = (16.5 - 2x)(23.5 - 2x)(x)
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2xx
x
V = lwh = (16.5 - 2x)(23.5 - 2x)(x)= (387.75
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2xx
x
V = lwh = (16.5 - 2x)(23.5 - 2x)(x)= (387.75 - 33x
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2xx
x
V = lwh = (16.5 - 2x)(23.5 - 2x)(x)= (387.75 - 33x - 47x
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2xx
x
V = lwh = (16.5 - 2x)(23.5 - 2x)(x)= (387.75 - 33x - 47x + 4x2)
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2xx
x
V = lwh = (16.5 - 2x)(23.5 - 2x)(x)= (387.75 - 33x - 47x + 4x2)(x)
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2xx
x
V = lwh = (16.5 - 2x)(23.5 - 2x)(x)= (387.75 - 33x - 47x + 4x2)(x)= 4x3 - 80x2 +387.75x
Sunday, March 1, 2009
16.5 - 2x
23.5 - 2xx
x
V = lwh = (16.5 - 2x)(23.5 - 2x)(x)= (387.75 - 33x - 47x + 4x2)(x)= 4x3 - 80x2 +387.75x in3
Sunday, March 1, 2009
Homework
Sunday, March 1, 2009
Homework
p. 683 #1-20
"The best doctor in the world is the veterinarian. He can't ask his patients what is
the matter-he's got to just know." – Will RogersSunday, March 1, 2009