1 / 23

Chapter 1 Algebra and functions

Chapter 1 Algebra and functions. C2. Example 1. Simplify this expression 4x 4 +5x 2 -7x x Here write these as three separate fractions. Another example. Simplify the following n 2 +8n +16 n 2 –16

gillian-vincent
Télécharger la présentation

Chapter 1 Algebra and functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 1 Algebra and functions C2

  2. Example 1 • Simplify this expression • 4x4+5x2-7x • x • Here write these as three separate fractions

  3. Another example • Simplify the following n2+8n +16 • n2 –16 • This is a perfect square and a difference of two squares- cookie cutters! • = (n+4)2 • (n-4)(n+4) • = (n+4) • (n-4)

  4. Dividing polynomials by cancelling • Always factorise first using the HCF and then cancel out common factors in the fraction • Example (2c2d3)2 • 8b4c4 • Quiz • Some classwork questions

  5. The family division • Remember your family • Dad • Mum • Sister • Brother

  6. Example 1 No remainder • Set you work out using the family steps • Divide x3 + 2 x2 -17x +6 by (x-3) • x-3 ) x3+2x2–17x +6

  7. No remainder again • Divide 6x3+28x2-7x+15 by (x+5)

  8. Leaving a gap! • Divide x3-3x-2 by (x-2)

  9. Example with a remainder • Divide 2x3–5x2-16x +10 by (x-4) • Now we must write the polynomial with highest power first! • x –4 ) 2x3 -5x2 –16x+ 10

  10. A summary of long division • Always follow Dad, mum, sister, brother • Always write the polynomial in order starting with the highest power • Always leave a space for any terms (powers) not in the question • More worked examples? • Click on the picture!

  11. Factor theorem • if x-a is a factor of f(x) then f(a)=0 • What does this mean? • If (x-2) is a factor of • f(x) = x3+x2-4x-4 then f(2) = 0. please check this. • F(2) = 8 +4-8-4

  12. Factor Theorem example 2 • Show the (x-1) is a factor of x3+6x2+5x-12 and hence fully factorize the expression.

  13. Example 3 • Given that (x+1) is a factor of 4x4-3x2+a find the value of a. • F(-1) = 4-3+a • 1 + a = 0 • a = -1

  14. Example 4 • Prove that (2x+1) is a factor of 2x3+x2-18x-9 • What do you substitute here? • Here we substitute x = -1/2 • F(-1/2) = 2 (-1/8) + ¼ +9-9 • = 0

  15. Finding factors of a polynomial • Fully factorise f(x) = 2x3+x2-18x-9 • The first step here is to look at the constant 9 and try the factors of 9. • We will try f(1), f(-1), f( 3) and see which one equals 0. • F(1) = 2+1-18-9 • F(3) = 54 + 9 -54 – 9! • So (x-3) is a factor. • Now we use family division to find the other factors. • Ex 1D.

  16. Classwork • Just one more practice question on Sos maths. Let’s do this together.

  17. Remainder Theorem • If when you substitute f(a) into the polynomial and it does not equal zero then this number is actually the remainder. • Example find the remainder when x3-20x+3 is divided by (x-4) • F(4) = -13 • Ex 1E Mixed exercise 1F

  18. A competition • 1) Show that x-2 is a factor of • f(x) = x3+x2-5x-2 and hence or otherwise find the exact solutions of the equation f(x) = 0

  19. A competition • 2) Given that x = -1 is a root of the equation 2x3-5x2-4x+3, find the other two positive roots.

  20. A competition • 3) H(x) = x3+4x2+rx+s. Given that • H(-1) = 0 and H(2) = 30, find the values of r and s. Find the remainder when H(x) is divided by (3x-1)

  21. A competition • 4) Given that g(x) = 2x3+9x2-6x-5, factorise g(x) and solve g(x) = 0 .

  22. A competition • 5) F(x) = 2x2+px+q. Given that F(-3)=0 and F(4) = 2 find the value of p and q and hence fully factorise.

  23. Five quick questions • Write five quick quiz questions on the sheet provided

More Related