Factoring Done by:Rashed salmeen Grade:9ASP2 Prime factorization - PowerPoint PPT Presentation

Factoring Done by:Rashed salmeen Grade:9ASP2

Prime factorization Prime factorization:is finding which prime numbers multiply together to make the original number. Examples: 27 18 2 9 3 9 3 3 3 3 18=2x3x3 27=3x3x3

greatest common factors(GCF) Greatest common factors(GCF):the greatest number that is a factor of two given number Example: 36 20 20=2x2x5 2 18 10 36=2x2x3x3 2 2 9 5 2 GCF=2x2=4 3 3

Factoring by grouping 12a3-9a2 +20a-15 GCF:1 First step find the GCF GCF:3a2 GCF:5 Separate the four terms to (3a2).4a-(3a2).3 +(5).4a-(5).3 two binomial 3a2(4a-3) +5(4a-3) Factor out the GCF of each group 3a2(4a-3)+5(4a-3) (4a-3) is a common factor (4a-3)(3a2+5) Factor out (4a-3)

Factoring quadratic trinomials where a=1 ax ² + bx + c Method 1 GCF:1 x ² + 5x + 6 First step find the GCF 6 Find the product ac: 1x6=6 3+2=5 look for factors of 6 whose sum is 5 x2+3x +2x+6 Write the expression in grouping GCF:x GCF:2 (x).x+(x).3 +(2).x+(2).3 Now factor the expression by grouping x(x+3) +2(x+3) x(x+3)+2(x+3) Now pull the GCF out and put the other (x+3)(x+2) numbers in bracket

Factoring quadratic trinomials where a=1 ax ² + bx + c Method 2 x ² +13x+36 GCF:1 First step find the GCF 1x36 Find the product ac: 36 look for factors of 36 whose sum is 13 4+9=13 (x+4)(x+9) Now take write x plus one of the factors then write x plus the other factor Note:in this method the variable should be equal to one

Factoring quadratic trinomials where a ≠ 1 ax ² + bx + c GCF:1 First step find the GCF 2x ² +9x+10 Find the product ac: 2x10=20 20 look for factors of 20 whose sum is 9 4+5=9 2x2+4x +5x+10 Write the expression in grouping GCF:2x GCF:5 (2x).x+(2x).2 +(5).x+(5).2 Now factor the expression by grouping 2x(x+3) +5(x+3) Now pull the GCF out and put the other 2x(x+3)+5(x+3) numbers in bracket (x+3)(2x+5)

Factoring a perfect square a ² + 2ab + b2 = (a + b) ² (a + b) ² Check whether it's a perfect square by 9x ² -12x+4 checking the square root for a and c First term: √ 9x ² =3x It's a perfect square,so we must but the Second term: √ 4=2 answer of the first term minus the answer Middle term:2x3xx2=12x of the second term in bracket and we must but a square (3x-2) ² Note:in perfect square the second term must be plus

Factoring a difference of two squares a ² – b ² = (a – b)(a + b) Check whether it's a perfect square by checking the square root for a and c 4r ² -25s ² First term: √ 4r6=2r3 It's a difference of two square,so we Last term: √ 25s6=5s3 must but the answer of the first term minus and plus the answer of the last (2r3) ² -(5s3) ² term in bracket (2r3-5s3)(2r3+5s3) Note:in difference of two square (a)must be minus (b) not plus

Factoring Difference of cube a^3 – b^3= (a – b)(a^2+ ab + b^2) 27y3-64 check the cube root for a and c First term:3 √ 27y^3=3y Last term:3 √ 64=4 It's a difference of cubes,so we must but the answer same as the (3y-4)(3y^2+3y.4+4^2) expression that is up (3y-4)(9y2+12y+16)

Factoring completely It's a difference of two squares so we need the the square root of the P^4-16 GCF:1 p^4 and 16 First term: √ p^4=p ² Last term: √ 16=4 we must but the answer of the first term minus and plus the answer of the last (P ² ) ² -(4) ² term in bracket (P2+4)(p2-4) (P) ² -(2) ² Now we can factor(p ² -4) because it is a difference of two squares (P ² +4)(p+2)(p-2)