September 21, 2017 Multiply the following factors on an index card.

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Presentation transcript:

September 21, 2017 Multiply the following factors on an index card. (𝟕𝒙+𝟑)(𝟖𝒙−𝟒)

X-box Factoring

Factor the x-box way y = ax2 + bx + c (x + m)(x + n) Product ac=mn m n First and ac=mn Last Coefficients m n b=m+n Sum

X- Box (x + 3)(x - 9) Product x + 3 -9 Sum

y = x2 + 7x + 12 y = x2 + 3x - 10 y = x2 - 7x - 18 y = x2 - 10x + 24 -10 x + 7 x + 3 -18 24 x + -7 x + -10 y = x2 - 7x - 18 y = x2 - 10x + 24

Factor the x-box way Example: Factor 3x2 -13x -10 (3)(-10)= -30 -15 2 3x2 -13x -10 = (x-5)(3x+2)

Examples Factor using the x-box method. 1. x2 + 4x – 12 -12 6 -2 4 Solution: x2 + 4x – 12 = (x + 6)(x - 2)

Examples continued 2. x2 - 9x + 20 -4 -5 -9 Solution: x2 - 9x + 20 = (x - 4)(x - 5)

Examples continued Examples continued 3. 2x2 - 5x - 7 -14 -7 2 -5 Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

Examples continued 4. 15x2 + 7x - 2 -30 10 -3 7 Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)

GCF Greatest common Factor What is the greatest common factor of each pairs of monomials? 15y and 30y2 -5a2b2 and -3ab? Use your answer to factor each of these. 15y + 30y2 -5a2b2 + -3ab?

5.4.2 Factoring Out a Negative Factor.

Grouping 𝑥 4 +2 𝑥 3 − 𝑥 2 −2𝑥−9𝑥−18

Continued

5.4.4 Factor by Grouping

5.4.4 Factor By Grouping

5.4.4 Factor By Grouping

5.4.4 Factor By Grouping

Always factor out the GCF first if you can! 5.4.4 Factor By Grouping Always factor out the GCF first if you can!

You may have to rearrange terms. 5.4.4 Factor By Grouping You may have to rearrange terms.

Factor By Grouping