1 / 8

5.7-5.9 More about Factoring Trinomials

5.7-5.9 More about Factoring Trinomials. To factor ax 2 +bx+c when a≠1 find the integers k,l,m,n such that ax 2 +bx+c=( k x+ m )( l x+ n ) = kl x 2 +( kn+lm ) x+ mn Therefore k and l must be factors of a m and n must be factors of c

cardea
Download Presentation

5.7-5.9 More about Factoring Trinomials

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. 5.7-5.9 More about Factoring Trinomials

  2. To factor ax2+bx+c when a≠1 find the integers k,l,m,n such that ax2+bx+c=(kx+m)(lx+n) = klx2+(kn+lm)x+mn Therefore k and l must be factors of a m and n must be factors of c The goal is to find a combination of factors of a and c such that the outer and inner products add up to the middle term bx. Factoring a trinomial of the form ax2+bx+c

  3. 3x2 + x -4 • The possible factors for the first term are 3,1 or 1,3. The possible factors of the last term are 2, -2; -2, 2; 4, -1; and -4, 1. Here are all the possible factors and what the middle term equals • (3x -2) (x + 2) = 4x for the middle term • (3x + 2) (x – 2) = -4x for the middle term • (3x -1) (x + 4) = 11x for the middle term • (3x-4) (x + 1) = -x for the middle term • (3x + 1) (x-4) = -11 for the middle term • (3x +4) (x – 1) = x for the middle term ANSWER Example

  4. 1) • 2) • 3) Examples:

  5. Factoring Completely • 4) • 5) Examples:

  6. Factor: 2x2+ x -15 • In order to ‘group’ this polynomial, we actually have to ‘break out’ the middle term. • In order to figure out what coefficients to use when we break out the middle term, we need to choose factors of the product ac that add up to b. • In the example above the product of ac is -30 (-15*2). The factors of -30 are +/- 1, 30, 5, 6, 3 10, 2 and 15. Looking at this factors, we see that -5 + 6 will equal one. • So now we can write out this polynomial like this: • 2x2 + 6x-5x -15. • 2x(x + 3) -5(x+3) • (2x-5)(x+3) Factoring by grouping

  7. If necessary, write the trinomial in standard form • Choose factors of the product ac that add up to b • Use these factors to rewrite the middle term as a sum. • Group factor and solve. Factoring by grouping

  8. 1) • 2) Examples by grouping:

More Related