06.07.2015 Views

4.3 Factoring Trinomials of the Form x2 + bx + c

4.3 Factoring Trinomials of the Form x2 + bx + c

4.3 Factoring Trinomials of the Form x2 + bx + c

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

<strong>4.3</strong> <strong>Factoring</strong> <strong>Trinomials</strong> <strong>of</strong> <strong>the</strong> <strong>Form</strong> x 2 + <strong>bx</strong> + c<br />

Expand.<br />

a) (x + 4)(x + 3) b) (x ­ 4)(x + 3)<br />

Notice that <strong>the</strong> sum <strong>of</strong> +3 and +4 is +7<br />

The product <strong>of</strong> +3 and +4 is +12!<br />

Notice that <strong>the</strong> sum <strong>of</strong> +3 and ­4 is ­1<br />

The product <strong>of</strong> +3 and ­4 is ­12!<br />

Remember factoring and expanding are inverse operations. We<br />

will use <strong>the</strong> rules developed above to factor trinomials.<br />

Factor.<br />

a) x 2 + 7x + 12<br />

sum +5<br />

product +6<br />

sum ­1<br />

product ­6<br />

b) x 2 ­ x ­ 12<br />

1


Factor <strong>the</strong> following:<br />

a) x 2 – 8x + 12<br />

sum ­8<br />

product +12<br />

e) n 2 +8n + 16<br />

sum +8<br />

product +16<br />

b) a 2 – 5a – 24<br />

sum ­5<br />

product ­24<br />

f) x 2 – 14x + 45<br />

sum ­14<br />

product +45<br />

c) s 2 – 8s – 20<br />

sum ­8<br />

product ­20<br />

g) x 2 ­ 10x + 25<br />

sum ­10<br />

product +25<br />

d) w 2 – w – 30<br />

sum ­1<br />

product ­30<br />

h) w 2 ­ 7w + 6<br />

sum ­7<br />

product +6<br />

2


Combining Greatest Common <strong>Factoring</strong> and <strong>Factoring</strong> <strong>Trinomials</strong><br />

Sometimes we can factor out a GCF, <strong>the</strong>n factor <strong>the</strong> trinomial.<br />

Eg) 4x 2 – 24x + 36<br />

product<br />

sum<br />

TRY<br />

a) 6x 2 + 24x ­ 30 b) 3a 2 – 15a – 72<br />

3


For <strong>the</strong> quadratic relation y = ­ x 2 + 2x + 3.<br />

i) Express <strong>the</strong> relation in factored form.<br />

ii) Determine <strong>the</strong> zeros.<br />

iii) Determine <strong>the</strong> coordinates <strong>of</strong> <strong>the</strong> vertex.<br />

iv) Sketch<br />

4


Homework: pg. 211 #3,<br />

4, 6 ­ 17<br />

5

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!