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
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<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 />
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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 />
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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 />
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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 />
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Homework: pg. 211 #3,<br />
4, 6 17<br />
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