8­6 Factoring a x2 + b x + c rewrite​
(verb) ree r y t Other Word Form:​
rewritten Main Idea:​
Sometimes you can rewrite trinomials in a different, but equivalent, way to make them easier to factor. Definition:​
Rewrite means to write in another form. Essential Understanding​
You can write some trinomials of the form ax2 + bx + c as the product of two binomials.
Consider the trinomial 6x2 + 23x + 7 . To factor it, think of 23x as 2x + 21x . 6x2 + 23x + 7 = 6x2 + 2x + 21x + 7 Rewrite 23x as 2x + 21x . = 2x (3x + 1) + 7 (3x + 1) Factor out the GCF of each pair of terms. = (2x + 7) (3x + 1) Distributive Property How do you know to rewrite 23x as 2x + 21x ? Notice that multiplying 2 and
gives 42, which is the product of the x2 ­ coefficient 6 and the constant term 7.
This example suggests that, to factor a trinomial of the form ax2 + bx + c , you
should look for factors of the product ac that have a sum of b . Factor each expression. A.) 3d2 + 23d + 14 B.) 4p2 + 7p + 3 C.) 8g2 − 14g + 3 Factor each expression. D.) 2k2 − 13k − 24 E.) 3x2 + 23x − 36 F.) 4d2 − 4d − 35 G.) ​
Crafts​
the area of a rectangular knitted blanket is 15x2 − 14x − 8 . What are the possible dimensions of the blanket? Use factoring. To factor a polynomial completely, first factor out the GCF of the polynomial’s terms. then factor the remaining polynomial until it is written as the product of polynomials that cannot be factored further. Factor each expression completely. H.) 8v2 + 34v − 30 I.) 20w2 − 45w + 10 J.) 9r2 + 3r − 30