7.3 Notes FACTORING QUADRATICS. What do we know about quadratics?  Have an x 2  ax 2 + bx + c  Degree is 2  Has 2 roots/x-intercepts/solutions  Make.

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Presentation transcript:

7.3 Notes FACTORING QUADRATICS

What do we know about quadratics?  Have an x 2  ax 2 + bx + c  Degree is 2  Has 2 roots/x-intercepts/solutions  Make a parabola

Factoring: FIRST check for...  Anything that the terms have in common  Numbers & variables  2x 2 – 32x  2x(x-16)  3x x – 27  3(x 2 + 6x – 9)  -12x  -3(4x 2 – 9)

Difference of Squares (b = 0)  Subtraction of 2 squared terms  x 2 – 4  Square root each piece into two sets of binomials  Separate with addition and subtraction  x 2 – 4  (x + 2)(x – 2)  -12x  -3(4x 2 – 9)  -3(2x + 3)(2x – 3)

Factoring Quadratic Trinomials(a = 1)  Quadratics with 3 terms  Find 2 numbers which multiply to the term with no x but add to the middle term.  x 2 + 5x + 6  2 and 3 because 2*3 = 6 and = 5  (x + 3)(x + 2)  x 2 – 8x – 20  -10*2 = - 20 and = - 8  (x – 10)(x + 2)

Factoring when a is NOT 1  2x 2 + 5x + 3  Make a chart  Multiply a and c and place on one side  Place b on the other side  Find numbers that multiply to be the same as the left column but add to the right column.  Rewrite the original but changing the middle term to your 2 new numbers being added.  2x 2 + 2x + 3x + 3  Break into 2 groups and factor out common factors.  2x(x + 1) + 3(x + 1)  Factor out the common group and leave the rest in the other.  (x + 1)(2x + 3) a*cb 65 2*3 = = 5

Factor each of the following  7x 2 + 9x  x(7x + 9)  12x 2 – 36  12(x 2 – 3)  9x 2 – 100  (3x + 10)(3x – 10)  36x 2 – 144  36(x 2 – 4)  36(x + 2)(x – 2)  x 2 – 11x + 30  (x – 6)(x – 5)  x 2 + 7x – 18  (x + 9)(x – 2)  9x 2 – 9x – 10  9x 2 – 15x + 6x – 10  3x(3x – 5) + 2(3x – 5)  (3x – 5)(3x + 2) *10 = = 1 -15* = -9