This is a free lesson from our course in Algebra I
In this lesson, you'll learn the approach to simplifying a 2nd order polynomial by factoring. You'll see here how to write a polynomial
equation in a standard form, use the zero factor property
and solve polynomial equation by factoring. On solving the quadratic equation, you'll get the value of x. For
example, x(14x - 15) = 9 gives two possible value of x,
-3/7 and 3/2. To Factorize ax2 + bx + c
steps are as follows:
• using the leading coefficient of a
you write the pair of incomplete factors.
• multiply a and c, the coefficients
of x2 and the constant term.
• find integers whose product is
a × c and the constant term.
• discard any common factor within
each parenthesis in Step 3. The result is
the desired factorization. (More text below video...)
(Continued from above) E.g. 6x2 + 7x – 3
• the lead coefficient is 6, so you
write
(6x )(6x ) • a × c = (6)(- 3) = -18
• two integers whose product is –18
and whose sum is 7 are 9 and –2. Then you
write (6x + 9)(6x – 2)
• reducing (6x + 9) to (2x + 3) and
(6x – 2) to (3x – 1) you have
6x2 + 7x – 3 = (2x+3)(3x-1)
Once you go through the instructor's explanation in the video above, you'll be comfortable in dealing with second order polynomials.
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