Factor: x2 5x - 24
A quadratic trinomial in which the last term is negative is factored.
Series: Factoring, Part Three
Subject: factor
Transcript: 5. THAT'S JUST WHAT WE WANT. NOW WE CAN WRITE THE TWO BINOMIAL FACTORS. THE FIRST TERM OF EACH FACTOR IS X, THE VARIABLE IN OUR TRINOMIAL. THE OTHER
Examples of Rationalizing the Denominator
Problems involving rationalizing the denominator are presented and a shortcut is given.
Subject: factor
Examples of Division Problems with Radicals
Two division problems with radicals are demonstrated.
Subject: factor
Transcript: LET'S TRY ANOTHER DIVISION PROBLEM. REMEMBER, YOU CAN ONLY REDUCE WHEN TERMS IN THE NUMERATOR HAVE A COMMON FACTOR. WE'LL START BY REDUCING THE
Factor: a2 - ac - ab bc
When grouping terms, the goal is to end up with an expression that is equal to the original polynomial. Close attention to the signs is necessary to ensure a correct outcome. Remember that a minus sign in front of parentheses is the same as subtract...
Series: Factoring, Part Two
Subject: factor
Transcript: SO FAR, EVERY TIME WE'VE FACTORED BY GROUPING WE'VE HAD A PLUS SIGN BETWEEN THE TWO GROUPS. A POSITIVE SIGN IN FRONT OF TERMS IN PARENTHESES DOESN
Multiplying then Simplifying Two Radicals
The procedure for simplifying radicals by beginning with multiplication is demonstrated.
Subject: perfect square factor
Transcript: LOOK AT THIS PROBLEM, WE HAVE ONE TERM WITH TWO RADICAL FACTORS SO WE HAVE TO SIMPLIFY. THE SQUARE ROOT OF 5 TIMES THE SQUARE ROOT OF 7 EQUALS THE
Variables and the Greatest Common Factor
To factor completely, the greatest common factor must include every number and variable that is a factor of each term in the polynomial. A
Series: Factoring, Part One
Subject: factor
Transcript: SO FAR WE'VE FOUND THE GREATEST COMMON FACTOR BY WORKING WITH THE COEFFICIENTS OF TERMS. BUT VARIABLES CAN ALSO BE A PART OF THE GREATEST COMMON
Using Multiplication to Eliminate the 'x' Variable
Solving a system of equations in which the variable terms are not multiples of each other and have no common factors, using multiplication to
Subject: factor
Transcript: TERMS. THE X-TERMS ARE NOT MULTIPLES OF EACH OTHER AND HAVE NO COMMON FACTORS. THAT'S ALSO THE CASE WITH THE Y-TERMS. MULTIPLYING ONE OF THE EQUATIONS BY
Using Factoring to Solve an Equation
An equation is presented for solution in which factoring must be used. The solution is detailed and checked.
Subject: factor
Transcript: TO FIND THE LEAST COMMON DENOMINATOR IN THE EQUATION, WE'LL HAVE TO FACTOR THE DENOMINATOR ON THE RIGHT SIDE. THE FACTORS OF X SQUARED MINUS 8X PLUS
Solve: x2 - 8x 16 = 0
Practice solving a quadratic equation: x2 8x 16 = 0. Because this equation has two identical binomial factors, it has a single solution called a
Subject: factor
Transcript: LET'S SOLVE ANOTHER QUADRATIC EQUATION. THIS ONE IS IN STANDARD FORM, SO WE CAN BEGIN BY FACTORING THE LEFT SIDE OF THE EQUATION. TO FACTOR THE
Dividing a Radical by a Whole Number
A radical can only be divided by another radical. In the examples demonstrated, the only radical is in the numerator. The radical simplified and the fraction reduced.
Subject: factor