Practice factoring a trinomial with a negative middle term: 12x2 - 17x 6.
Series: Factoring, Part Three
Subject: factor
Transcript: NOW LET'S FACTOR A TRINOMIAL THAT INCLUDES A NEGATIVE TERM. WE'LL USE THE SAME METHOD, BUT WE'LL HAVE TO BE CAREFUL ABOUT THE SIGNS OF THE TERMS. WE
A new guideline for simplifying radicals is introduced: the terms in a fully-simplified radical expression must have no common radical factors
Subject: perfect square factor
Transcript: SQUARE ROOT OF 5. THE WAY WE WORK WITH EXPRESSIONS LIKE THIS IS SIMILAR TO THE WAY WE WORK WITH POLYNOMIALS TO SIMPLIFY 3A PLUS 4A, WE FACTOR. A IS THE
Simplifying a radical by multiplying first to get a perfect square in the radicand.
Subject: perfect square factor
Transcript: PROBLEM. LET'S LOOK AT THE FACTORS BEFORE WE DECIDE WHETHER TO MULTIPLY FIRST OR SIMPLIFY FIRST. IF WE MULTIPLY THE RADICALS, WE'LL HAVE A PERFECT SQUARE IN
The process of simplifying to find a common radical factor is demonstrated.
Subject: perfect square factor
Transcript: RADICAL FACTOR UNTIL WE SIMPLIFY EACH OF THEM. 24 HAS A PERFECT SQUARE FACTOR, IT'S 4. THE OTHER FACTOR IS 6. IN SIMPLEST FORM, THE SQUARE ROOT OF 24 IS 2
Instances are demonstrated where simplifying radicals before multiplying are indicated.
Subject: perfect square factor
Transcript: RADICALS IS SIMPLIFIED, SO WE CAN ALSO START BY SIMPLIFYING EACH OF THEM. LET'S SEE WHAT HAPPENS WHEN WE SIMPLIFY FIRST. THE PERFECT SQUARE FACTOR OF 8 IS 4
Practice factoring: 5c2 3c - 20cd - 12d.
Series: Factoring, Part Two
Subject: factor
Transcript: TRY TO FACTOR THIS POLYNOMIAL YOURSELF. INSPECT THE TERMS FIRST AND WORK CAREFULLY WITH THE NEGATIVE SIGNS WHEN YOU GROUP TERMS. WE CAN GROUP THE
Rational expressions that equal -1 are recognizable: the terms in the numerator are identical to the terms in the denominator except for their signs, which are opposite.
Subject: factor
Transcript: 'T BE FACTORED, AND THERE ARE NO FACTORS WE CAN CANCEL. BUT SUPPOSE WE FACTOR NEGATIVE 1 FROM THE DENOMINATOR. WE GET NEGATIVE 1 TIMES NEGATIVE B PLUS A
Practice with factoring involving minus signs: ax - x - 5a 5.
Series: Factoring, Part Two
Subject: factor
Transcript: THE TERMS CORRECTLY. NOW WE'LL FACTOR EACH GROUP. THE FACTORS OF THE FIRST GROUP ARE X AND A MINUS 1. THE FACTORS OF THE SECOND GROUP ARE 5 AND A MINUS
A review of how to multiply signed numbers.
Subject: factor
Transcript: NARRATOR: LET'S SAY WE WANT TO MULTIPLY TWO NUMBERS. THEY'RE CALLED FACTORS. SAY 3 AND NEGATIVE 4. THE ANSWER, OR PRODUCT, WILL HAVE TWO PARTS. AN
Using multiplication of polynomials in a practical problem.
Subject: factor
Transcript: NUMBER AND A VARIABLE. IF WE KNOW WHAT THE VARIABLE STOOD FOR, WE COULD COMPLETE THE JOB. BUT WE DON'T. SO THE BEST WE CAN DO IS WRITE THE TWO FACTORS