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## Section 1.5 : Factoring Polynomials

For problems 1 – 4 factor out the greatest common factor from each polynomial.

- \(6{x^7} + 3{x^4} - 9{x^3}\) Solution
- \({a^3}{b^8} - 7{a^{10}}{b^4} + 2{a^5}{b^2}\) Solution
- \(2x{\left( {{x^2} + 1} \right)^3} - 16{\left( {{x^2} + 1} \right)^5}\) Solution
- \({x^2}\left( {2 - 6x} \right) + 4x\left( {4 - 12x} \right)\) Solution

For problems 5 & 6 factor each of the following by grouping.

- \(7x + 7{x^3} + {x^4} + {x^6}\) Solution
- \(18x + 33 - 6{x^4} - 11{x^3}\) Solution

For problems 7 – 15 factor each of the following.

- \({x^2} - 2x - 8\) Solution
- \({z^2} - 10z + 21\) Solution
- \({y^2} + 16y + 60\) Solution
- \(5{x^2} + 14x - 3\) Solution
- \(6{t^2} - 19t - 7\) Solution
- \(4{z^2} + 19z + 12\) Solution
- \({x^2} + 14x + 49\) Solution
- \(4{w^2} - 25\) Solution
- \(81{x^2} - 36x + 4\) Solution

For problems 16 – 18 factor each of the following.

- \({x^6} + 3{x^3} - 4\) Solution
- \(3{z^5} - 17{z^4} - 28{z^3}\) Solution
- \(2{x^{14}} - 512{x^6}\) Solution

## IMAGES

## VIDEO

## COMMENTS

There is no one specific person who invented the polynomials, but their history can be traced back to the Babylonians. They used verbal instructions for solving problems related to quadratics.

The motion of an object that’s thrown 3m up at a velocity of 14 m/s can be described using the polynomial -5tsquared + 14t + 3 = 0. Factorizing the quadratic equation gives the time it takes for the object to hit the ground.

Examples of prime polynomials include 2x2+14x+3 and x2+x+1. Prime numbers in mathematics refer to any numbers that have only one factor pair, the number and 1. A polynomial is considered prime if it cannot be factored into the standard line...

... . 117. Factoring Polynomials. Practice and Problem Solving: A/B. Simplify each polynomial, if possible. Then factor it. 1. 2. 3. 48 n -. 2. 3. 3. 75 x x.

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LESSON Practice B. 6-4 Factoring Polynomials. Date. Class. Determine whether the given binomial is a factor of the polynomial. P(x). 2. 1. (x − 4); P(x) = x²+

Factoring Worksheet. Remember these steps for factoring polynomials. 1). 2). 3). Is there a common factor? If so factor it out. How many terms in the polynomial

Here is a set of practice problems to accompany the Factoring Polynomials section of the Preliminaries chapter of the notes for Paul Dawkins

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If none of these occur, the binomial does not factor. 3) If the problem is a trinomial, check for one of the following possibilities. A. Square of a binomial:.

This algebra video explains how to factor hard polynomial expressions and special cases such as the difference of two squares and perfect

Finding Rational Solutions of Polynomial Equations. Practice and Problem Solving: A/B. Solve each polynomial equation by factoring. 1. 3 2 4 x x x 4 1 0

Factoring Polynomials: Very Difficult Problems with Solutions. By Catalin David. Problem 1. Factor 3x3 - x2y +6x2y - 2xy

Add and subtract polynomials. Solve real-life problems. Finding the Degrees of Monomials. A monomial is a number, a variable