Polynomials-Target+C-Factoring+GCF-Quick+Check+Solutions

1) To factor the polynomial -10x 5 + 14x 3 - 8x first find the GCF for all 3 terms. The GCF is -2x. Remember to factor out the negative when the leading coefficient for the polynomial is negative. Then use either division or fill in the blanks to factor the polynomial: -2x(5x 4 - 7x 2 + 4)

2) There are an infinite number of solutions to this problem. When creating a binomial that has a GCF of 5x, make sure that there are only 2 terms, that the coefficient for each term is divisible by 5, and that each term has a variable, x, component. Here is one possible solution: 20x 3 - 35x. Both terms are divisible by 5 and have x as the variable. If you were to write the binomial in factored form it would lool like this: 5x(4x 2 - 7).

3) The factored form of 12x 3 + 18x 2 - 6x is NOT 3x(4x 2 + 6x - 2). Although you can factor out 3x, 3x is not the GREATEST common factor between all three terms of the polynomial. The GCF is actually 6x. So the polynomial written in factored form would be: 6x(2x 2 + 3x - 1).

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