Quick Check Solutions Polynomials Target C
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 look 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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