Rewrite the expression as a product of four linear factors: (3x^(2)-x)^(2)-6(3x^(2)-x)+8 Answer:

Question

Rewrite the expression as a product of four linear factors:  (3x^(2)-x)^(2)-6(3x^(2)-x)+8 Answer:

Bytelearn · Accepted Answer

Recognize Quadratic Form: Recognize the given expression as a quadratic in form The expression (3x^(2)-x)^(2)-6(3x^(2)-x)+8 resembles a quadratic equation in the form of (ax)^2 - bx + c, where 'ax' is (3x^2 - x). To factor it, we can treat (3x^2 - x) as a single variable, say 'y'. So, let y = (3x^2 - x). The expression then becomes y^2 - 6y + 8.Factor Quadratic Expression: Factor the quadratic expression Now we factor y^2 - 6y + 8. This factors into (y - 2)(y - 4), because (y - 2)(y - 4) = y^2 - 4y - 2y + 8 = y^2 - 6y + 8.Substitute and Expand: Substitute back (3x^2 - x) for y We now replace y with (3x^2 - x) in the factors we found. So, (y - 2)(y - 4) becomes ((3x^2 - x) - 2)((3x^2 - x) - 4).Find Linear Factors: Expand the factors to find the linear factors We need to expand ((3x^2 - x) - 2) and ((3x^2 - x) - 4) to find the linear factors. First, we simplify the expressions: (3x^2 - x - 2) = (3x^2 - 3x + 2x - 2) = 3x(x - 1) + 2(x - 1) = (3x + 2)(x - 1) (3x^2 - x - 4) = (3x^2 - 3x + 2x - 4) = 3x(x - 1) + 2(x - 2) = (3x + 2)(x - 2)Write Product of Factors: Write the product of four linear factors The product of the four linear factors is then (3x + 2)(x - 1)(3x + 2)(x - 2). However, we notice that (3x + 2) is repeated, so we can write the factors as (3x + 2)^2(x - 1)(x - 2).

Rewrite the expression as a product of four linear factors: $\newline$ $\left(3 x^{2}-x\right)^{2}-6\left(3 x^{2}-x\right)+8$ $\newline$ Answer:

Full solution

More problems from Identify factors

Related topics

Rewrite the expression as a product of four linear factors:\newline(3x2−x)2−6(3x2−x)+8 \left(3 x^{2}-x\right)^{2}-6\left(3 x^{2}-x\right)+8 (3x2−x)2−6(3x2−x)+8\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(3 x^{2}-x\right)^{2}-6\left(3 x^{2}-x\right)+8$ $\newline$ Answer: