Rewrite the expression as a product of four linear factors: (10x^(2)+x)^(2)-11(10x^(2)+x)+18 Answer:

Define y as expression: Let's denote the expression inside the parentheses as y, where y = 10x^2 + x. This will simplify our expression to a quadratic in terms of y.Rewrite as quadratic in y: Now we rewrite the expression as a quadratic in y: (y)^2 - 11y + 18.Factor quadratic expression: We need to factor the quadratic expression. To do this, we look for two numbers that multiply to 18 and add up to -11. These numbers are -9 and -2.Substitute back for x: Factoring the quadratic expression gives us (y - 9)(y - 2).Factor each quadratic further: Now we substitute back in for y to get the expression in terms of x: (10x^2 + x - 9)(10x^2 + x - 2).Combine all factors: Each of these quadratic expressions can be factored further. We look for two numbers that multiply to -90 (10 * -9) and add up to 1 (the coefficient of x) for the first quadratic, and two numbers that multiply to -20 (10 * -2) and add up to 1 for the second quadratic.For the first quadratic, the numbers are 10 and -9. This gives us (10x - 9)(x + 1).For the second quadratic, the numbers are 5 and -4. This gives us (2x - 1)(5x + 2).Combining all the factors, we get the expression as a product of four linear factors: (10x - 9)(x + 1)(2x - 1)(5x + 2).

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Rewrite the expression as a product of four linear factors:

(10x^(2)+x)^(2)-11(10x^(2)+x)+18
Answer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(10 x^{2}+x\right)^{2}-11\left(10 x^{2}+x\right)+18$ $\newline$ Answer:

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Q. Rewrite the expression as a product of four linear factors:

\newline

\left(10 x^{2}+x\right)^{2}-11\left(10 x^{2}+x\right)+18

\newline

Answer:

Define $y$ as expression: Let's denote the expression inside the parentheses as $y$ , where $y = 10x^2 + x$ . This will simplify our expression to a quadratic in terms of $y$ .
Rewrite as quadratic in $y$ : Now we rewrite the expression as a quadratic in $y$ : $(y)^2 - 11y + 18$ .
Factor quadratic expression: We need to factor the quadratic expression. To do this, we look for two numbers that multiply to $18$ and add up to $-11$ . These numbers are $-9$ and $-2$ .
Substitute back for $x$ : Factoring the quadratic expression gives us $(y - 9)(y - 2)$ .
Factor each quadratic further: Now we substitute back in for $y$ to get the expression in terms of $x$ : $(10x^2 + x - 9)(10x^2 + x - 2)$ .
Combine all factors: Each of these quadratic expressions can be factored further. We look for two numbers that multiply to $-90$ ( $10 \times -9$ ) and add up to $1$ (the coefficient of $x$ ) for the first quadratic, and two numbers that multiply to $-20$ ( $10 \times -2$ ) and add up to $1$ for the second quadratic.
Combine all factors: Each of these quadratic expressions can be factored further. We look for two numbers that multiply to $-90$ ( $10 \times -9$ ) and add up to $1$ (the coefficient of $x$ ) for the first quadratic, and two numbers that multiply to $-20$ ( $10 \times -2$ ) and add up to $1$ for the second quadratic.For the first quadratic, the numbers are $10$ and $-9$ . This gives us $(10x - 9)(x + 1)$ .
Combine all factors: Each of these quadratic expressions can be factored further. We look for two numbers that multiply to $-90$ ( $10 \times -9$ ) and add up to $1$ (the coefficient of $x$ ) for the first quadratic, and two numbers that multiply to $-20$ ( $10 \times -2$ ) and add up to $1$ for the second quadratic.For the first quadratic, the numbers are $10$ and $-9$ . This gives us $(10x - 9)(x + 1)$ .For the second quadratic, the numbers are $10 \times -9$ $0$ and $10 \times -9$ $1$ . This gives us $10 \times -9$ $2$ .
Combine all factors: Each of these quadratic expressions can be factored further. We look for two numbers that multiply to $-90$ $(10 \times -9)$ and add up to $1$ (the coefficient of $x$ ) for the first quadratic, and two numbers that multiply to $-20$ $(10 \times -2)$ and add up to $1$ for the second quadratic.For the first quadratic, the numbers are $10$ and $-9$ . This gives us $(10x - 9)(x + 1)$ .For the second quadratic, the numbers are $(10 \times -9)$ $0$ and $(10 \times -9)$ $1$ . This gives us $(10 \times -9)$ $2$ .Combining all the factors, we get the expression as a product of four linear factors: $(10 \times -9)$ $3$ .