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We want to factor the following expression:

(x-1)^(2)+(x-1)+4
Which pattern can we use to factor the expression?

U and
V are either constant integers or single-variable expressions.
Choose 1 answer:
(A)
(U+V)^(2) or
(U-V)^(2)
(B)
(U+V)(U-V)
(C) We can't use any of the patterns.

We want to factor the following expression: $\newline$ $(x-1)^{2}+(x-1)+4$ $\newline$ Which pattern can we use to factor the expression? $\newline$ $U$ and $V$ are either constant integers or single-variable expressions. $\newline$ Choose $1$ answer: $\newline$ (A) $(U+V)^{2}$ or $(U-V)^{2}$ $\newline$ (B) $(U+V)(U-V)$ $\newline$ (C) We can't use any of the patterns.

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Compare linear and exponential growth

Full solution

Q. We want to factor the following expression:

\newline

(x-1)^{2}+(x-1)+4

\newline

Which pattern can we use to factor the expression?

\newline

U

and

V

are either constant integers or single-variable expressions.

\newline

Choose

1

answer:

\newline

(A)

(U+V)^{2}

or

(U-V)^{2}

\newline

(B)

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

Write and analyze given expression: Write down the given expression and analyze its form. $\newline$ The given expression is $(x-1)^{2}+(x-1)+4$ . We need to determine if this expression fits any of the factoring patterns provided in the choices.
Check for square of a binomial pattern: Check if the expression fits the square of a binomial pattern. $\newline$ The square of a binomial pattern is either $(U+V)^{2}$ or $(U-V)^{2}$ , which expands to $U^{2} + 2UV + V^{2}$ or $U^{2} - 2UV + V^{2}$ , respectively. Our expression is $(x-1)^{2}+(x-1)+4$ , which is close to the pattern but does not have the middle term in the form of $2UV$ .
Check for difference of squares pattern: Check if the expression fits the difference of squares pattern. $\newline$ The difference of squares pattern is $U+V)(U-V)\, which expands to \$U^2 - V^2$ . Our expression is x\(-1)^{ $2$ }+(x $-1$ )+ $4$ \, which does not fit this pattern because it has a middle term and a constant term that is not subtracted.
Determine if expression can be factored: Determine if the expression can be factored using any of the given patterns. $\newline$ The expression $(x-1)^{2}+(x-1)+4$ does not fit the square of a binomial pattern exactly because the coefficient of the middle term is not double the product of the square roots of the first and last terms. It also does not fit the difference of squares pattern because it has a middle term and a positive constant term. Therefore, we cannot use any of the given patterns to factor the expression.

More problems from Compare linear and exponential growth

Question

We want to factor the following expression:

\newline

x^{4}+10 x+25

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

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\newline

1

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We want to factor the following expression:

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Which pattern can we use to factor the expression?

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V

are either constant integers or single-variable expressions.

\newline

1

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(U+V)^{2}

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We want to factor the following expression:

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16 x^{4}-25

\newline

Which pattern can we use to factor the expression?

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U

V

are either constant integers or single-variable expressions.

\newline

1

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(U+V)^{2}

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We want to factor the following expression:

\newline

x^{4}+3 x^{2} y+9 y^{2}

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

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We want to factor the following expression:

\newline

(x+5)^{4}+2(x+5)^{2}-1

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

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Question

We want to factor the following expression:

\newline

(x-3)^{2}-10(x-3)+25

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

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Question

We want to factor the following expression:

\newline

(x+7)^{2}+2 y(x+7)+y^{2}

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

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We want to factor the following expression:

\newline

9 x^{6}+6 x^{3} y+y^{2}

\newline

Which pattern can we use to factor the expression?

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U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

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\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

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