If y = 2 - x - x 1 + 1 + x , then what is the value of 1 y + 1 + 2 y + 1 y 2 - 1 ?

2 ( 1 - x ) ( x + 2 ) x ( x - 4 )

MEDIUM

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Identify the fourth degree polynomial from the given graph.

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Important Questions on Seeing Structure in Expressions

MEDIUM

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

x^{4} + x^{2} y^{2} + y^{4} = 273

and

x^{2} - x y + y^{2} = 13

, then the value of

x y

is:

MEDIUM

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

On simplifiication,

\frac{x^{3} - y^{3}}{x [{(x + y)}^{2} - 3 x y]} \div \frac{y [{(x - y)}^{2} + 3 x y]}{x^{3} + y^{3}} \times \frac{{(x + y)}^{2} - {(x - y)}^{2}}{x^{2} - y^{2}}

is equal to:

EASY

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

The expression

{(a + b - c)}^{3} + {(a - b + c)}^{3} - 8 a^{3}

is equal to:

MEDIUM

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

a^{2} + b^{2} = 82

and

a b = 9

, then a possible value of

a^{3} + b^{3}

is _____.

MEDIUM

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

f (x) = 2 x + 1

then number of real values of

x

for which three unequal functions

f (x), f (2 x), f (4 x)

are in G.P

EASY

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

a + b + c = 0

, then the value of

\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b}

is _____.

MEDIUM

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

x^{4} + x^{2} y^{2} + y^{4} = 21

and

x^{2} + x y + y^{2} = 7

, then the value of

(\frac{1}{x^{2}} + \frac{1}{y^{2}})

is:

MEDIUM

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

x - \frac{1}{x} = 2 \sqrt{2}

, then

x^{2} + \frac{1}{x^{2}}

is equal to:

EASY

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

\sqrt{y} = \sqrt{4} - \sqrt{6},

Then find the value of

(y^{2} - 20 y + 12) .

EASY

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

y = \frac{2 - x - x}{1 + 1 + x}

, then what is the value of

\frac{1}{y + 1} + \frac{2 y + 1}{y^{2} - 1}

MEDIUM

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

x^{2} + 8 y^{2} + 12 y - 4 x y + 9 = 0

, then the value of

(7 x + 8 y)

is:

EASY

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

The graphs of $y = p (x)$ are given in figure below for some polynomials $p (x)$ . Find the number of zeros of $p (x)$ .

Question Image

MEDIUM

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

x + y + z = 17, x y z = 171

and

x y + y z + z x = 111

, then the value of

\sqrt[3]{(x^{3} + y^{3} + z^{3} + x y z)}

is _____.

MEDIUM

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

x + y + z = 19

x y z = 216

and

x y + y z + z x = 114

, then the value of

\sqrt{x^{3} + y^{3} + z^{3} + x y z}

is:

MEDIUM

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

x^{2} - 3 x + 1 = 0

, then the value of

(x^{4} + \frac{1}{x^{2}}) \div (x^{2} + 1)

is:

HARD

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

{(x - 2)}^{3} + {(x - 3)}^{3} + {(x - 10)}^{3} = (x - 2) (x - 3) (3 x - 30)

, then what is the value of

x

EASY

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

a + b = 8, a b = - 12

then,

a^{3} + b^{3} =

MEDIUM

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

(5 x + 2 y) ∶ (10 x + 3 y) = 5 : 9

, then

(2 x^{2} + 3 y^{2}) : (4 x^{2} + 9 y^{2}) = ?

EASY

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

The number of zeros of the polynomial in the graph is _____

Question Image

EASY

Mathematics>Algebra>Seeing Structure in Expressions>Use the structure of an expression to identify ways to rewrite it.

For the graph, in the figure, $y = P (x)$ has _____zero $/$ zeros.

Question Image

Identify the fourth degree polynomial from the given graph.

Important Questions on Seeing Structure in Expressions

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