5x2 - 31x + 28 FACTORIZE
Answers
Answer:
Given,
Factorise the given expression,
\sqrt { 3 } x ^ { 2 } + 10 x + 7 \sqrt { 3 }
3
x
2
+10x+7
3
For factorising, splitting out the middle terms in the given expression, the middle term becomes as follows,
= \sqrt { 3 } x ^ { 2 } + 3 x + 7 x + 7 \sqrt { 3 }=
3
x
2
+3x+7x+7
3
as 7 + 3 = 10 and 7 × 3 = 21
\begin{lgathered}\begin{array} { l } { = \sqrt { 3 } x ( x + \sqrt { 3 } ) + 7 ( x + \sqrt { 3 } ) } \\\\ { = ( \sqrt { 3 } x + 7 ) ( x + \sqrt { 3 } ) } \\\\ { \sqrt { 3 } x ^ { 2 } + 10 x + 7 \sqrt { 3 } = ( \sqrt { 3 } x + 7 ) ( x + \sqrt { 3 } ) } \end{array}\end{lgathered}
=
3
x(x+
3
)+7(x+
3
)
=(
3
x+7)(x+
3
)
3
x
2
+10x+7
3
=(
3
x+7)(x+
3
)
Thus, the factorisation of \sqrt { 3 } x ^ { 2 } + 10 x + 7 \sqrt { 3 }
3
x
2
+10x+7
3
will be (\sqrt3 x+7)(x+\sqrt3)(
3
x+7)(x+
3
)
Explanation:
Given,
Factorise the given expression,
\sqrt { 3 } x ^ { 2 } + 10 x + 7 \sqrt { 3 }
3
x
2
+10x+7
3
For factorising, splitting out the middle terms in the given expression, the middle term becomes as follows,
= \sqrt { 3 } x ^ { 2 } + 3 x + 7 x + 7 \sqrt { 3 }=
3
x
2
+3x+7x+7
3
as 7 + 3 = 10 and 7 × 3 = 21
\begin{lgathered}\begin{array} { l } { = \sqrt { 3 } x ( x + \sqrt { 3 } ) + 7 ( x + \sqrt { 3 } ) } \\\\ { = ( \sqrt { 3 } x + 7 ) ( x + \sqrt { 3 } ) } \\\\ { \sqrt { 3 } x ^ { 2 } + 10 x + 7 \sqrt { 3 } = ( \sqrt { 3 } x + 7 ) ( x + \sqrt { 3 } ) } \end{array}\end{lgathered}
=
3
x(x+
3
)+7(x+
3
)
=(
3
x+7)(x+
3
)
3
x
2
+10x+7
3
=(
3
x+7)(x+
3
)
Thus, the factorisation of \sqrt { 3 } x ^ { 2 } + 10 x + 7 \sqrt { 3 }
3
x
2
+10x+7
3
will be (\sqrt3 x+7)(x+\sqrt3)(
3
x+7)(x+
3
)