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How do you factor the expression $2{x^2} - 4x?$

Last updated date: 25th Feb 2024
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IVSAT 2024
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Hint: First check for common factors among each term of the expression, and then take out the common factor from each term of the expression and rewrite the expression in its factored form. In order to find common factors you need to list all the factors of each term.

Complete step by step solution:
To factorize an expression, we should firstly check if there any common factor between all terms of the expression lies,
Checking for common factors between the terms ${x^2}\;{\text{and}}\;5x$ by listing all their factors
We can list them as $2{x^2} = 2 \times x \times x\;{\text{and}}\;4x = 2 \times 2 \times x$
We can see there are two common factors between them which are $2\;{\text{and}}\;x$
Now taking $2x$ common from the given expression we will get
= 2{x^2} - 4x \\
= 2x(x - 2) \\
That is factored form of the expression $2{x^2} - 4x$ is $2x(x - 2)$
Multiplying $2x$ with $x - 2$ in order to check whether our factorization is correct or not
$ = 2x \times (x - 2)$
Using distributive property of multiplication to multiply the terms
= 2x \times x - 2x \times 5 \\
= 2{x^2} - 4x \\
We got the given expression after the multiplication of terms of the resultant factor. It means our factorization and result is correct.

Note: We can also solve this by sum product method for factorization of algebraic expressions. Sum product method can only be applied for quadratic polynomial expressions, it can be understood as a quadratic polynomial expression $a{x^2} + bx + c$ where $a,\;b\;{\text{and}}\;c$ are constant, can be factorized by splitting the middle term i.e. the coefficient of $x$ in such a way that the multiplication of the separated terms should be equal to product of $a\;{\text{and}}\;c$ and their sum should be equal to $b$ Try this method by yourself for this question. Hint: Take value of $c = 0$