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Factorize the following expressions : x^...

Factorize the following expressions : `x^4+4x^2+3`

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To factorize the expression \( x^4 + 4x^2 + 3 \), we can follow these steps: ### Step 1: Substitute Let \( y = x^2 \). This transforms the expression into \( y^2 + 4y + 3 \). ### Step 2: Factor the Quadratic Now we need to factor the quadratic expression \( y^2 + 4y + 3 \). We look for two numbers that multiply to \( 3 \) (the constant term) and add up to \( 4 \) (the coefficient of \( y \)). The numbers \( 1 \) and \( 3 \) satisfy these conditions. ...
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Knowledge Check

  • Factorize the following expressions : 15x^(4) + 3x^(2) - 18

    A
    `3(5x^(2) + 6)(x+1)(x-1)`
    B
    `3(5x^(2) + 6)(x-1)^(2)`
    C
    `3(5x^(2) + 6)(x+1)^(2)`
    D
    `(5x^(2) + 6)(x-1)`

  • Factorize the following expressions : 8x^(3) + (1)/(8x^(3)) + 2x + (1)/(2x)

    A
    `(2x + (1)/(2x)) (2x - (1)/(2x))`
    B
    `(2x + (1)/(2x))^(2)`
    C
    `(2x + (1)/(2x))(4x^(2) + (1)/(4x^(2)))`
    D
    None of these

  • Factorize the following expressions : (x + (1)/(x))^(3) - 2x - (2)/(x)

    A
    `(x + (1)/(x)) (x-(1)/(x))`
    B
    `(x + (1)/(x)) (x^(2)+(1)/(x^(2)))`
    C
    `(x - (1)/(x)) (x^(2)-(1)/(x^(2)))`
    D
    None of the above

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