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t asked in Science & MathematicsMathematics · 7 years ago

maths gcse exam question: x is a positive integer, prove why it cannot be a prime number in the expression (2x^2)+5x+2?

my maths gcse is tomz and i am doing past papers, i can handle most of the questions, but im kinda confused on algebraic proof

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  • kb
    Lv 7
    7 years ago

    Note that 2x^2 + 5x + 2 = (2x + 1)(x + 2).

    Since x is a positive integer (so that x > 0), observe that both

    2x + 1 > 1 and x + 2 > 2.

    So, (2x + 1)(x + 2) gives a nontrivial factorization of 2x^2 + 5x + 2

    for any positive integer x.

    Thus, 2x^2 + 5x + 2 is not prime for any positive integer x.

    I hope this helps!

  • Elizabeth M
    Lv 7
    7 years ago

    For the question asked, x CAN be a prime number..

    Its the number (2x²+5x+2) which cannot be prime.

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