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What is X2 plus 8X plus 16?
X2 + 8x + 16 = 10x +16x2 + 8x + 16=2x + 8x + 16=10x + 16
Put the equation in the form ax2 plus bx plus c equals 0 x2-3 equals 3x2 plus 8x?
2x^2 + 8x + 3 = 0
Factor x2 plus 8x plus 15?
x2 + 8x + 15 = (x + 3)(x + 5)
What number should you add to complete the square x2 plus 8x equals -3?
You ignore the constant part (-3 in this case), calculate half of the coefficient of the linear part (8, in this case), and square this half. (1/2 of 8 is 4; the square of 4 is 16). This gives you the perfect square x2 + 8x + 16. To get something equivalent to the original expression, you must both add and subtract 16, and include the term which I previously ignored (-3): x2 + 8x + 16 - 16 - 3, which you can write as (x2 + 8x + 16) - 16 - 3. The part within parentheses is the perfect square.
The polynomial y equals x2 - 8x plus 16 has a repeated factor?
Why, yes, indeed, it has! Look at the factors: x2 - 8x + 16 = (x - 4)2 = (x - 4)(x - 4). If you multiply it out, you will see that it is so. Note that ' (x - 4) ' appears twice in the factorisation. That is what we mean, by a 'repeated factor'.
