By HOLT MCDOUGAL
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Additional resources for Math Resource. Algebra
Example text
A) x2 – x + 12 = 0 b) 6x2 – x – 12 = 0 c) x2 = 81 Solutions: a) This is a simple quadratic equation. After a bit of searching, we can factor the expression on the left to create an equivalent equation. x2 – x + 12 = 0 (x – 4)(x + 3) = 0 ← factor the quadratic expression on the left x – 4 = 0 or x + 3 = 0 ← corollary of the mult. prop. of zero x=4 or x = -3 ← solve the appropriate equations This gives the two possible solutions to the quadratic equation. b) 6x2 – x – 12 = 0 (2x – 3)(3x + 4) = 0 2x – 3 = 0 or 3x + 4 = 0 3 4 or x= − x= 2 3 c) x2 = 81 x2 – 81 = 0 (x – 9)(x + 9) = 0 x – 9 = 0 or x+9 =0 x=9 or x = -9 ← factor the quadratic expression on the left ← corollary of the mult.
1 is then a rational expression because is a because any polynomial can be written 1 1 ratio of polynomials. 19 Rational expressions, in a manner of speaking, resemble fractions. Instead of having integers in the numerator and denominator, rational expressions have polynomials in those positions instead. It’s time to revisit our examples for the arithmetic of fractions and the cancellation law. Recall the cancellation law from much earlier – it is rewritten here for your convenience. The cancellation law says, in essence, that when a common factor appears in both the numerator and the denominator of an expression, it can be cancelled out provided the denominator not equal 0.
X2 – x + 12 = 0 (x – 4)(x + 3) = 0 ← factor the quadratic expression on the left x – 4 = 0 or x + 3 = 0 ← corollary of the mult. prop. of zero x=4 or x = -3 ← solve the appropriate equations This gives the two possible solutions to the quadratic equation. b) 6x2 – x – 12 = 0 (2x – 3)(3x + 4) = 0 2x – 3 = 0 or 3x + 4 = 0 3 4 or x= − x= 2 3 c) x2 = 81 x2 – 81 = 0 (x – 9)(x + 9) = 0 x – 9 = 0 or x+9 =0 x=9 or x = -9 ← factor the quadratic expression on the left ← corollary of the mult. prop. of zero ← solve the appropriate equations ← add the additive inverse of 81 to each side ← factor the difference of two squares ← corollary of the mult.
Math Resource. Algebra by HOLT MCDOUGAL
by Thomas
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