Q: Factor completely and check mentally 15x squared plus 5x?

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you do 2 sets of parenthesis and check it. for example: w2(w squared)-7w-8 (w+1) (w-8) *if you add 1w and -8w you will get -7w, which is what they want you to get. and w & w multiply to get w2(w squared), which is also what the factoring wants. another example: 3w2 (3w squared)+2-8 (3w-4) (w+2) *same thing applies with 3w x w = 3w2, and -4 +2=2, which is the answer. use this theory in all of them, unless there is a greatest common factor (GCF).

2x2 - 72 would be factored into (2x - 12)(x + 6) or (2x + 12)(x - 6) To double check, multiply each pair: (2x - 12)(x + 6) = 2x2 + 12x - 12x - 72 = 2x2 - 72 (2x + 12)(x - 6) = 2x2 - 12x + 12 x - 72 = 2x2 - 72

The height or altitude of triangle: (2*45)/15 = 6cm Check: 0.5*15*6 = 45 square cm

You use the Pythagorean theorem. Remember that Asq + Bsq = Csquared, where A and B are the sides of a right triangle and C is the diagonal. (Remember that a right triangle is just a square cut in half slantwise.) Based on the theorem, you know that the sum of A squared and B squared equals 20 squared (20 squared = 20 x 20 or 400.) Also, since it's a square you concerned with, you know that the sides are the same length. So whatever length "A" side is, "B" side is the same. So we might as well say two times A is the same as A plus B. So two times A squared equals 400. We only want to know what ONE side of the square measures, so we can reduce both sides of the equation by dividing each side by 2. In other words, if TWO times A squared equals 400, then ONE times A squared equals 200. But we don't want to know what the length of A squared is, we want to know what the length of A is. So take the square root. A equals the square root of 200. The square root of 200 is fourteen plus a fraction. So your square is fourteen plus a fraction on each side. Check your work: 14 squared plus 14 squared = 196 + 196 = 392, which is is very close to the C squared we started with of 400. The square root of 400 is 20, and you are back to the beginning.

The way to do this is get an expression equal to zero, then solve (in this case it's a quadratic), so either factor or use the quadratic equation. x2 + x - 56 = 0: Factors into: (x - 7)(x + 8) = 0, x = 7 & x = -8To factor, find two numbers which when added equal 1 (the coefficient of the x term) and when multiplied equal -56. So one of the numbers must be positive and the other negative. Factor pairs of 56 are (1,56) (2,28) (4,14) and (7,8). Seven & eight are one apart, so if the seven is negative, they will add to equal 1. If either of the binomial factors is zero, then the result is zero, so for (x-7)=0, {x=7} solves it, and for (x+8)=0, {x=-8} solves it. Check your answers in the original equation, to make sure you did it correctly:7^2 + 7 = 49 + 7 = 56 (check) (-8)^2 + -8 = 64 - 8 = 56 (check) STANLY WAS HERE

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you do 2 sets of parenthesis and check it. for example: w2(w squared)-7w-8 (w+1) (w-8) *if you add 1w and -8w you will get -7w, which is what they want you to get. and w & w multiply to get w2(w squared), which is also what the factoring wants. another example: 3w2 (3w squared)+2-8 (3w-4) (w+2) *same thing applies with 3w x w = 3w2, and -4 +2=2, which is the answer. use this theory in all of them, unless there is a greatest common factor (GCF).