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A number of algebra questions and solutions

A number of high school/college algebra questions and solutions including factorization and solving simulataneous equations, 11 questions in total

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1. Factor out the greatest common factor from the expression
-3xyz^2 + 6xz^2 - 15xyz^2

Let f(x) = -3xyz^2 + 6xz^2 - 15xyz^2

We can see that in f(x) the factor 3xz^2 is common so we can take this out

So f(x) = 3xz^2{-y + 2 - 5y} it is answer option (3)

2. Factor out the greatest common factor from the expression
9x^4y^4 + 7x^6y^3 - 12x^4y^3

Greatest common fact to all terms in the above is x^4*y^3 so taking this term out we are left with the factorised expression

x^4*y^3{9y + 7x2 - 12}

3. Megan factored the expression 12x^2+13x -14 as (3x +2)(4x -7). But when Jacob applied the FOIL principle and multiplied out
(3x +2)(4x -7) he got 12x^2 - 13x -14; thus, Megan's solution does not appear to check. Why is that? Please help Megan to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.

Multiplying out Megan's solution we get:

(3x +2)(4x -7) = 3x*4x - 7*3x +2*4x +2(-7) = 12x^2 - 21x + 8x - 14

= 12x^2 - 13x - 14

It does not equate to her original expression to factor of 12x^2+13x -14 if she wants to get +13x instead of -13x as her factorisation (3x +2)(4x -7) equates to she should replaced the +2 with a -ve 2 and the - 7 with a +ve 7 to get the correct factorisation

(3x - 2)(4x + 7) =3x*4x + 7*3x - 2*4x -2(+7) = 12x^2 + 21x - 8x - 14
= 12x^2 + 13 - 14

She has got her signs round the wrong way in her factorisation

4. Use the "difference of squares" rule to factor the following expression:
16x^4 -121y^4

Generally the difference of squares says that the difference between two squares of say numbers A & B can be expressed as

A^2 - B^2 = (A+B)(A-B)

We can see that ...

Solution Summary

A number of high school/college algebra questions and solutions including factorization and solving simulataneous equations

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