# Write as the product of two factorise x2+3x-40 Compare the two factorisations. The larger integer b. Example 2 The sum of two integers is We can use the approach outlined on page to obtain the equation. How much is invested at each rate? Once again, we will follow the six steps out- lined on page when we solve the problems. Solution Steps We first write what we want to find as word phrases.

## Mathway functions

Solution b. Another type of mixture problem is one that involves the mixture of the two liquids. Then, we represent each phrase in terms of a variable. Once again, we will follow the six steps out- lined on page when we solve the problems. Example 1 One integer is three more than another. We say that these factors are irreducible over the rational numbers. Example 4 One integer is five more than a second integer. These identities are generally covered in senior mathematics and are useful in beginning calculus and for finding limits. The larger integer. Step 4 We can now write an equation relating the amounts of pure acid before and after combining the solutions. Compare the two factorisations. If x represents the smaller integer, represent in terms of X a. Then, we proceed to solve the equation by first writing equivalently the equation without parentheses.

Polynomials will be discussed further in the module Polynomials. Step 4 Now, we can write an equation relating the interest from each in- vestment and the total interest received.

## Mathway functions

There are methods of factoring such expressions. It will be noted that not all quadratic equations have rational solutions. Once again, we will follow the six steps out- lined on page when we solve the problems. Example 2 The sum of two integers is This can be verified by expansion. Five times the smaller integer. Example 4 One integer is five more than a second integer. Other techniques will be developed in the module Quadratic Equations to handle such equations. There are 16 more dimes than quarters. The square of the smaller integer c. Step 5 Solving the equation yields Step 6 The grocer should use 60 kg of the candy. Compare the two factorisations.

Sometimes it is impossible to factor polynomial into linear factors using rational numbers, but it may be possible to factor an expression containing terms with degree 6 say into a product containing terms with x3.

Find the integers. A table like the one shown in the next example is helpful in solving interest problems. The expressions in each bracket cannot be further factored using only rational numbers.

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