Solving-Word-Problems-Involving-the-Factoring-of-Polynomials-1.pptx

Solving Word Problems

1. Solving Word Problems Involving Factoring of Polynomials Jian Harvey Belaras Batondo Miael Angeline Rivera Guerzon Nazrene Ivy Guetang Banayos

2. Solving Word Problems Involving Factoring of Polynomials Jian Harvey Belaras Batondo Miael Angeline Rivera Guerzon Nazrene Ivy Guetang Banayos

3. WORD PROBLEM TYPES

4. PROBLEM A A R E

5. PROBLEM A A R E PROBLEM P E R I M E T E R

6. PROBLEM A A R E PROBLEM P E R I M E T E R PROBLEM N U M B E R

7. PROBLEM A A R E Area problems in math involve calculating the amount of space a two-dimensional shape occupies. You'll use specific formulas for each shape, like squares (side * side), rectangles (length * width), triangles (1/2 * base * height), and circles (π * radius²), to find the area, which is measured in square units like square inches and square meters Area Problem

8. PROBLEM A A R E Area problems in math involve calculating the amount of space a two-dimensional shape occupies. You'll use specific formulas for each shape, like squares (side * side), and rectangles (length * width), to find the area, which is measured in square units like square inches and square meters Area Problem

9. Alpha inherited a rectangular land in Cagayan Valley from his late father; it has a length four times as long as its width. When he sold a portion of his inherited land in Cagayan Valley, the length of his land decreased by 10 kilometers, and its width decreased by 6 kilometers. The new area of the land was 120 km² . With the given information, find the dimensions and the area of the inherited rectangular land in Cagayan Valley inherited by Alpha. 1 STEP 2 STEP 3 STEP 4 STEP

10. 1 STEP 2 STEP 3 STEP 4 STEP

11. 1 STEP Recall that the area of a rectangle can be found by multiplying the length ( l ) and the width ( w ) of the rectangle. In symbols, Area = (length)(width) or Area = lw 2 STEP 3 STEP 4 STEP

12. 1 STEP Recall that the area of a rectangle can be found by multiplying the length ( l ) and the width ( w ) of the rectangle. 2 STEP 3 STEP 4 STEP

13. 2 STEP Substitute the values in the problem to the formula in finding the area of a rectangle.

14. 2 STEP New Area = 120 km ² . Let width = w length ( l ) = 4 w – 10 width ( w ) = w – 6 Since Area = lw , by substitution, 120 = (4 w – 10)( w – 6) Consider the illustration: 1 STEP Recall that the area of a rectangle can be found by multiplying the length ( l ) and the width ( w ) of the rectangle. 3 STEP 4 STEP

15. 1 STEP Recall that the area of a rectangle can be found by multiplying the length ( l ) and the width ( w ) of the rectangle. 2 STEP Substitute the values in the problem to the formula in finding the area of a rectangle. 3 STEP 4 STEP

16. 3 STEP Simplify the expression and solve for what is asked.

17. 3 STEP 120 = ( 4 w – 10)( w – 6) 120 = 4 w ² - 24 w - 10 w + 60 120 = 4 w ² - 34 w + 60 120 - 120 = 4 w ² - 34 w + 60 - 120 0 = 4 w ² - 34 w – 60 0 = 4 w ² - 40 w + 6 w – 60 0 = (4 w ² - 40 w ) + (6 w – 60) Area = lw Distributive Property of Multiplication Add Similar Terms Place all polynomials on one side of the equation and set to 0 by Addition Property of Equality Resulting Equation Factoring Trinomials Factoring by Group

18. 3 STEP 0 = 4 w ( w – 10) + 6( w - 10) 0 = (4 w + 6)( w - 10) 4 w + 6 = 0 or w - 10 = 0 4 w + 6 – 6 = 0 – 6 or w - 10 + 10 = 0 + 10 4 w /4 = -6/4 w = -1.5 or w = 10 Factoring by GCMF Factored Form Zero Product Property Addition Property of Equality Multiplication Property of Equality Resulting Equations

19. 3 STEP Now, there are two values of the unknown -1.5 or 10 . Since there is no negative dimension, 10 is the measure of the width. Therefore, the dimensions are:   width ( w ) = 10 length ( 4w ) = 4(10) = 40   L et us now solve for the Area. We know that Area = lw . Let’s substitute and solve for the area of the land.   Area = lw Area = (40)(10) = 400   1 STEP Recall that the area of a rectangle can be found by multiplying the length ( l ) and the width ( w ) of the rectangle. 2 STEP Substitute the values in the problem to the formula in finding the area of a rectangle. 4 STEP

20. 1 STEP Recall that the area of a rectangle can be found by multiplying the length ( l ) and the width ( w ) of the rectangle. 2 STEP Substitute the values in the problem to the formula in finding the area of a rectangle. 3 STEP Simplify the expression and solve for what is asked. 4 STEP

21. 4 STEP State your Final Answer in a Complete Sentence Form The rectangular land inherited by Alpha in Cagayan Valley from his late father has a length of 40 km and a width of 10 km. Its Area measures 400 km ² 1 STEP Recall that the area of a rectangle can be found by multiplying the length ( l ) and the width ( w ) of the rectangle. 2 STEP Substitute the values in the problem to the formula in finding the area of a rectangle. 3 STEP Simplify the expression and solve for what is asked.

22. 1 STEP Recall that the area of a rectangle can be found by multiplying the length ( l ) and the width ( w ) of the rectangle. 2 STEP Substitute the values in the problem to the formula in finding the area of a rectangle. 3 STEP Simplify the expression and solve for what is asked. 4 STEP State your Final Answer in a Complete Sentence Form

23. Solving Word Problems Involving Involving Factoring of Polynomials Jian Harvey Belaras Batondo Miael Angeline Rivera Guerzon Nazrene Ivy Guetang Banayos

24. Thank You