Step 1: Find the GCF: 4x
^{2 }
Step 2: We want to find a product of the GCF (4x
^{2}) and another polynomial that when multiplied equals the original polynomial.
Step 3: Use an empty set of parentheses as a placeholder for three terms:
4x
^{2} (__ - __+__)
Step 4: 4x
^{2} times what will give me 20x
^{5} ?
4x
^{2} (
5x^{3} -__ + __)
Step 5: 4x
^{2} times what will give me -8x
^{4} ?
4x
^{2} (__ -
2x^{2 }+ __)
- Step 6: 4x^{2} times what will give me 12x^{2} ?
- 4x^{2} (__ -__ + 3)
Step 7: You can check using multiplication.
4x^{2} (5x^{3} -2x^{2} +3) = 20x^{5}-8x^{4} +12x^{2}