LEARNER JOURNEY LABSFactor ax² + bx + c when a is not 1 and solve the resulting zero product.
Standalone concept packageNo prior equation-solving skill is assumed. Arithmetic operations, variables, equality, and every new algebra decision are explained on this page.
Factor ax² + bx + c when a is not 1 and solve the resulting zero product.
Construct the reasoning path, solve at least 4 of 5 mastery problems, and revise an unfamiliar explanation.
For ax² + bx + c, the leading factors must multiply to a, the constant factors must multiply to c, and the cross-products must add to b.
Checking the middle term prevents a factorization that matches only the first and last terms.
Move from left to right. Each decision prepares the next one; on a phone, follow the numbered cards from top to bottom.
Factor and solve 2x² + 5x + 2 = 0.
The reasoning path changes as each decision is selected.
Every example identifies the goal, explains the next move, carries out the algebra, and checks or interprets the result.
Predict first. Then use the visual relationship and reasoned feedback to check two decisions.
1. Solve 2x² + 2x − 24 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
2. Solve 3x² − 9x − 30 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
A prompt supplies part of the reasoning. Predict the missing mathematical move before choices appear.
1. Solve 6x² + 6x − 72 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Solve all six. Use the specific feedback to revise a method or sign error.
1. Solve 4x² + 20x − 56 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
2. Solve 10x² − 10x − 60 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
3. Solve 6x² + 6x − 120 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
4. Solve 10x² + 10x − 60 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
5. Solve 12x² + 12x − 72 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
6. Solve 6x² − 30x + 36 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Attempt all five. At least four correct answers are required for mastery.
1. Solve 10x² + 10x − 120 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
2. Solve 12x² − 12x − 144 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
3. Solve 14x² + 42x − 140 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
4. Solve 20x² − 60x − 200 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
5. Solve 30x² − 90x − 300 = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Factor 6x² + 7x − 3 and verify the middle term before solving.
Judge the locked first attempt against every criterion. Each judgment gives revision guidance.
The factorization is (3x − 1)(2x + 3) because the cross-products 9x and −2x add to 7x. Setting the factors to zero gives x = 1/3 or x = −3/2.
The record reveals exact answers and model reasoning only after the corresponding attempt or self-check has occurred.