Mathematics
Grade 11
15 min
Multiplication facts up to 12: find the missing factor
Multiplication facts up to 12: find the missing factor
What you'll learn
- Identify the missing factor in multiplication equations up to 12 with 80% accuracy on a worksheet.
- Solve for the missing factor in multiplication problems presented in story form, using numbers up to 12, in at least 2 out of 3 problems.
- Explain the relationship between multiplication and division when finding a missing factor, using terms like 'factor', 'product', and 'divide' in their own words.
- Apply known multiplication facts to determine the missing factor in equations with products up to 144 (e.g., _ x 7 = 49) and correctly complete at least 4 out of 5 problems.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Apply the principles of finding a missing factor to polynomial expressions.
Perform polynomial long division to find a missing polynomial factor.
Use synthetic division as a shortcut to find a missing linear factor's corresponding polynomial quotient.
Apply the Factor Theorem to verify if a binomial is a factor of a given polynomial.
Deconstruct a higher-degree polynomial into its constituent factors, where coefficients are integers up to 12.
Solve for an unknown polynomial factor `Q(x)` in the equation `P(x) = D(x) * Q(x)`.
You mastered `8 * ? = 96` in elementary school. But how do you find the missing piece in `(x - 8) * ? = x² + 4x - 96`? 🤔 Let's level up that same skill!
This tutorial bridges a simple concept—finding a missing number in a...
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Key Concepts & Vocabulary
TermDefinitionExample
Polynomial FactorA polynomial that divides another polynomial evenly, with a remainder of zero. It's the algebraic equivalent of a factor in arithmetic.In the expression `x² - 9 = (x - 3)(x + 3)`, both `(x - 3)` and `(x + 3)` are polynomial factors of `x² - 9`.
DividendThe polynomial that is being divided. In the problem 'find the missing factor of P(x) given D(x)', P(x) is the dividend.In `(x³ + 2x² - 5x - 6) ÷ (x - 2)`, the dividend is `x³ + 2x² - 5x - 6`.
DivisorThe polynomial by which another polynomial is divided. This is the 'known factor'.In `(x³ + 2x² - 5x - 6) ÷ (x - 2)`, the divisor is `(x - 2)`.
QuotientThe result of a polynomial division. This is the 'missing factor' we are looking for.For `(x² - 4) ÷ (x - 2)`, the quoti...
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Core Formulas
The Division Algorithm for Polynomials
P(x) = D(x) \cdot Q(x) + R(x)
This states that any polynomial Dividend `P(x)` can be expressed as the product of the Divisor `D(x)` and the Quotient `Q(x)`, plus a Remainder `R(x)`. To find the missing factor `Q(x)`, we need to ensure the remainder `R(x)` is zero.
The Factor Theorem
(x - c) \text{ is a factor of } P(x) \iff P(c) = 0
This is a powerful test to confirm if a linear binomial `(x-c)` is a factor without performing the full division. If substituting `c` into the polynomial results in zero, then `(x-c)` is a factor.
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Challenging
Given that (x - 2) and (x + 3) are factors of the polynomial P(x) = x⁴ + 2x³ - 7x² - 8x + 12, find the other missing quadratic factor.
A.x² + x - 2
B.x² - x + 2
C.x² + 3x - 4
D.x² - 6
Challenging
If (x - c) is a factor of the polynomial P(x) = x³ - 8x² + 11x + c, what is a possible non-zero integer value for c?
A.4
B.1
C.6
D.3
Challenging
A cubic polynomial is P(x) = x³ - 2x² - 5x + 6. Given that (x - 1) is a factor, find the other missing factor, which is a quadratic polynomial.
A.x² + x + 6
B.x² - x - 6
C.x² - 3x + 2
D.x² + 2x - 3
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Frequently asked questions
What grade level is "Multiplication facts up to 12: find the missing factor"?
Multiplication facts up to 12: find the missing factor is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Multiplication facts up to 12: find the missing factor?
You'll be able to: Identify the missing factor in multiplication equations up to 12 with 80% accuracy on a worksheet; Solve for the missing factor in multiplication problems presented in story form, using numbers up to 12, in at least 2 out of 3….
Is "Multiplication facts up to 12: find the missing factor" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Multiplication facts up to 12: find the missing factor?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.