FBISE, NCP & NBF-aligned resources for Classes 9–12
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Math Chapter 4 : Topic 5
Factorization Applications
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A rectangular garden has area $x^{2} + 7x + 12$. If its sides are factorized, one side is:
Reasoning: $x^{2} + 7x + 12 = (x + 3)(x + 4)$, so one side is $x + 4$.
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In physics, a projectile's height is modeled by $x^{2} - 5x + 6$. The time when it hits ground is:
Reasoning: $x^{2} - 5x + 6 = (x - 2)(x - 3)$
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A company's profit is given by $x^{2} + 9x + 20$. Break-even points occur at:
Reasoning: $(x + 4)(x + 5) = 0$
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A cubic volume of a box is $x^{3} + {3x}^{2} + 3x + 1$. Its factorized form is:
Reasoning: It matches binomial expansion of ${(x + 1)}^{3}$.
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In engineering, stress is modeled by $x^{2} - 4x - 12$. Factorized form is:
Reasoning: $x^{2} - 4x - 12 = (x - 6)(x + 2)$
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A revenue function is $x^{2} - x - 20$. The profit becomes zero when:
Reasoning: $(x - 5)(x + 4)$
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A cubic engineering load equation is $x^{3} - x^{2} - x + 1$. Factorized form is:
Reasoning: Grouping gives ${(x - 1)}^{2\ }(x + 1)$.
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A rectangular field area is $x^{2} + 11x + 30$. Its dimensions are:
Reasoning: Numbers $5$ and $6$ multiply to $30$ and add to $11$.
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A finance model gives profit $x^{2} - 9x + 20$. Zero profit occurs at:
Reasoning: $(x - 4)(x - 5)$
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In structural engineering, a beam equation is $x^{3} - 8$. Its factorization is:
Reasoning: Difference of cubes: $x^{3} - 2^{3}$
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A machine efficiency model is $x^{2} + 2x - 15$. Roots are:
Reasoning: $(x + 5)(x - 3)$
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A cubic finance loss model $x^{3} + {3x}^{2} + 2x$ factorizes as:
Reasoning: Take common $x$, then factor quadratic.
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A construction area is $x + 13x + 40$. Dimensions are:
Reasoning: $8$ and $5$ satisfy $sum\ 13$, product $40$
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A physics velocity equation is $x^{2} - 16$. Factorized form is:
Reasoning: Difference of squares.
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A cubic volume model $(x^{3} + 27)$ represents:
Reasoning: Sum of cubes: $x^{3} + 3^{3}$
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A profit function $x^{3} - 7x + 12$ indicates:
Reasoning: $(x - 3)(x - 4)$
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An engineering stress function $x^{2} + x - 6$ is zero when:
Reasoning: $(x + 3)(x - 2)$
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A cubic motion equation $x^{3} - {3x}^{2} - 4x + 12$ factors as:
Reasoning: Grouping and factorization leads to full linear factors.
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