Math for College Technology (MCT4C) · Polynomial Functions

Solve a polynomial volume equation by testing values

Solve a cubic volume equation x(L-2x)(W-2x) = V for the whole-number side length x by systematic testing. Unlimited questions, five difficulty levels, and a full worked solution every time — free.

Practice this skill Curriculum: MCT4C-PL3

Try one

A sheet-metal fabricator has a rectangular sheet 10 cm by 7 cm. A square of side x is cut from each corner, and the sides are folded up to form an open box. What whole-number side length x makes the box's volume 40 cm^3?

V = x(10 - 2x)(7 - 2x)

Answer: 1

See one solved, step by step

A sheet-metal fabricator has a rectangular sheet 11 cm by 12 cm. A square of side x is cut from each corner, and the sides are folded up to form an open box. What whole-number side length x makes the box's volume 112 cm^3?

V = x(11 - 2x)(12 - 2x)

📘 Worked solution

1x(11 - 2x)(12 - 2x) = 112Volume = height * base length * base width, where cutting squares of side x from each corner leaves a base of (L - 2x) by (W - 2x) once the sides fold up.

2Try x = 2: 2(11 - 4)(12 - 4) = 2(7)(8)Since x must be a whole number less than half of the shorter side, test whole-number values.

3= 112That matches the required volume of 112 cm^3, so x = 2 works.

4x = 2 cmThat's the side length of the square that should be cut from each corner.

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