Factor –8x3 – 2x2 – 12x – 3 by grouping. What is the resulting expression?
(2x2 – 3)(4x + 1)
(–2x2 – 3)(–4x + 1)
(2x2 – 3)(–4x + 1)
(–2x2 – 3)(4x + 1)

The resulting expression is (-2x² - 3)(4x + 1) ⇒ 4th answer

Step-by-step explanation:

Factorization by grouping means take the greatest common factor from each two terms to reduce the 4 terms to two terms with common bracket, then take the bract as a common factor to reduce them to one term

Ex : ax + by + bx + ay = (ax + ay) + (bx + by)

Take x as a common factor from first bracket and y as a common factor from the second bracket

(ax + ay) + (bx + by) = a(x + y) + b(x + y) ⇒ take the bracket (x + y) as a common factor

a(x + y) + b(x + y) = (x + y)(a + b)

The factorization of ax + by + bx + cy is (x + y)(a + b)

Now lets solve the problem

The expression is -8x³ - 2x² - 12x - 3

Let us take -8x³ and -2x² in a bracket and -12x and -3 in other bracket

∵ -8x³ - 2x² - 12x - 3 = (-8x³ - 2x²) + (-12x - 3)

- Let us factorize the first bracket (-8x³ - 2x²)

∵ The greatest common factor of -8 and -2 is -2

∵ The greatest common factor of x³ and x² is x²

∴ The greatest common factor of -8x³ and -2x² is -2x²

- Divide each term in the bracket by -2x² to find the terms inside

   the bracket

∵ -8x³ ÷ -2x² = 4x

∵ -2x² ÷ -2x² = 1

∴ (-8x³ - 2x²) = -2x²(4x + 1)

Let us do the same with the other bracket (-12x - 3)

∵ The greatest common factor of -12 and -3 is -3

- Divide each term in the bracket by -3 to find the terms inside

∵ -12x ÷ -3 = 4x

∵ -3 ÷ -3 = 1

∴ (-12x - 3) = -3(4x + 1)

∴ (-8x³ - 2x²) + (-12x - 3) = -2x²(4x + 1) + -3(4x + 1)

- Take the bracket (4x + 1) as a common factor

∴ -2x²(4x + 1) + -3(4x + 1) = (4x + 1)(-2x² + -3)

∴ -2x²(4x + 1) + -3(4x + 1) = (4x + 1)(-2x² - 3)

- Switch the two brackets

∴ The resulting expression is (-2x² - 3)(4x + 1)

when studying polynomials, you often hear the terms zeros, roots, factors and x x the multiplicity of a zero is important because it tells us how the graph of the let's look at the graph of a function that has the same zeros

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