Answer: 1) (x - 7)(x - 8)
2) 2x(2x-7)(x + 2)
3) (4x + 7)²
4) (9ab² - c³)(9ab² + c³)
Step-by-step explanation:
1) x² - 15x + 56 → use standard form for factoring
∧
-7 + -8 = -15
(x - 7) (x - 8)
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2) 4x³ - 6x² - 28x → factor out the GCF (2x)
2x(2x² - 3x - 14) → factor using grouping
2x[2x² + 4x - 7x - 14]
2x[ 2x(x + 2) -7(x + 2)]
2x(2x - 7)(x + 2)
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3) 16x² + 56x + 49 → this is the sum of squares
√(16x²) = 4x √(49) = 7
(4x + 7)²
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4) 81a²b⁴ - c⁶ → this is the difference of squares
√(81a²b⁴) = 9ab² √(c⁶) = c³
(9ab² - c³)(9ab² + c³)
The required factor of x² - 15x + 56 is (x-7)(x-8)
The factor of 4x³ - 6x² - 28x is 2x(x-7)(2x+4)
The factor of 16² + 56x + 49 is (4x+7)(4x+7) = (4x+7)²
The factor of [tex]81a^{2}b^{4} - c^{6}\\[/tex] is (9ab² + c³)(9ab² - c³)
A factor is a number that divides another number, leaving no remainder.
The given expression is
x² - 15x + 56
=x² - 7x - 8x + 56
= x(x-7) -8(x-7)
=(x-7)(x-8)
This is actually the standard way of factorization.
The required factor of x² - 15x + 56 is (x-7)(x-8)
The given expression is
4x³ - 6x² - 28x
=2x(2x² - 3x - 14)
=2x(2x² - 7x + 4x - 14)
=2x{2x(x - 7) + 4(x - 7)}
=2x(x-7)(2x+4)
The factor of 4x³ - 6x² - 28x is 2x(x-7)(2x+4)
The given expression is
16² + 56x + 49
=16x² + 28x + 28x + 49
=4x(4x +7) + 7(4x + 7)
=(4x+7)(4x + 7)
=(4x+7)²
The given expression is
[tex]81a^{2}b^{4} - c^{6}\\[/tex]
=(9ab²)² -(c³)²
=(9ab² + c³)(9ab² - c³)
∴ The factor of [tex]81a^{2}b^{4} - c^{6}\\[/tex] is (9ab² + c³)(9ab² - c³)
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