Question

2x + 1 as a factor?
5. Using factor theorem, show that (x – 3) is a factor of (x3 - 7x2 + 15x – 9). Hence, factori
given expression completely.
6. Using factor theorem, show that (r
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Answer 1

By using factor theorem

x-3=3

p(3)=(3)3-7(3)2+15(3)-9

=9-42+45-9

=3

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Answer 2

Answer:

Factors are (x - 3), (x - 3) and (x - 1)

Step-by-step explanation:

p(x) = x³ - 7x² + 15x - 9

Let (x - 3) be a factor of p(x)

Then x - 3 = 0

x = 3

Using Factor theorem

Putting x = 3 in p(x) as p(3)

And remember if it is a factor then p(3) = 0

p(3) = (3)³ - 7(3)² + 15(3) - 9

0 = 27 - 7×9 + 45 - 9

0 = 27 - 63 + 45 - 9

0 = 72 - 72

0 = 0

Since there is no remainder (x - 3) is a factor of p(x)

Now to find the other factors we must divide p(x) by (x - 3)

so,

(x³ - 7x² + 15x - 9) ÷ (x - 3)

= x² - 4x + 3

Now we must find (x² - 4x + 3) factors

x² - 4x + 3 = 0

ax² + bx + c = 0

where a = 1, b = -4, c = 3

Sum = b = -4

Product = a × c = 3

Thus factors are -3 and -1

x² - 3x - x + 3

x(x - 3) -1(x - 3) = 0

(x - 3)(x - 1) = 0

Thus, Factors of x³ - 7x² + 15x - 9 are:-

(x - 3), (x - 3) and (x - 1)

Hope it helped and you understood it........All the best