Question

When 3x² - 5x + p is divided by (x - 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x² - 5x + p - 3.
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Answer 1

Step-by-step explanation:

Let us assume x–2=0

Then, x=2

Given, f(x)=3x2–5x+p

Now, substitute the value of x in f(x),

So, f(2)=3(2)

2

–5(2)+p

=3(4)–10+p

=12–10+p

=2+p

From the question it is given that, remainder is 3.

So, 2+p=3

p=3–2

p=1

Therefore, f(x)=3x

2

–5x+1

Consider the polynomial, 3x

2

–5x+p–3

Now, substitute the value of p in polynomial,

=3x

2

–5x+1–3

=3x

2

–5x–2

Now, by factorizing the polynomial 3x

2

–5x–2,

Dividing 3x

2

–5x–2byx–2 we get,

Therefore,3x

2

–5x–2=(x–2)(3x+1)

solution

Answer 2

Answer:

Let us assume x–2=0

Then, x=2

Given, f(x)=3x2–5x+p

Now, substitute the value of x in f(x),

So, f(2)=3(2)

2

–5(2)+p

=3(4)–10+p

=12–10+p

=2+p

From the question it is given that, remainder is 3.

So, 2+p=3

p=3–2

p=1

Therefore, f(x)=3x

2

–5x+1

Consider the polynomial, 3x

2

–5x+p–3

Now, substitute the value of p in polynomial,

=3x

2

–5x+1–3

=3x

2

–5x–2

Now, by factorizing the polynomial 3x

2

–5x–2,

Dividing 3x

2

–5x–2byx–2 we get,

Therefore,3x

2

–5x–2=(x–2)(3x+1)