Question

if the polynomial p(x)= x⁴-2x³+3x²-ax+8 is divided by x-2, it leaves a remainder 10. Find the value of a ?
tell the and fast
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Answer 1

AnswEr :

When p(x) = x⁴ - 2x³ + 3x² - ax + 8 divided by (x - 2). It leaves a remainder 10.

We've to find the value of a.

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$:\implies\sf \Bigg( x - 2 \Bigg) \\\\\\:\underline{\sf{Equating \ with \ 0 \ :}} \\\\\\:\implies\sf x - 2 = 0 \\\\\\:\implies\boxed{\sf{\purple{x = 2}}}$

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$:\implies\sf x^4 - 2x^3 + 3x^2 - ax + 8 = 10 \\\\\\\qquad \quad \quad \underline{\sf{Substituting \ the \ Value \ of \ x \ in \ given \ polynomial \ :}} \\\\\\:\implies\sf (2)^4 - 2(2)^3 + 3(2)^2 - a(2) + 8 = 10 \\\\\\:\implies\sf \cancel{16} - \cancel{16} + 12 - 2a + 8 = 10 \\\\\\:\implies\sf 20 - 2a = 10 \\\\\\:\implies\sf - 2a = 10 - 20 \\\\\\:\implies\sf 2a = 10\\\\\\:\implies\sf a = \cancel\dfrac{10}{2} \\\\\\:\implies\boxed{\frak{\purple{a = 5}}}$

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${\therefore} \ \underline{\textsf{\textbf{ The \ Value \ of \ a \ is \ 5.}}}$

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⠀⠀⠀$\boxed{\bf{\mid{\overline{\underline{\bigstar\: About \ Polynomials \ : }}}}\mid}$

⠀⠀⠀⠀⠀ ⠀Any expression which have more than two algebraic terms is know as Polynomials.

⠀Types of polynomials :

• Monomial
• Binomial
• Trinomial

Monomial : It contains only one term.

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Binomial : It contains two terms.

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Trinomial : It contains three terms.

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Answer 2

Step-by-step explanation:

Given that, p(x)= x⁴-2x³+3x²-ax+8 is divided by x-2, it leaves a remainder 10.

We have to find the value of a.

From above data p(x) is 10 and value of x is 2 as x - 2 = 0, x = 2.

Simply substitute the value of p(x) and x in x⁴ - 2x³ + 3x² - ax + 8

→ 10 = (2)⁴ - 2(2)³ + 3(2)² - a(2) + 8

Solve the power,

→ 10 = 16 - 2(8) + 3(4) - 2a + 8

→ 10 = 16 - 16 + 12 - 2a + 8

→ 10 = 12 + 8 - 2a

→ 10 = 20 - 2a

→ 2a = 20 - 10

→ 2a = 10

Divide by 2 on both sides,

→ 2a/2 = 10/2

On solving we get,

→ a = 5

Hence, the value of a is 5.