Question

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If polynomial (2a + 3 ) is multiplied by (2a² + 5a + 3 ) then the degree of the answer?*

1️⃣ 1
2️⃣ 2
3️⃣ 4
4️⃣ 3
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Answer 1

EXPLANATION.

If polynomial (2a + 3) is multiply by (2a² + 5a + 3).

As we know that,

Multiply both the equation, we get.

⇒ (2a + 3) x (2a² + 5a + 3).

⇒ 2a(2a² + 5a + 3) + 3(2a² + 5a + 3).

⇒ 4a³ + 10a² + 6a + 6a² + 15a + 9.

⇒ 4a³ + 16a² + 21a + 9.

As we can see that,

Highest degree of polynomial = 3.

Hence, option [4] is correct answer.

Answer 2

Question: This question says that if a polynomial (2a + 3 ) is multiplied by (2a² + 5a + 3 ) then what is the degree of the answer?

Solution: A polynomial (2a + 3 ) is multiplied by (2a² + 5a + 3 ) then the degree of the answer is 3(Option 4)

Full Solution:

↪️ (2a + 3 ) × (2a² + 5a + 3)

↪️ 2a(2a² + 5a + 3) + 3(2a² + 5a + 3)

↪️ 4a³ + 10a² + 6a + 6a² + 15a + 9

↪️ 4a³ + 10a² + 6a² + 6a + 15a + 9

↪️ 4a³ + 16a² + 21a + 9

↪️ 3 is the highest degree

Additional information:

• Factorised identities:

$\begin{gathered}\\\;\sf{\leadsto\;\;(a\:+\;b)^{2}\; =\;a^{2}\:+\:b^{2}\:+\:2ab}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto\;\;(a\:-\:b)^{2}\;=\;a^{2}\:+\:b^{2}\:-\:2ab}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto\;\;(a\:+\:b\:+\:c)^{2}\;=\;a^{2}\:+\:b^{2}\:+\:c^{2}\:+\:2ab\:+\:2bc\:+\:2ac}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto\;\;(a\:+\;b)^{3}\;=\;a^{3}\:+\:b^{3}\:+\:3ab(a\:+\:b)}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto\;\;(a\:-\;b)^{3}\;=\;a^{3}\:-\:b^{3}\:-\:3ab(a\:-\:b)}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto \;\;(a+b)^{2} \: = \: a^{2} + 2ab + b^{2}}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto \;\;(a-b)^{2} \: = a^{2} - 2ab + b^{2}}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto \;\;(a+b)(a-b) \: = \: a^{2} - b^{2}}\end{gathered}$

• Algebraic identities:

$\; \; \; \; \; \; \;{\sf{\leadsto (A+B)^{2} \: = \: = A^{2} \: + \: 2AB \: + B^{2}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto (A-B)^{2} \: = \: = A^{2} \: - \: 2AB \: + B^{2}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto A^{2} \: - B^{2} \: = \: (A+B) \: (A-B)}}$

$\; \; \; \; \; \; \;{\sf{\leadsto (A+B)^{2} \: = (A-B)^{2} \: +4AB}}$

$\; \; \; \; \; \; \;{\sf{\leadsto (A-B)^{2} \: = (A+B)^{2} \: -4AB}}$

$\; \; \; \; \; \; \;{\sf{\leadsto (A+B)^{3} \: = A^{3} + \: 3AB \: (A+B) \:+ B^{3}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto (A-B)^{3} \: = A^{3} - \: 3AB \: (A-B) \: + B^{3}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto A^{3} \: + B^{3} = \: (A+B) (A^{2} - AB + B^{2})}}$

• Knowledge about Quadratic equations -

★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a

★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a

★ A quadratic equation have 2 roots

★ ax² + bx + c = 0 is the general form of quadratic equation

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