Question

p(x)=2x^3+7x^2-24x-45 g(x)=x-3

Answer 1

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: AnSwer :- \: \star}}}}}$

Using factor theorem show that g(x) is a factor of p(x) when p(x)=2x³+7x²- 24x-45,gx=x-3

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

(x - 3) is a factor of 2x³ + 7x² - 24x - 45

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

$p \: (x) \: = \: 2x³ \: + \: 7x² \: - 24x - \: 45 \\ </p><p></p><p>g \: (x) \: = \: (x - 3) \\ </p><p></p><p>→ \: (x - 3) \: = \: 0 \\ </p><p></p><p>→ \: x \: = \: 3 \\ </p><p>$

Putting the value of x

$p \: (x) \: = \: 2x³ \: + \: 7x² \: - 24x - \: 45 \\ </p><p></p><p>p \: (x) \: = \: 2 (3)³ \: + \: 7(3)² \: - 24*3 \: - \: 45 \\ </p><p></p><p>p \: (x) \: = \: 2 \: × \: 27 \: + \: 7 \: × \: 9 \: - \: 72 \: - \: 45 \\ </p><p></p><p>p \: (x) \: = \: 54 \: + \: 63 \: - \: 117 \\ </p><p></p><p>p \: (x) \: = \: 117 \: - 117 \\ </p><p></p><p>p \: (x) \: = \: 0$

$\mathfrak{\huge{\blue{\underline{\underline{Hence }}}}}$

(x - 3) is a of 2x³ + 7x² - 24x - 45

Note

◉ If f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then

★ (x-a) is a factor of f(x), if f(a)=0

★ Its converse “ if (x-a) is a factor of the polynomial f(x), then f(a)=0”

Answer 2

Answer:

p(x)=0

hope this helps u