Question

use factor therem to determine whether x+3 is a factor of x^2+2x-3 or not ​

Answer 1

GIVEN :-

$\implies \: \bf \: p(x) = x ^{2} + 2x - 3$

TO PROVE :-

$\implies \bf \: whether \: \{x + 3 \} \: is \: a \: factor \: of \: p(x) \: or \: not$

SOLUTION :-

$\star \sf \: let \: x + 3 = 0 \\ \to \sf \: x = - 3 \\ \\ \to \sf p(x) = x ^{2} + 2x - 3 \\ \\ \to \sf \: p( - 3) = ( - 3) ^{2} + 2 \times ( - 3) - 3 \\ \\ \to \sf \: 9 + ( - 6) - 3 \\ \\ \to \sf \: 9 - 6 - 3 \\ \\ \to \sf \: \cancel{9} \cancel{ - 9} \\ \\ \to \: \boxed{ \red{ \bf 0}}$

◉ Hence we got the Remainder 0

∴ By Factor theorem,

x + 1 is a Factor of p(x).

ADDITIONAL INFORMATION :-

➠Every linear polynomial in one variable has a unique zero, a non - zero constant polynomial has no zero, and every real number is a zero of the zero polynomial.

➠ Remainder theorem :- If p(x) is is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial x - a , Then the reminder is p(a).

➠ Factor theorem :- x - a is a factor of the polynomial p(x) , If p(a) = 0. Also, If x - a is a Factor of p(x) , Then p(a) = 0.

Answer 2

g(x) = x + 3 = 0

→ x = 0 - 3

.°. x = -3

__________....

p(x) = x² + 2x - 3

→ (-3)² + 2(-3) - 3

→ 9 + (-6) - 3

→ 9 - 6 - 3

→ 3 - 3

→ 0

.°. (x + 3) is a factor of (x² + 2x - 3)...