Question

Match the following expressions and its factors.

Column I	Column II
(A) $x^3+2x^2-13x+10$	(p) $x-2$
(B) $x^2-7x+10$	(q) $x+5$
(C) $x^2-5x+6$	(r) $x-3$

• A. A - q, B - r, C -p
• B. A - r, B - q, C - p
• C. A - r, B - p, C - q
• D. A - q, B - p, C - r

Answer 1

The correct option is D A - q, B - p, C - r

Using factor theorem, if $x-a$ is factor of $p\left(x\right)$, then $p\left(a\right)=0$.

(A)
Substitute $-5$ for $x$ in $x^3+2x^2-13x+10$, we get:
$r=(-5{)}^3+2\times (-5{)}^2-13\times (-5)+10$
$r=-125+50+65+10=0$
Hence, $x+5$ is a factor of $x^3+2x^2-13x+10$

B)
Substitute $2$ for $x$ in $x^2-7x+10$, we get:
$r=2^2-7\times 2+10$
$r=4-14+10=0$
Hence, $x-2$ is a factor of $x^2-7x+10$

C)
Substitute $3$ for $x$ in $x^2-5x+6$, we get:
$r=3^2-5\times 3+6$
$r=9-15+6=0$
Hence, $x-3$ is a factor of $x^2-5x+6$