Q5 of 105 Page 274

Factories the following expressions

x2 – 4x – 32

The given expression looks as


x2 + (a + b)x + ab


where a + b = -4; and ab = -32;


factors of -32 their sum


1 × -32 1-32 = -31


-16 × 2 2 -16 = - 14


-8 × 4 4 -8 = -4


∴ the factors having sum -4 are -8 and 4


x2 – 4x – 32 = x2 + (4 -8)x - 32


= x2 + 4x - 8x - 32


= x(x + 4) -8(x + 4)


= (x + 4)(x-8)


Hence the factors of x2 – 4x – 32 are (x + 4) and (x-8)


More from this chapter

All 105 →
5

Factories the following expressions

x2 + 9x + 18

 5

Factories the following expressions

p2 – 10p + 21

 6

The lengths of the sides of a triangle are integrals, and its area is also integer. One side is 21 and the perimeter is 48. Find the shortest side.

 7

Find the values of ‘m’ for which x2 + 3xy + x + my –m has two linear factors in x and y, with integer coefficients.