a) x(squared) - 11x + 30
b) a(squared) - 7a + 10
c) b(squared) + 10b + 24
d) y(squared) - 9y + 20
e) p(squared) -7p -18
f) x(cubed) + x(squared) - 6x
Help on these would be much appreciated, thank you
Hi,
If
x² + px + q = (x + a)(x + b)
then q = a * b
and p = a + b
Therefore: if q is positive then a and b have the same sign (both + or both -)
if q is negative then a and b have different signs.
Use these hints to do:
a) x² - 11x + 30 = (x - 5)(x - 6)
b) a² - 7a + 10 = (a - 5)(a - 2)
c) b² + 10b + 24 = (b + 4)(b + 6)
d) y² - 9y + 20 = (y - 5)(y - 4)
e) p² -7p -18 = (p - 9)(p + 2) That's the first problem where the last summand is negative. Therefore the numbers a and b you are looking for must have different signs. The absolute value of the negative number must be greater than the positive one because the coefficient of x is negative.
f) x³ + x² - 6x = x(x² + x - 6) = x(x - 2)(x + 3) Factor out the x. In the bracket is a quadratic term which can be factorized as usual
EB