High School Common Core Mathematics

Front 1

What is the Remainder Theorem?

Back 1

For a polynomial p(x) and a number a, the remainder on division by (x-a) is p(a), so p(a)=0 if and only if (x-a) is a factor of p(x)

Front 2

Consider the polynomial function p(x)=x⁴-3x³+ax²-6x+14 where a is an unknown real number. if (x-2) is a factor of this polynomial, what is the value of a?

Back 2

p(x)=x⁴-3x³+ax²-6x+14
If (x-2) is a factor of p(x), then p(2) must equal 0. To find the value of a, we must calculate p(2).
p(2)=(2)⁴-3(2)³+a(2)²-6(2)+14=0
16-3(8)+a(4)-12+14=0
-6+4a=0
4a=6
a=6/4=3/2

Front 3

Find the remainder of (k²-9k-5)/(k-4)

Back 3

(k²-9k-5)/(k-4)
p(4)=(4²-9(4)-5)
p(4)=16-36-5
p(4)=-7

Front 4

Find the remainder of (3x³-5x+6)/(x-3)

Back 4

(x³-5x+6)/(x-3)
p(3)=(-3³-5(-3)+6)
p(3)=-27-16+6
p(3)=-42+6
p(3)=-36

Front 5

Find the remainder of (3x⁴-5x²-20x-8)/(x+1)

Back 5

(3x⁴-5x²-20x-8)/(x+1)
p(1)=3(1)⁴-5(1)²-20(1)-8
p(1)=3-5-20-9
p(1)=-30

Front 6

Find the remainder of (2x³-2x²+3x-2)/(x-2)

Back 6

(2x³-2x²+3x-2)/(x-2)
p(-2)=2(-2)³-2(-2)²+3(2)-2
p(-2)=2(-8)-2(4)+(-6)-2
p(-2)=-16-8-6
p(-2)=-30

Front 7

Identify the zeroes of the following equation. (x+4)(x-9)=0

Back 7

x=-4 x=9

Front 8

Now that you have identified the zeroes for (x+4)(x-9)=0 as -4 and 9, construct a rough graph of the function defined by (x+4)(x-9)=0.

Back 8

Front 9

Identify the zeroes of the following equation. x2-13x-20=0

Back 9

x=15 x=-2

Front 10

Now that you have identified the zeroes for x2-13x-20=0 as 15 and -2, construct a rough graph of the function defined by x2-13x-20=0.

Back 10

Front 11

Identify the zeroes of the following equation. x2+30x+125=0

Back 11

x=-5 x=-25

Front 12

Now that you have identified the zeroes for x2+30x+125=0 as -5 and -25, construct a rough graph of the function defined by x2+30x+125=0.

Back 12