Alg. 2 - 5.4 Synthetic Division and Zeros

True or False?

Since 2 + 3i is a zero of

f(x) = x² - 4x + 13,

then 2 - 3i is also a zero.

• True

• False

Given that 4 - 6i is a zero of f(x), what is another zero of f(x)?

Answer explanation

Remember that non-real complex zeros come in pairs. Both conjugates are zeros.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

• Cam wrote the remainder incorrectly.

• Cam did not use a zero place holder for the x³ term.

• Cam added instead of subtracting the rows.

• Cam should have used -2 as his division since the factor was x-2.

Tags

CCSS.HSA.APR.D.6

Use synthetic division: (2x³ - 5x - 7) ÷ (x - 2)

• 2x³ - 4x² + 3x - 13
• 2x³ + 4x² +3x - 1
• 2x² - 4x + 3 - 13/x-2
• 2x² + 4x + 3 - 1/x-2

Answer explanation

When you set it up, don't forget to put in your placeholder since you skip the x^2 term:

(2x³ + 0x^2 - 5x - 7) ÷ (x - 2)

2 0 -5 -7 as your coefficients

with 2 on the outside.

Tags

CCSS.HSA.APR.D.6

Use synthetic division: if 𝒙²+𝟑𝒙+𝟕 is divided by  𝒙+𝟐, then what is the remainder?

• 0
• -3
• 9
• 5

Answer explanation

Remember to put -2 on the outside since it makes your x + 2 that you're dividing by = 0.

Tags

CCSS.HSA.APR.D.6

Find all the x-intercepts of the function

f(x) = 2x³ - 19x² + 38x + 24 given that (x-4) is a factor.

• x = 1/2, -6

• x = -1/2, 6

• x = 4, -1/2, 6

• x = -4, 1/2, -6

Answer explanation

f(x) = 2x³ - 19x² + 38x + 24 given that (x-4) is a factor.

Divide by x-4. You should get 2x^2 - 11x + 6 and then can that.

Tags

CCSS.HSF-IF.C.7C

Find all the other factors of x³ -3x² -4x +12 given that x+2 is a factor..

• (x-2)

• (x+5)

• (x+3)

• (x-3)

Answer explanation

Divide by x+2, and you should get x^2 - 5x + 6. Then factor your result.

Tags

CCSS.HSA.APR.B.2

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

• -2, 3 (multiplicity 2), 4

• -2 (multiplicity 2), 3, 4

• 2, -3 (multiplicity 2), -4

• 2 (multiplicity 2), -3, -4

Answer explanation

Remember that the multiplicity is the number of times the factor associated with the zero shows up in the polynomial.

Tags

CCSS.HSF-IF.C.7C

Factor x³ -3x² -4x +12 given that -2 is a zero.

• (x-2) (x+2) (x+3)

• (x-2) (x-2) (x+3)

• (x+2) (x+2) (x+3)

• (x-2) (x+2) (x-3)

Answer explanation

Divide by x +2 using synthetic division, then factor the result.

Tags

CCSS.HSA.APR.B.2

• 6i

• -6i

• 6

• -4i

• 4i

Answer explanation

Divide by x -2 to get x^2 + 36.

Then set x^2 + 36 = 0 and solve

x^2 = -36

x = +6i, -6i