Mathematics 10 Second Quarter Exam

Which of the following is the shorter procedure wherein we write only the coefficients when a polynomial is to be divided by a binomial of the form (x - c).

• long division

• scientific division

• synthetic division

• short division

In x2 + 3x + 2 divided by x + 1 is equal to x + 2, what is x + 1?

• dividend

• divisor

• quotient

• remainder

Determine which of the following synthetic division set up would give the correct quotient of the equation 4x3-3x2-25x-30÷x-4.

• 4 -4 3 25 -30

• 4 4 3 -25 -30

• 4 4 -3 -25 -30

• 4 -4 3 -25 30

If (7x4 - 5x5 - 7x3 + 2x - 3) is divided by (x + 3) using synthetic division, the numbers in the first row would be

• -5 7 -7 0 2 -3

• -7 -7 -5 0 2 -3

• -5 7 -7 0 2 3

• -3 7 -7 0 2 -5

Which of the following expresses the third row as a polynomial of x in the solution when P(x) = x2 + 6x + 8 is divided by x + 2.

• x - 4

• x - 1

• x + 4

• x + 1

Which of the following shows the correct solution to 3x4-2x3+4x2-1 divided by x+1?

• 1 3 -2 4 0 -1

• -1 3 -2 4 -1

• 1 3 -2 4 0 -1

• -1 3 -2 4 0 -1

Which polynomial gives a quotient of (2x3 - 3x2 + 1) and a remainder of 11 when divided by (x - 1)?

• 2x4 - 5x3 + 3x2 + x +10

• 2x4 + 5x3 + 3x2 - x + 10

• 2x4 - 5x3 - 3x2 + x +10

• 2x4 - 5x3 + 3x2 - x - 10

Gabriel used a synthetic division to find the quotient if (5x2 - 16x + 4x3 - 3) is divided by (x - 2). He obtained -19 as remainder. His solution is shown below. What is the error?

• The sign of the divisor was not changed.

• The terms of the polynomial are not in standard form.

• The sum entries in the third row are incorrect.

• The numerical coefficients of the first row were not properly written.

The polynomial P(x) has x-r as a factor if and only if P(r) is equal to 0.

• Factor Theorem

• Remainder Theorem

• Synthetic Division

• Long Division

The polynomial P(x) has x-r as a factor if and only if P(r) is equal to 0.

• always true

• sometimes true

• never true

• none of the above