Determine the sum.
(9x2 + 2) + (4x2 – 5)
(6x2 – 15x + 14) + (7x – 41)
(12x – 5 + 9x2) + (x3 – 3x + 18)
Add the polynomials.
t2 – 6t – 5, t2 + 7t – 8
Determine the difference.
(2x2 – 4x + 7) – (2x2 + x – 2)
(9x3 – 2) – (18x3 + 7x2 – x + 5)
(–3x3 + x – 5) – (2x3 + x2 – x)
(12x3 – 6x2 + 5x) – (x3 – x2 + 3)
Subtract the second polynomial from the first.
Simplify.
(3 x + 5) – (12x – 8) + (5x +2)
– (3x3 + 2) + (5x3 + 3x) – (3x2 – 4)
5(2t2 – 5) – 4(2t2 – 5) + 3(2t2 – 5)
7b(ab – cd)
5(x2 – 2x + 4) + 2(4x2 – 5)
3(2m2 + 4) – 5(m2 – 3) + 2
6a(x – y) + a(x + y) + 4ay
4[3p2 – q(2p + 3q)] – 4[3q2 – 2p(2p – 3q)]
Find the product using the FOIL pattern.
(y + 4)(y – 7)
Multiply the polynomials using the FOIL pattern:
(5x – 2)(3x + 1)
Determine the product of the polynomials.
(x – 11)(x – 13)
(x + 4)(x2 – 5x + 8)
(5x2 – 2)(x2 + 5x + 5)
(x2 + x + 6)(4x2 – x + 3)
Determine the product of the binomials.
(x + 5)(x – 1)(x – 3)
Multiply.
(3x + 4)2
(3y – 5) (3y + 5)
(x – y)3
Determine the product.
(5x – 4)3
(4x + 5y)3
Find f(x + h) for the function:
f(x) = 3x2
(m –n)(m3 + m2n + mn2 + n3)
(a + b)(a – b)(a2 + b2)
What polynomial must be added to
2x2 – x + 6
to obtain
–x2 – 3x + 2?
Find the value of a, b, and c.
(5t3 – at2 – 3bt + 6) – (ct3 + 3t2 – 7t + 4) = 2t3 – 2t + d
(2x2 + ax + 2b) + (x2 – 2bx + 3a) = cx2 – 6x + 8
Find the value of k.
(5x – k)(2x + 2k) = 10x2 + 8kx – 72
Find the number of terms the simplified product has.
(x +y + z)(x + y – z)
(4x – 9)3 = ?
The options are:
A. 64x3 – 432x2 + 972x – 729
B. 64x3 – 432x2 + 972x + 729
C. 64x3 – 144x2 + 972x – 729
D. 64x3 – 432x2 + 144x – 729
Find the area of the shaded region.
Add the areas of the given rectangles and write the sum as a polynomial in simplest form.
Find an expression for the area of the triangle with base length 3x – 4 and height is x + 1.
Determine the volume of the figure shown.
Suppose you start with an 8–inch–square piece of cardboard. Squares with side length x are cut out of the corners, and the sides are folded up to make a box. Write polynomials for the volume of the box and for the surface area of the outside.
(3x + 5) – (12x – 8) + (5x +2)
(m – n)(m3 + m2n + mn2 + n3)
(x + y + z)(x + y – z)
