Factoring Polynomials: Summary and Word Problems
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Problems 32
- Which special pattern (used for factoring) describes the following polynomial: 25x2−3625x^2 - 3625x2−36
- Which of these algebraic equations describes the distributive law? \\ Hint: think about the how the distributive law is used to factor and what factoring does!
- A rectangular prism has a volume given by 2x3−3x2−2x+32x^3 - 3x^2-2x+32x3−3x2−2x+3. Which of the following choices gives a possible length, width, and height of this rectangular…
- Factor x2+10xy+24y2x^2 + 10xy + 24y^2x2+10xy+24y2.
- Cassidy wants to knit a scarf. She wants the scarf to be 555 feet longer than it is wide. She has enough yarn for 242424 square feet of material. What should the length of the s…
- A cylinder has a volume of πx3+2πx2+πx\pi x^3 + 2\pi x^2 + \pi xπx3+2πx2+πx. Which of the following choices gives a possible radius and height of the cylinder, in terms of xxx? …
- What should the factorization of a polynomial x2+ax+bx^2+ax+bx2+ax+b look like? Mark all possibilities.
- Chris has a passion for spaghetti. Plate A has a radius of 4x−24x - 24x−2, plate B has a radius of 2x+12x + 12x+1, plate C has a radius of x+2x + 2x+2, and plate D has a radius …
- Allison hula hoops professionally. If she works best with a hula hoop that has an area of π(x2−16x+64)\pi(x^2 - 16x + 64)π(x2−16x+64), what should the radius of her hula hoop be?
- Which property can be thought of as the opposite of factoring?
- Which of the following is not a step in factoring x2−2x+4x−8x^2 - 2x + 4x - 8x2−2x+4x−8 by grouping the first two and last two terms?
- Which of the following cannot be factored (over the integers) as a difference of perfect squares? (Factoring over the integers means factoring into polynomials of lower degree, …
- If a rectangle has an area of 16x4−916x^4 - 916x4−9, where x=2018x = 2018x=2018, what are its possible dimensions?
- If aaa and bbb are two consecutive whole numbers, and a2=b2−99a^2=b^2-99a2=b2−99, what is aaa?
- What was the dimension of the lasagna before he changed it?
- If the area of her new patio is x2+4x+3 ft2x^2+4x+3\text{ ft}^2x2+4x+3 ft2, by how many feet should Elizabeth increase the length and width of her original patio?
- Henry wants to expand his photo large enough to fit in a bigger frame. If the original picture is a square of side length xxx inches, and the new frame is x2+12x+36 in2x^2 + 12x…
- Can you write a function (in its most expanded form) showing the area of the new design?
- Can you write a function showing the area of the new design?
- Lydia is helping Cameron record his sales. She decides to factor the function for simpler calculations. \\ Write the function in factored form.
- Lydia is helping Cameron record his sales. She decides to factor the function for simpler calculations. \\ Write the function in factored form and determine if Cameron should st…
- The above image shows a portion of a cubic function with leading coefficient 110\frac{1}{10}101. Which of the following polynomials are representations of this graph?
- Find the largest integer xxx such that x2+1x^2+1x2+1 divides x3+x−1000x^3+x-1000x3+x−1000. Source: Lexington Math Tournament
- There exist many triples of real numbers (A,B,C)(A,B,C)(A,B,C) such that A+6=BA+6 = BA+6=B and if f(x)=Ax2+Bx+Cf(x) = Ax^2+Bx+Cf(x)=Ax2+Bx+C then f(A)=f(B)f(A) = f(B)f(A)=f(B). …
- Right before takeoff, the pilot tells the passengers that the height of the plane at ttt hours is h(t)=−t3+3t2+4th(t) = -t^3+3t^2+4th(t)=−t3+3t2+4t and that they are currently a…
- A baseball player is practicing his throwing by throwing as far as he can in front of him. On one throw, the height of the ball is h(x)=−0.05(x2−49x−50)h(x) = -0.05(x^2-49x-50)h…
- What factoring trick can we use to factor the following fourth degree polynomial? 9x4−16x29x^4-16x^29x4−16x2
- Shelby was practicing soccer after school. She kicked the ball, and the height of the ball was h(x)=−3x2−2x+1h(x)= -3x^{2}-2x+1h(x)=−3x2−2x+1, where xxx is the distance the ball…
- Ted had to bake cookies for the school bake sale tomorrow. He had to figure out how long he had to bake the cookies for. His mom told him that the cookies had to bake for xxx mi…
- It was snowing in Pittsburgh, PA yesterday. Nancy was trying to figure out how many inches it snowed. Her professor told her that 5x2−2x=x2+x+1,5x^{2}-2x=x^{2}+x+1,5x2−2x=x2+x+1…
- Faith was playing fetch with her dog in her backyard. She threw a ball, and the path the ball traveled could be described by the equation h(x)=−4x2+27x+7,h(x)=-4x^{2}+27x+7,h(x)…
- Slizard Games is developing a new type of rectangular playing card where each card is twice as tall as it is wide. If the width of their new cards is (x+3)(x+3)(x+3), what is th…