Factoring Quadratic x²+bx+c Negative b
Read this topicExplanations 3
- When tasked with factoring a polynomial of the form x2+bx+cx^2 + bx + cx2+bx+c (where bbb is negative), you first must determine what two numbers equal ccc when multiplied toget…
By Vinitha Ranganeni, Moor Xu, Naomi Burgess, Jonathan Heller, Anusha Rahman
- Visual Model of Factoring Take notice of what b<0b<0b<0 and c>0c>0c>0 mean. This means the coefficient in front of xxx, which we call bbb is less than 000, and the constant that…
By Stefan Cuevas, Amy Feraco, Jonathan Heller, Anusha Rahman
- (Video) Factoring Trinomials by mathman1024 This video by mathman1024 goes over some examples of factoring quadratics that contain a mix of addition and subtraction. Summary\lar…
By Alex Federspiel, Naomi Burgess, Amy Feraco, Jonathan Heller, Anusha Rahman
Problems 42
- Factor x2−12x+35x^2 - 12x + 35x2−12x+35.
- Factor x2−10x+24x^2 - 10x + 24x2−10x+24.
- Solve for xxx. x2+8=22x−1\sqrt{x^2+8}=2\sqrt{2x-1}x2+8=22x−1
- Find all solutions to: 4=x2−6x+124=x^2-6x+124=x2−6x+12
- Say you want to factor a polynomial x2+bx+cx^2 + bx + cx2+bx+c but the only thing you know about bbb and ccc is that bbb is negative, and ccc is positive. Which form will the fa…
- Factor x2−120x+2000x^2 - 120x + 2000x2−120x+2000 into (x−r)(x−s)(x-r)(x-s)(x−r)(x−s). What is ∣r−s∣|r-s|∣r−s∣?
- Factor x2−30x+216x^2 - 30x + 216x2−30x+216 into (x−r)(x−s)(x-r)(x-s)(x−r)(x−s). What is ∣r−s∣|r-s|∣r−s∣?
- Which of the following equals x2+x−12x2−x−12\frac{x^2+x-12}{x^2-x-12}x2−x−12x2+x−12?
- Simplify x−7x2−6x−7 ⋅x2−13x+42x+1\frac{x-7}{x^2-6x-7}\ \cdot\frac{x^2-13x+42}{x+1}x2−6x−7x−7 ⋅x+1x2−13x+42 when x2−6x−7≠0x^2-6x-7\ne 0x2−6x−7=0 and x+1≠0x+1\ne 0x+1=0.
- Simplify 2x2+6x−8x2−3x−28 ⋅2x2−6x−56x2−7x+6\frac{2x^2+6x-8}{x^2-3x-28}\ \cdot \frac{2x^2-6x-56}{x^2-7x+6}x2−3x−282x2+6x−8 ⋅x2−7x+62x2−6x−56 when x2−3x−28≠0x^2-3x-28\ne0x2−3x−2…
- Simplify x2−x−2x2+x−6 ÷x2+6x+8x2+7x+12\frac{x^2-x-2}{x^2+x-6}\ \div\frac{x^2+6x+8}{x^2+7x+12}x2+x−6x2−x−2 ÷x2+7x+12x2+6x+8 when x>10x>10x>10.
- Simplify x2−4x+4x2+5x−14÷3x2−17x−6x2+x−42\frac{x^2-4x+4}{x^2+5x-14}\div\frac{3x^2-17x-6}{x^2+x-42}x2+5x−14x2−4x+4÷x2+x−423x2−17x−6 when xxx is not an integer.
- Simplify x2−17x+70x2−14x+40 ÷x2−2x−35x2+x−20\frac{x^2-17x+70}{x^2-14x+40}\ \div\frac{x^2-2x-35}{x^2+x-20}x2−14x+40x2−17x+70 ÷x2+x−20x2−2x−35 when xxx is not an integer.
- Find all solutions to the equation ∣x2−6x+7∣=2|x^2-6x+7| = 2∣x2−6x+7∣=2.
- For how many positive integer values nnn is n2−3n+2n^2-3n+2n2−3n+2 a prime number?
- Evaluate x2−5x+6x2−3x+2÷x2−7x+12x2−5x+4\frac{x^2-5x+6}{x^2-3x+2} \div \frac{x^2-7x+12}{x^2-5x+4}x2−3x+2x2−5x+6÷x2−5x+4x2−7x+12 when x=2017x = 2017x=2017.
- Find the smallest solution xxx to the equation x2−5x+4=0x^2-5x+4 = 0x2−5x+4=0.
- If a rectangle has an area of x2−5x+4x^2 - 5x + 4x2−5x+4, where x=100x = 100x=100, what are some possible dimensions of the rectangle?
- Factor: x2−12x+32x^2-12x+32x2−12x+32
- Which of the following are possible values of the constant bbb if b<0b<0b<0? Check all that apply.
- Which are possible values of the constant bbb if b<0b<0b<0? Check all that apply.
- Which are possible values of ccc if c>0c > 0c>0? Check all that apply.
- Rounded to the nearest hundredth, the constant π\piπ ("pi") is 3.143.143.14. Without using a calculator, can you tell if π2−7π+12\pi^2 - 7\pi + 12π2−7π+12 positive, zero, or neg…
- Is π2−5π+6\pi^2 - 5\pi + 6π2−5π+6 positive, zero, or negative? (Hint: Factor and use the fact that π\piπ is greater than 333.)
- If x2−20x+100=25x^2-20x+100 = 25x2−20x+100=25, what are possible values of xxx? Check all that apply.
- Choose the most descriptive choices below for (a) and (b).
- If x2−5x+6x^2-5x+6x2−5x+6 is equal to a prime number, what is the value of the integer xxx? Check all that apply.
- Which of the following is equivalent to x2+3x+2x÷33x2−3x−18\frac{x^2+3x+2}{x}\div\frac{3}{3x^2-3x-18}xx2+3x+2÷3x2−3x−183 assuming xxx and 3x2−3x−183x^2-3x-183x2−3x−18 are nonz…
- Simplify x2−5x+6x2−4÷x2+9−6xx2.\frac{x^2-5x+6}{x^2-4}\div \frac{x^2+9-6x}{x^2}.x2−4x2−5x+6÷x2x2+9−6x.
- Factor 30+x2−11x30+x^2-11x30+x2−11x.
- Suppose b,c>0b,c > 0b,c>0 and x2+bx+cx^2+bx+cx2+bx+c can be factored. Must we be able to factor x2−bx+cx^2-bx+cx2−bx+c?
- Which of the following are able to be factored?
- Which of the following is equal to x2−2019x+2018x^2-2019x+2018x2−2019x+2018?
- Find the factorization for x2−11x+30x^2-11x+30x2−11x+30.
- Let f(x)=x2−3x+2f(x) = x^2-3x+2f(x)=x2−3x+2. Choose all the values of nnn such that f(n)f(n)f(n) is divisible by 555.
- Let f(x)=x2−7x+10f(x) = x^2-7x+10f(x)=x2−7x+10. Express f(163)f(\frac{16}{3})f(316) in simplest form.
- Let f(x)=x2−21x+20f(x) = x^2-21x+20f(x)=x2−21x+20. Approximate f(1.5)f(1.5)f(1.5) by choosing the correct range out of the following choices.
- Let f(x)=x4−13x2+40f(x) = x^4-13x^2+40f(x)=x4−13x2+40. Evaluate f(5)f(\sqrt{5})f(5).
- Let f(x)=x2−13x+36f(x) = x^2-13x+36f(x)=x2−13x+36 and g(x)=x2−16x+48g(x) = x^2-16x+48g(x)=x2−16x+48. Find xxx such that f(x)g(x)=15.\frac{f(x)}{g(x)} = \frac{1}{5}.g(x)f(x)=51.
- Let x=2095x = 2095x=2095. Ricky wants to build a rectangular pool that has area x2−14x+48x^2-14x+48x2−14x+48. Which of the following are possible dimensions of the pool?
- Let f(x)=x2−5x+6f(x) = x^2-5x+6f(x)=x2−5x+6 and g(x)=x2−12x+36g(x) = x^2-12x+36g(x)=x2−12x+36. If f(x)=g(2x)f(x) = g(2x)f(x)=g(2x) then find all possible values of xxx.
- Let f(x)=x2−4x+cf(x) = x^2-4x+cf(x)=x2−4x+c. Given that we can write f(x)=(x−p)(x−q)f(x) = (x-p)(x-q)f(x)=(x−p)(x−q) where p,qp,qp,q are positive integers, find the sum of all p…