Factoring Quadratic x²+bx+c with c<0
Read this topicExplanations 3
- Factoring Quadratics with c<0c<0c<0 Let's take a look at another way to factor trinomials. These will be trinomials with the form x2+bx−cx^2+bx - cx2+bx−c. This method will be a…
By Vinitha Ranganeni, Naomi Burgess, Jonathan Heller, Anusha Rahman
- It is important to consider what c<0c<0c<0 means. When a number is less than 000 that means it is a negative number. So generally, we are looking at the case when ccc is a negat…
By Stefan Cuevas, Naomi Burgess, Amy Feraco, Jonathan Heller, Anusha Rahman
- (Video) Factoring Quadratics with Negative c by Anusha Rahman In this video, Anusha Rahman covers how to factor quadratic expressions in standard form when c<0c<0c<0. Summary Th…
By Anusha Rahman
Problems 32
- Factor x2−3x−40x^2 - 3x - 40x2−3x−40.
- Factor x2+7x−8x^2 + 7x - 8x2+7x−8 as (x+m)(x−n)(x+m)(x-n)(x+m)(x−n), where m,nm,nm,n are positive. What is m+nm+nm+n?
- Joe solves x−3=30−2xx-3=\sqrt{30-2x}x−3=30−2x by squaring to get (x−3)2=30−2x(x-3)^2 = 30-2x(x−3)2=30−2x, and solving the resulting quadratic. Which of the solutions to the qua…
- 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…
- Find the roots of the quadratic equation: 12=x2−3x−612=x^2-3x-612=x2−3x−6
- Find the roots of the quadratic equation: 40=x2−7x−8040=x^2-7x-8040=x2−7x−80
- Factor x2−x−2x^2 - x - 2x2−x−2 as (x+r)(x+s)(x+r)(x+s)(x+r)(x+s), for some integers rrr and sss. What is ∣r−s∣|r-s|∣r−s∣?
- Factor x2+900x−100000x^2 + 900x - 100000x2+900x−100000 as (x+m)(x−n)(x+m)(x-n)(x+m)(x−n), where m,nm,nm,n are positive. What is m+nm+nm+n?
- Which of the following are possible factorizations of a polynomial x2+bx+cx^2 + bx + cx2+bx+c, when c<0c<0c<0?
- If x2−900x−100000=(x−a)(x−b)x^2 - 900x - 100000 = (x-a)(x-b)x2−900x−100000=(x−a)(x−b) for some integers aaa and bbb, what is a+ba+ba+b?
- Simplify x2+x−42x2−x−56 ⋅x2+x−72x2+12x+27\frac{x^2+x-42}{x^2-x-56}\ \cdot \frac{x^2+x-72}{x^2+12x+27}x2−x−56x2+x−42 ⋅x2+12x+27x2+x−72 when xxx is not an integer.
- Simplify x2+17x+72x2+14x+45 ⋅x2+4x−5x2+7x−8\frac{x^2+17x+72}{x^2+14x+45}\ \cdot \frac{x^2+4x-5}{x^2+7x-8}x2+14x+45x2+17x+72 ⋅x2+7x−8x2+4x−5 when x<−100x < -100x<−100.
- 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−xx2+x−2 ÷1+1xx2+3x+2\frac{x^2-x}{x^2+x-2}\ \div\frac{1+\frac{1}{x}}{x^2+3x+2}x2+x−2x2−x ÷x2+3x+21+x1 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.
- How many such nnn's are there?
- Which of the following equals x2+x−2x^2+x-2x2+x−2?
- Find the domain of f(x)=x−8x2+8x−9f(x)=\dfrac{x-8}{x^2+8x-9}f(x)=x2+8x−9x−8.
- If a+b=3a + b = 3a+b=3 and a×b=−4a\times b = -4a×b=−4, what are aaa and bbb?
- If a+b=1a + b = 1a+b=1 and a×b=−6a \times b = -6a×b=−6, what are aaa and bbb?
- Factor x2−3x−18x^2 - 3x - 18x2−3x−18.
- Factor 2x2−4x−162x^2 - 4x - 162x2−4x−16.
- Find all real values of xxx such that 8x+2x24=6.\frac{8x+2x^2}{4}=6.48x+2x2=6.
- Factor the quadratic x2−7x−18x^2-7x-18x2−7x−18.
- Solve the quadratic equation x2−4x−18=3x^{2}-4x-18= 3x2−4x−18=3.
- Factor x2+5x−84x^{2}+5x-84x2+5x−84 as (x+m)(x−n)(x+m)(x-n)(x+m)(x−n), where mmm and nnn are positive numbers. What is m2+3nm^{2}+3nm2+3n?
- After a long time, Richard finally figures out that f(x)=x2−11x−840=(x+24)(x−35)f(x) = x^2-11x-840 = (x+24)(x-35)f(x)=x2−11x−840=(x+24)(x−35). He still needs to factor x2+11x−84…
- Solve the quadratic equation 3x2−9x−54=03x^{2}-9x-54=03x2−9x−54=0.
- Suppose we can write x2+bx−2018=(x+p)(x+q)x^2+bx-2018 = (x+p)(x+q)x2+bx−2018=(x+p)(x+q) where ppp and qqq are (not necessarily positive) integers. Check off all possible values …
- Suppose we can write x2+bx−120=(x+p)(x+q)x^2+bx-120 = (x+p)(x+q)x2+bx−120=(x+p)(x+q) where p,qp,qp,q are integers. What is the maximum value of bbb? Looking at this problem may …
- Suppose we can factor x2+bx−120=(x+p)(x+q)x^2+bx-120 = (x+p)(x+q)x2+bx−120=(x+p)(x+q) where p,qp,qp,q are integers. What is the minimum value of bbb? Looking at this problem may…