Factoring Quadratic ax²+bx+c with ac>0
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- Factoring Quadratics: ax2+bx+c,ac>0ax^2+bx+c, ac>0ax2+bx+c,ac>0 Here, we're going to learn factor by grouping of the general form of quadratics! The first step to factor a polyn…
By Vinitha Ranganeni, Moor Xu, Naomi Burgess, Jonathan Heller, Anusha Rahman, Caroline K
- Factoring trinomials algorithmically This algorithmic method of factoring works the first time every time if you follow the steps in order. Note: if you can first factor out a G…
By Kendra Din, Joe Cleary, Liza Sulkin, Joshua Siktar, Anusha Rahman
- (Video) Common Factor Fail by mathman1024 Here's a really helpful video by mathman1024 that teaches you a trick to factor trinomials more quickly. Summary\large{\text{Summary}}S…
By Alex Federspiel, Naomi Burgess, Joshua Siktar, Amy Feraco, Jonathan Heller
- Factoring Quadratics when a≠1a \neq 1a=1 We're going to quickly review some basics before we dive into this type of factorization. It can be more challenging to factor a trinom…
By Nicole Jurewicz, Amy Feraco, Jonathan Heller, Anusha Rahman
Problems 30
- Factor x2−10x+24x^2 - 10x + 24x2−10x+24.
- Factor 6x2−17x+126x^2 - 17x + 126x2−17x+12.
- Factor 2x2+13x+202x^2 + 13 x + 202x2+13x+20.
- Find the roots of the quadratic equation: 50=5−3x2−24x50=5-3x^2-24x50=5−3x2−24x
- Find the roots of the quadratic function y(x)=−2x2+7x−6.y(x)=-2x^2+7x-6.y(x)=−2x2+7x−6. Try to factor, but if that isn't working or is too hard, remember the quadratic formula i…
- Find the roots of 3x2+4x+1=0.3x^2+4x+1=0.3x2+4x+1=0. Try to factor, but if that isn't working or is too hard, remember the quadratic formula is x=−b±b2−4ac2a.x=\frac{-b\pm\sqrt{…
- 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 3x2−8x+43x^2 -8x + 43x2−8x+4 as (3x+a)(x+b)(3x+a)(x+b)(3x+a)(x+b), where a,ba,ba,b are integers. What is ∣a−b∣|a-b|∣a−b∣?
- Which of the following are factors of 5x2−19x+125x^2 -19x + 125x2−19x+12?
- Factor 5x2+19x+125x^2 + 19x + 125x2+19x+12 as (5x+m)(x+n)(5x+m)(x+n)(5x+m)(x+n), where m,nm,nm,n are integers. What is m+nm+nm+n?
- 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.
- Find all solutions to the equation ∣x2−6x+7∣=2|x^2-6x+7| = 2∣x2−6x+7∣=2.
- Find the smallest solution xxx to the equation x2−5x+4=0x^2-5x+4 = 0x2−5x+4=0.
- Which of the following are the correct values of the linear term and the constant term in 2x2−3x+12x^2 - 3x + 12x2−3x+1, respectively?
- The factored form of the quadratic equation 2x2−3x+1=02x^2 - 3x + 1 = 02x2−3x+1=0 is (2x+a)(x+b)=0(2x + a)(x + b) = 0(2x+a)(x+b)=0. What are aaa and bbb?
- Factor 2x2−6x+42x^2 - 6x + 42x2−6x+4.
- If (2x+a)(3x+b)=6x2+7x+2(2x + a)(3x + b) = 6x^2 + 7x + 2(2x+a)(3x+b)=6x2+7x+2, what could aaa and bbb be?
- Factor: 2x2+14x+202x^{2}+14x+202x2+14x+20
- 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.
- Find the smallest positive integer ccc such that 4x2−cx+94x^2 - cx + 94x2−cx+9 factors into a product of two, first degree polynomials with real coefficients.
- If x2−20x+100=25x^2-20x+100 = 25x2−20x+100=25, what are possible values of xxx? Check all that apply.
- 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.
- Suppose the coefficients a,b,ca,b,ca,b,c are integers with no common factor dividing all three coefficients. What is the value of bbb?
- Factor the polynomial −4x2−8x−3-4x^{2}-8x-3−4x2−8x−3.
- Simplify and factor (x2−5x+3)−(−2x2+5x)(x^{2}-5x+3) - (-2x^{2}+5x)(x2−5x+3)−(−2x2+5x) as (ax+m)(bx+n)(ax+m)(bx+n)(ax+m)(bx+n), where a,b,m,na,b,m,na,b,m,n are all integers. What…
- Find the zeros of x2+5x+6=0x^{2}+5x+6=0x2+5x+6=0 by factoring.
- Find the solutions of the equation −7x2−50x−7=0-7x^{2}-50x-7=0−7x2−50x−7=0.