Factoring Quadratic ax²+bx+c with ac<0
Read this topicExplanations 3
- Factoring Quadratics - ax2+bx+c,ac<0ax^2+bx+c, ac<0ax2+bx+c,ac<0 Here is another way to evaluate a common quadratic form with factor by grouping. The first step to factor a poly…
By Vinitha Ranganeni, Naomi Burgess, Jonathan Heller, Anusha Rahman, Caroline K
- Let's start with a factorization where a=1a=1a=1 to get into the factoring mindset. When factoring a trinomial (333 terms) in the standard form ax2+bx+cax^2+bx+cax2+bx+c it can …
By Amy Feraco, Jonathan Heller, Anusha Rahman
- (Video) Example: Factoring a Quadratic with a Negative Leading Coefficient by Global Freshman Academy This video by Global Freshman Academy discusses how to factor a quadratic w…
By Amy Feraco, Jonathan Heller, Anusha Rahman
Problems 33
- Find the unique positive root of the quadratic 28x2+x−1528x^2+x-1528x2+x−15.
- Factor 2x2+11x−62x^2 + 11x - 62x2+11x−6.
- Factor 4x2+5x−64x^2 + 5x - 64x2+5x−6.
- Which special pattern (used for factoring) describes the following polynomial: 25x2−3625x^2 - 3625x2−36
- If 5x+4=3x,\sqrt{5x+4}=3x,5x+4=3x, what could xxx be? Select all that apply.
- Find solutions to the quadratic equation: 12−4x−x2=012-4x-x^2=012−4x−x2=0
- Find the zeros of 0=−3x2+3x+60=-3x^2+3x+60=−3x2+3x+6.
- Find the roots of the quadratic: 0=3x2+7x−60=3x^2+7x-60=3x2+7x−6
- Factor 3x2+4x−43x^2 +4x - 43x2+4x−4 as (3x+a)(x+b)(3x+a)(x+b)(3x+a)(x+b), where a,ba,ba,b are integers. Find a+ba+ba+b.
- Factor 3x2−4x−43x^2 -4x - 43x2−4x−4 as (3x+a)(x+b)(3x+a)(x+b)(3x+a)(x+b), where a,ba,ba,b are integers. Find a−ba-ba−b.
- Which of the following are factors of −3x2−4x+4-3x^2 -4x +4−3x2−4x+4?
- 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…
- If you want the area of the triangle to be 444 square inches and the base has to be 222 inches more than the height, what should hhh be in inches?
- Simplify 3x2+11x−70x2+x−42 ÷−3x2+31x−70x2−13x+42\frac{3x^2+11x-70}{x^2+x-42}\ \div\frac{-3x^2+31x-70}{x^2-13x+42}x2+x−423x2+11x−70 ÷x2−13x+42−3x2+31x−70 when x>10x > 10x>10.
- Find the unique positive zero of the quadratic 3x2+5x−23x^2+5x-23x2+5x−2. Simplify your answer completely.
- The equation 4x2+13x−35=04x^2+13x-35 = 04x2+13x−35=0 has a single negative solution x=−nx = -nx=−n. What is nnn?
- The length of a rectangle is 555 more than 333 times the width. Find the dimensions that would give the rectangle an area of 100 ft2100\text{ ft}^2100 ft2.
- Which of the following is not a pair of factors for the constant term in 2x2−3x−42x^2 - 3x - 42x2−3x−4?
- Find the factored form of the equation 3x2−x−4=03x^2 - x - 4 = 03x2−x−4=0.
- Which of the following is not a step in factoring 2x2+4x−62x^2 + 4x - 62x2+4x−6?
- Find the factored form of the equation 4x2+4x−3=04x^2 + 4x - 3 = 04x2+4x−3=0.
- Factor 2x2−4x−162x^2 - 4x - 162x2−4x−16.
- Factor 5x2−4x−15x^2 - 4x - 15x2−4x−1.
- Factor 4x2−494x^2 - 494x2−49.
- Factor 7x2−31x−207x^2-31x-207x2−31x−20.
- Factor the quadratic polynomial −3x2+4x+15-3x^{2}+4x+15−3x2+4x+15.
- Factor −x2+4x+77-x^{2}+4x+77−x2+4x+77 as −(x+m)(x−n)-(x+m)(x-n)−(x+m)(x−n), where mmm and nnn are positive numbers. What is m⋅nm \cdot nm⋅n?
- Find the zeros of −8x2−7x=8x−2-8x^{2}-7x=8x-2−8x2−7x=8x−2 by factoring.
- Factor the quadratic expression −7x2−12x+4-7x^{2}-12x+4−7x2−12x+4.
- Find the zeros of −3x2+6x+24=0-3x^{2}+6x+24=0−3x2+6x+24=0 by factoring.
- Rewrite the equation x2−40=x+2x^{2}-40= x+2x2−40=x+2 into the factored form (x+m)(x−n)=0(x+m)(x-n)=0(x+m)(x−n)=0, where mmm and nnn are positive numbers. What is m+nm+nm+n?
- Find the unique positive solution to the quadratic equation −x2−5x=4x−90-x^{2}-5x=4x-90−x2−5x=4x−90.
- Find the zeros of 5x2+8x−13=05x^{2}+8x-13=05x2+8x−13=0 by factoring.