Factoring Quadratic x²+bx+c with Positive b
Read this topicExplanations 3
- When tasked with factoring a polynomial of the form x2+bx+cx^2 + bx + cx2+bx+c, you must first find two numbers that equal ccc when multiplied together and equal bbb when added …
By Vinitha Ranganeni, Naomi Burgess, Jonathan Heller, Anusha Rahman
- Visual Factoring Model Take notice of what the b>0b>0b>0 and c>0c>0c>0 mean. It describes these numbers are positive (they are greater than 000.) Let's model some factoring. x2+…
By Stefan Cuevas, Amy Feraco, Jonathan Heller, Anusha Rahman
- (Video) Factoring by mathman1024 This video by mathman1024 shows how to factor some basic trinomials. Summary\large{\text{Summary}}Summary While the general form of a trinomial …
By Alex Federspiel, Naomi Burgess, Amy Feraco, Jonathan Heller, Anusha Rahman
Problems 38
- Factor x2+15x+56x^2+15x+56x2+15x+56 into (x+u)(x+v)(x+u)(x+v)(x+u)(x+v). What is ∣u−v∣|u-v|∣u−v∣?
- Factor x2+32x+256x^2+32x+256x2+32x+256.
- Factor x2+5x+6x^2 + 5x + 6x2+5x+6.
- Factor x2+8x+15x^2 + 8x + 15x2+8x+15 as (x+u)(x+v)(x+u)(x+v)(x+u)(x+v). What is ∣u−v∣|u-v|∣u−v∣?
- Find the roots of the quadratic equation: x2+4x+3=0x^2 + 4x + 3 = 0x2+4x+3=0
- If U=x2−1U = x^2 -1U=x2−1 and V=x2+2x+1V = x^2 + 2x+1V=x2+2x+1, what is UUU divided by VVV? (Hint: It is a good idea to factor UUU and/or VVV before you divide.)
- Factor x2+10xy+24y2x^2 + 10xy + 24y^2x2+10xy+24y2.
- Solve −2x−6=x+3\sqrt{-2x-6}=x+3−2x−6=x+3.
- Factor x2+120x+2000x^2 + 120x + 2000x2+120x+2000 as (x+u)(x+v)(x+u)(x+v)(x+u)(x+v). What is ∣u−v∣|u-v|∣u−v∣?
- Which of the following are factors of the polynomial x3+3x2+2xx^3 + 3x^2 + 2xx3+3x2+2x?
- Simplify the following expression. x+5x2+25x+100\dfrac{x+5}{x^2+25x+100}x2+25x+100x+5
- Which of the following equals x2+x−12x2−x−12\frac{x^2+x-12}{x^2-x-12}x2−x−12x2+x−12?
- 3x+3 +2xx2+7x+12=?\frac{3}{x+3}\ +\frac{2x}{x^2+7x+12} = ?x+33 +x2+7x+122x=?
- When x≠−3x\ne -3x=−3, simplify the following expression: x2+5x+1x+3 −4x−5x+3 +7x+9x+3=?\frac{x^2+5x+1}{x+3}\ -\frac{4x-5}{x+3}\ +\frac{7x+9}{x+3}=?x+3x2+5x+1 −x+34x−5 +x+37x+…
- 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.
- Cindy wants to put a square patio in her yard. Her yard has an area of 2x2+5x+52x^2 + 5x + 52x2+5x+5. The free area left in her yard after she puts in the square patio is x2+x+1…
- 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−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 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.
- Suppose that (x+3)(x+q)=x2+bx+12(x+3)(x+q) = x^2 + bx + 12(x+3)(x+q)=x2+bx+12 for some real numbers bbb and qqq. Find bbb.
- Which of the following equals x2+6x+8x^2+6x+8x2+6x+8?
- Factor x2+15x+14x^2 + 15x + 14x2+15x+14.
- Factor x2+6x+8x^2 + 6x + 8x2+6x+8.
- Factor x2+15x+14x^2 + 15x + 14x2+15x+14.
- Factor x2+20x+100x^2 + 20x + 100x2+20x+100.
- Factor the quadratic x2+3x+2x^2+3x+2x2+3x+2.
- Factor: 2x2+14x+202x^{2}+14x+202x2+14x+20
- Factor: x2+8x+16x^{2}+8x+16x2+8x+16
- (x+j)(x+10)=x2+15x+k(x + j)(x+10) = x^2+15x + k(x+j)(x+10)=x2+15x+k Find the missing values jjj and kkk.
- 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…
- 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…
- Which of the following quadratics can be factored?
- Which of the following quadratics can be factored?
- Given that bbb is an integer such that x2+bx+2019x^2+bx+2019x2+bx+2019 is able to be factored, what is the maximum possible value of bbb?
- Check all the ways to factor 40+x2+13x40+x^2+13x40+x2+13x listed below.
- 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?