To determine: Factor a) x^{2}-4x+3 b) 2y^{2}-5y+2 c) 6z^{2}-13z+6

Juan Hewlett

Juan Hewlett

Answered question


To determine: Factor
a) x24x+3
b) 2y25y+2
c) 6z213z+6

Answer & Explanation



Beginner2021-12-29Added 35 answers

Step 1
a) Factoring Quadratics:
We can get a quadraric by multiplying two first-degree polynomials
For example:
By using FOIL method
Factoring quadratics needs FOIL backward because factoring is the reverse of multiplication
Given: x24x+3
We have to find integers b and d such that
Since the constant coefficients on each side of the equation ought to be equal, we must have bd=3 (i.e) b and d are factors of 3.
Similarly, the coefficients of x must be the same, so that b+d=4
The following table shows the possibilities
Factors b, d of 3Sum b+d=41×31+3=41(3)13=2(1)(3)13=4
From the above table, the only factors with product 3 and the sum -4 are -1 and -3
So the correct factorization os x24x+3=(x1)(x3)
To check:
Juan Spiller

Juan Spiller

Beginner2021-12-30Added 38 answers

Step 1
b) Given: 2y25y+2
We have to find integers a, b, c and d such that
Since the coefficient of y2 ought to be same on both sides, we find that ac=2. Likewise, the constant term bd=2. The positive factors of 2 are 2 and 1. Since the midterm is negative, we consider only negative factors of 2. The possibilities are -2 and -1. Now we have to try various arrangements of these factors until we find the one which gives correct coefficient of y.
The last trial gives the correct factorization.


Expert2022-01-05Added 613 answers

Step 1c)Given:6z213z+66z213z+5=(az+b)(cz+d)=acz2+adz+bcz+bd6z213z+6=acz2+(ad+bc)z+bdStep 2(3z1)(2z6)=3z(2z6)1(2z6)=6z218z2z+6=6z220z+6(2z3)(3z2)=2z(3z2)3(3z2)=6z24z9z+6=6z213z+6

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