Factor Factor axax22 + bx + c + bx + c

March 31, 2014

Pages 593-596

1. Factor 2x2 – 7x + 3.

When b is negative and c is positive, both factors of c must be negative. Make a table to organize your work.

Check your answer using FOIL.

– x – 6x = – 7x(x – 3)(2x – 1)23, 211, 2

– 3x – 2x = – 5x(x – 1)(2x – 3)– 1, – 31,2

Middle term

when multiplied

Possible

factorization

Factors

of 3

Factors of 2

Correct

=(x – 3)(2x – 1)ANSWER

2. Factor 3n2 + 14n – 5.

When b is positive and c is negative, the factors of c must have different signs.

n – 15n = –14n(n – 5)(3n + 1)– 5, 11, 3

– n + 15n = 14n(n + 5)(3n – 1)5, – 11, 3

5n – 3n = 2n(n – 1)(3n + 5)–1, 51, 3

– 5n + 3n = – 2n(n + 1)(3n – 5)1, –51, 3

Middle term

when multiplied

Possible

factorization

Factors of –5

Factors of 3

Correct

= (n + 5)(3n – 1)ANSWER

Factor the trinomial.3. 3t2 + 8t + 4.

Because b is positive and c is positive, both factors of c are positive.

Check your answer using FOIL.

= (t + 2)(3t + 2)

2t + 6t = 8t(t + 2)(3t + 2)2, 21, 3

t + 12t = 13t(t + 4)(3t + 1)4, 11, 3

4t + 3t = 7t(t + 1)(3t + 4)1, 41, 3

Middle term

when multiplied

Possible

factorization

Factors of 4

Factors of 3

Correct

4. 4s2 – 9s + 5.

Because b is negative and c is positive, both factors of c must be negative. Make a table to organize your work.

Check your answer using FOIL.

= (s – 1)(4s – 5)

– 10s – 2s = – 12s(2s – 1)(2s – 5)– 1, – 52, 2

– s – 20s = – 21s(s – 5)(4s – 1)– 5, – 11, 4

– 5s – 4s = – 9s(s – 1)(4s – 5)– 1, – 51, 4

Middle term

when multiplied

Possible

factorization

Factors of 5

Factors of 4

Correct

5. 2h2 + 13h – 7.

Because b is positive and c is negative, the factors of c have different signs.

– h + 14h = 13h(h + 7)(2h – 1)7, – 11, 2

7h – 2h = 5h(h – 1)(2h + 7)– 1, 71, 2

h – 14h = – 13h(h – 7)(2h + 1)– 7, 11, 2

– 7h + 2h = 5h(h + 1)(2h – 7)1, – 71, 2

Middle term

when multiplied

Possible

factorization

Factors of – 7

Factors of 2

Correct

= (h + 7)(2h – 1)

SOLUTION

6. Factor – 4x2 + 12x + 7.

STEP 1

Factor – 1 from each term of the trinomial.– 4x2 + 12x + 7 = –(4x2 – 12x – 7)

STEP 2

Factor the trinomial 4x2 – 12x – 7. Because b and c are both negative, the factors of c must have different signs. As in the previous examples, use a table to organize information about the factors of a and c.

14x – 2x = 12x(2x – 1)(2x + 7)– 1, 72, 2

– 14x + 2x = – 12x(2x + 1)(2x – 7)1, – 72, 2

x – 28x = – 27x(x – 7)(4x + 1)– 7, 11, 4

7x – 4x = 3x(x – 1)(4x + 7)– 1, 71, 4

– x + 28x = 27x(x + 7)(4x – 1)7, – 11, 4

– 7x + 4x = – 3x(x + 1)(4x – 7)1, – 71, 4

Middle term

when multiplied

Possible

factorization

Factors

of – 7

Factors

of 4

Correct

ANSWER – 4x2 + 12x + 7 = –(2x + 1)(2x – 7)

Factor the trinomial.7. – 2y2 – 5y – 3

STEP 1Factor – 1 from each term of the trinomial.

– 2y2 – 5y – 3 = –(2y2 + 5y + 3)STEP 2Factor the trinomial 2y2 + 5y + 3. Because b and c are both positive, the factors of c must have both positive. Use a table to organize information about the factors of a and c.

ANSWER

= – (y + 1)(2y + 3)

8. – 5m2 + 6m – 1

STEP 1Factor – 1 from each term of the trinomial.

– 5m2 + 6m – 1 = – (5m2 – 6m + 1)

STEP 2Factor the trinomial 5m2 – 6m + 1. Because b is negative and c is positive, the factors of c must be both negative. Use a table to organize information about the factors of a and c.

ANSWER

= – (m – 1)(5m – 1)

9. – 3x2 – x + 2

STEP 1Factor – 1 from each term of the trinomial.

– 3x2 – x + 2 = – (3x2 + x – 2)

STEP 2Factor the trinomial 3x2 + x – 2. Because b is positive and c is negative, the factors of c must have different signs. Use a table to organize information about the factors of a and c.

ANSWER

– 3x2 – x + 2 = – (x + 1)(3x – 2)

HOMEWORKHOMEWORK

Worksheet