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Factoring Expressions Practice Questions

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Updated on Oct 3, 2011

Review these concepts at Factoring Expressions Study Guide.

Factoring Expressions Practice Questions

Problems

Practice 1

Factor each expression.

  1. 6x + 2
  2. 5x2 + x
  3. 15y – 20y4
  4. –2x5 + 4x4
  5. 13h2 – 13h
  6. a4a3 + a2
  7. 6s + 15s4– 21s8
  8. 14z6– 35z9–42z4
  9. 9p3 + 27p5 – 6p10+ 12p12
  10. –20q8–8q20 –40q12– 80q10

Practice 2

Factor each expression.

  1.  18g8h2– 45g2h8
  2. –36x7y3 + 12y2
  3. 5a9bc3 – 11a6b5c5
  4. 6j11k3l2 + 48j7k10l4– 28j9k6l6
  5. 50r5t4 + 35s5t4 + 45r5s5t4

Solutions

Practice 1

  1. The factors of 6x are x, 1, 2, 3, and 6, and the factors of 2 are 1 and 2. Both numbers have 2 as a common factor, so we can factor a 2 out of each term.

    Only the first term has an x, so we cannot factor out an x.

    Divide both terms by 2: 6x ÷ 2 = 3x, and 2 ÷ 2 = 1.

    Write 2 outside the parentheses to show that both terms are multiplied by it: 2(3x + 1).

  2. The factors of 5x2 are x2, 1, and 5, and the factors of x are 1 and x. Both terms have x as a common factor, so we can factor an x out of each term.

    Divide both terms by 5x2 ÷ x = 5x, and x ÷ x = 1.

    Write x outside the parentheses to show that both terms are multiplied by it: x(5x + 1).

  3. The factors of 15y are y, 1, 3, 5, and 15, and the factors of 20y4 are y4, 1, 2, 4, 5, 10, and 20. Both terms have 5 and y as common factors, so we can factor 5y out of each term.

    Divide both terms by 5y: 15y ÷ 5y = 3, and 20y4 ÷ 5y = 4y3.

    Write 5y outside the parentheses to show that both terms are multiplied by it: 5y(3 – 4y3).

  4. The factors of –2x5 are –1, 2, x5, and the factors of 4x4 are 1, 2, 4, and x4.

    Both terms have 2 and x as common factors. In fact, we can factor 2x4 out of both terms.

    Divide both terms by 2x4: –2x5 ÷ 2x4 = –x, and 4x4 ÷ 2x4 = 2.

    –2x5 + 4x4 factors into 2x4(–x + 2).

  5. The factors of 13h2 are h2, 1, and 13, and the factors of 13h are h, 1, and 13.

    Both terms have 13 and h as common factors.

    Divide both terms by 13h: 13h2 ÷ 13h = h, and 13h ÷ 13h = 1.

    13h2 – 13h factors into 13h(h – 1).

  6. Each term in a4a3 + a2 has no coefficient, but a is a common factor of every term. The smallest exponent of a is 2, in the term a2.

    Divide every term by a2: a4 ÷ a2 = a2, a3 ÷ a2 = a, and a2 ÷ a2 = 1.

    a4a3 + a2 factors into a2(a2a + 1).

  7. The greatest common factor of 6, 15, and 21 is 3. Every term has s as a common factor, and the smallest exponent of s is 1, in the term 6s.

    Divide every term by 3s: 6s ÷ 3s = 2, 15s4 ÷ 3s = 5s3, and 21s8 ÷ 3s = 7s7.

    6s + 15s4 – 21s8 factors into 3s(2 + 5s3 – 7s7).

  8. The greatest common factor of 14, 35, and 42 is 7. Every term has z as a common factor, and the smallest exponent of z is 4, in the term 42z4.

    Divide every term by 7z4:14z6 ÷ 7z4 = 2z2, 35z9 ÷ 7z4 = 5z5, and 42z4 ÷ 7z4 = 6.

    14z6 – 35z9 – 42z4 factors into 7z4(2z2 – 5z5 – 6).

  9. The greatest common factor of 9, 27, 6, and 12 is 3. Every term has p as a common factor, and the smallest exponent of p is 3, in the term 9p3.

    Divide every term by 3p3: 3p3 ÷ 3p3 = 3, 27p5 ÷ 3p3 = 9p3, 6p10 ÷ 3p3 = 2p7,and 12p12 ÷ 3p3 = 4p9.

    9p3 + 27p5 – 6p10 + 12p12 factors into 3p3(3 + 9p2 – 2p7 + 4p9).

  10. The greatest common factor of 20, 8, 40, and 80 is 4. Since every term is negative, –1 should be factored out of the expression, too. Every term has p as a common factor, and the smallest exponent of q is 8, in the term –20q8.

    Divide every term by –4q8: –20q8 ÷ –4q8 = 5, –8q20 ÷ –4q8 = 2q12, –40q12 ÷ –4q8 = 10q4, and –80q10 ÷ –4q8 = 20q10.

    –20q8 – 8q20 – 40q12 – 80q10 factors into –4q8(5 + 2q12 + 10q4 + 20q2).

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