We read your photo as:

Factorize the quadratic expression 3f2 - 13f + 4.

Mathematics

ScanSolve AI Answer

Answer

(3f - 1)(f - 4)

Step-by-step solution

5 steps

To factorize the quadratic expression 3f2−13f+43f^2 - 13f + 4, we will use the method of splitting the middle term.

  1. Identify the coefficients.

    The expression is in the form af2+bf+caf^2 + bf + c, where a=3a=3, b=−13b=-13, and c=4c=4.

  2. Find two numbers that multiply to acac and add up to bb.

    We need two numbers that multiply to a×c=3×4=12a \times c = 3 \times 4 = 12 and add up to b=−13b = -13.
    The two numbers are −1-1 and −12-12, because (−1)×(−12)=12(-1) \times (-12) = 12 and (−1)+(−12)=−13(-1) + (-12) = -13.

  3. Rewrite the middle term using these two numbers.

    3f2−13f+4=3f2−f−12f+43f^2 - 13f + 4 = 3f^2 - f - 12f + 4
  4. Factor by grouping.

    Group the terms and factor out the common factors from each pair.

    (3f2−f)+(−12f+4)(3f^2 - f) + (-12f + 4)

    Factor ff from the first group and −4-4 from the second group.

    f(3f−1)−4(3f−1)f(3f - 1) - 4(3f - 1)
  5. Factor out the common binomial.

    Now, (3f−1)(3f - 1) is a common factor.

    (3f−1)(f−4)(3f - 1)(f - 4)
Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp