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Complete the factoring. x^(2)+6x-40=(x-4)(◻)

Complete the factoring.\newlinex2+6x−40=(x−4)(□)x^{2}+6x-40=(x-4)(\square)

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Full solution

Q. Complete the factoring.\newlinex2+6x−40=(x−4)(□)x^{2}+6x-40=(x-4)(\square)
  1. Identify Factors: To factor the quadratic polynomial x2+6x−40x^2 + 6x - 40, we need to find two numbers that multiply to give −40-40 (the constant term) and add to give 66 (the coefficient of the xx term).
  2. Find Pair Sum: We list pairs of factors of −40-40 and check which pair sums up to 66. The pairs are (−1,40)(-1, 40), (1,−40)(1, -40), (−2,20)(-2, 20), (2,−20)(2, -20), (−4,10)(-4, 10), and (4,−10)(4, -10). The pair that adds up to 66 is (10,−4)(10, -4).
  3. Write as Binomials: Now we write the polynomial as a product of two binomials using the numbers 1010 and −4-4. The factored form is (x+10)(x−4)(x + 10)(x - 4).

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