Mod 10 part 2 Factoring Polynomials

• There is no GCF

Answer explanation

To factor 4r^5 + 2r^3, first identify the GCF, which is 2r^3. Factoring this out gives 2r^3(2r^2 + 1), making the correct choice the second option.

Answer explanation

To factor the quadratic expression x^2 - 9x + 20, we look for two numbers that multiply to 20 and add to -9. The numbers -5 and -4 satisfy this, leading to the factorization (x-5)(x-4).

Mathematical Equivalence

ON

Mathematical Equivalence

ON

Match the following expressions with their factors.

Answer explanation

To factor \(x^2 - 9\), recognize it as a difference of squares: \(a^2 - b^2 = (a-b)(a+b)\). Here, \(a = x\) and \(b = 3\), so it factors to \((x-3)(x+3)\). Thus, the correct choice is \((x-3)(x+3)\).

Tags

CCSS.HSA.APR.C.4

Mathematical Equivalence

ON

Tags

CCSS.HSA.APR.C.4

Mathematical Equivalence

ON

Factor
3v² - 4v - 7

• (3v-7)(v+1)

• 3(v-7)(v-1)

• (3v+1)(v-9)

• (3v+1)(v-10)

Answer explanation

To factor 3v² - 4v - 7, we look for two numbers that multiply to -21 (3*-7) and add to -4. The correct factors are (3v-7)(v+1), which can be verified by expanding.

w⁴ - 625

• (w² + 25) (w² - 25)

• (w² - 25) (w² - 25)

• (w²+ 25) (w+5) (w-5)

• (w+25)(w-25)

Answer explanation

To factor w^4 - 625, recognize it as a difference of squares: (w^2)^2 - (25)^2. This factors to (w^2 + 25)(w^2 - 25). The term (w^2 - 25) can be further factored into (w + 5)(w - 5), leading to the final factorization: (w^2 + 25)(w + 5)(w - 5).

Tags

CCSS.HSA.APR.C.4

7r³-8r²+42r-48

• (r²+6)(7r+8)

• (r²+6)(7r-8)

• (r²+6)(r²+8)

• (r²+6)(7r+6)

Answer explanation

To factor 7r^3-8r^2+42r-48, we can group terms and use the factor theorem. The correct factorization is (r^2+6)(7r-8), as it satisfies the original polynomial when expanded.