Question

question 21
factor completely:
3x⁴ + 21x³ + 30x²
○ 3x²(x + 2)(x + 1)
○ 3x(x + 2)(x + 2)
○ 3x²(x + 2)(x + 5)
○ 3x(x + 2)(x + 3)
question 22
factor:
y² - 14y + 49
○ (y + 14)(y - 1)
○ (y - 7)(y - 7)
○ (y - 7)(y + 7)
○ (y + 7)(y + 7)

Explanation:

Question 21

Step1: Factor out GCF

Identify and factor out the greatest common factor $3x^2$ from the polynomial.
$3x^4 + 21x^3 + 30x^2 = 3x^2(x^2 + 7x + 10)$

Step2: Factor quadratic trinomial

Factor the quadratic $x^2 + 7x + 10$ into two binomials by finding two numbers that multiply to 10 and add to 7 (2 and 5).
$x^2 + 7x + 10 = (x + 2)(x + 5)$

Step3: Combine factors

Combine the GCF and the factored quadratic.
$3x^2(x + 2)(x + 5)$

Question 22

Step1: Recognize perfect square trinomial

The polynomial $y^2 -14y +49$ matches the form $a^2 - 2ab + b^2$, where $a=y$ and $b=7$ (since $2ab=2*y*7=14y$).

Step2: Apply perfect square formula

Use the formula $a^2 - 2ab + b^2=(a-b)^2=(a-b)(a-b)$.
$y^2 -14y +49=(y-7)(y-7)$

Answer:

Question 21: $\boldsymbol{3x^2(x + 2)(x + 5)}$
Question 22: $\boldsymbol{(y - 7)(y - 7)}$