Sure! Let's find the product of each pair of polynomials step-by-step.
### Problem (a)
Find the product of [tex]\(x^2 + 3x + 2\)[/tex] and [tex]\(x + 1\)[/tex].
[tex]\[
(x^2 + 3x + 2) \cdot (x + 1) = x^3 + 4x^2 + 5x + 2
\][/tex]
### Problem (b)
Find the product of [tex]\(x^2 - 7x + 12\)[/tex] and [tex]\(x - 3\)[/tex].
[tex]\[
(x^2 - 7x + 12) \cdot (x - 3) = x^3 - 10x^2 + 33x - 36
\][/tex]
### Problem (c)
Find the product of [tex]\(a^2 - 11a + 30\)[/tex] and [tex]\(a - 5\)[/tex].
[tex]\[
(a^2 - 11a + 30) \cdot (a - 5) = a^3 - 16a^2 + 85a - 150
\][/tex]
### Problem (d)
Find the product of [tex]\(a^2 - 49a + 60\)[/tex] and [tex]\(2a + 5\)[/tex].
[tex]\[
(a^2 - 49a + 60) \cdot (2a + 5) = 2a^3 - 93a^2 - 125a + 300
\][/tex]
### Problem (e)
Find the product of [tex]\(3x^2 + 10x + 3\)[/tex] and [tex]\(x + 3\)[/tex].
[tex]\[
(3x^2 + 10x + 3) \cdot (x + 3) = 3x^3 + 19x^2 + 33x + 9
\][/tex]
### Problem (f)
Find the product of [tex]\(2x^2 + 11x + 5\)[/tex] and [tex]\(2x + 1\)[/tex].
[tex]\[
(2x^2 + 11x + 5) \cdot (2x + 1) = 4x^3 + 24x^2 + 21x + 5
\][/tex]
### Problem (g)
Find the product of [tex]\(5x^2 + 11x + 2\)[/tex] and [tex]\(4x + 3\)[/tex].
[tex]\[
(5x^2 + 11x + 2) \cdot (4x + 3) = 20x^3 + 59x^2 + 41x + 6
\][/tex]
### Problem (h)
Find the product of [tex]\(2x^2 + 17x + 21\)[/tex] and [tex]\(2x + 3\)[/tex].
[tex]\[
(2x^2 + 17x + 21) \cdot (2x + 3) = 4x^3 + 40x^2 + 93x + 63
\][/tex]
