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Find the product of:

(a) [tex]$x^2 + 3x + 2$[/tex] and [tex]$x + 1$[/tex]

(b) [tex]$x^2 - 7x + 12$[/tex] and [tex][tex]$x - 3$[/tex][/tex]

(c) [tex]$a^2 - 11a + 30$[/tex] and [tex]$a - 5$[/tex]

(d) [tex]$a^2 - 49a + 60$[/tex] and [tex][tex]$2a + 5$[/tex][/tex]

(e) [tex]$3x^2 + 10x + 3$[/tex] and [tex]$x + 3$[/tex]

(f) [tex]$2x^2 + 11x + 5$[/tex] and [tex][tex]$2x + 1$[/tex][/tex]

(g) [tex]$5x^2 + 11x + 2$[/tex] and [tex]$4x + 3$[/tex]

(h) [tex]$2x^2 + 17x + 21$[/tex] and [tex][tex]$2x + 3$[/tex][/tex]



Answer :

GinnyAnswer
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]

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