Question

Match each polynomial function with its leading coefficient.

Column A
1.
P(x) = (x + 2) (2x – 3) (4x +7):
P(x) = (x + 2) (2x – 3) (4x +7)
2.
P(x) = 1/2(x – 2) (2x – 3) (4x + 7):
P(x) = 1/2(x – 2) (2x – 3) (4x + 7)
3.
P(x)= 5(x – 2) (2x – 3) (4x + 7):
P(x)= 5(x – 2) (2x – 3) (4x + 7)
4.
P(x) = -(x – 2) (2x – 3) (4x + 7):
P(x) = -(x – 2) (2x – 3) (4x + 7)
5.
P(x) = 1/4(X + 2) (2x – 3) (4x + 7):
P(x) = 1/4(X + 2) (2x – 3) (4x + 7)
Column B
a.2
b.8
c.-8
d.4
e.40

1. linhdan
The correct match for each leading coefficient will be as below:-
1.  ⇒ b ⇒ 8
2. ⇒ d ⇒ 4
3. ⇒ e ⇒ 40
4. ⇒ c ⇒ – 8
5. ⇒ a ⇒  2

### What is a polynomial?

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
The leading coefficient of the polynomial is defined as the coefficient of the variable having the highest power in the polynomial.
For the given polynomials calculate the highest power variable in each polynomial with the coefficient.
1.
P(x) = (x + 2) (2x – 3) (4x +7):
P(x) = 8x³
2.
P(x) = 1/2(x – 2) (2x – 3) (4x + 7):
P(x) = 4x³
3.
P(x)= 5(x – 2) (2x – 3) (4x + 7):
P(x)= 40x³
4.
P(x) = -(x – 2) (2x – 3) (4x + 7):
P(x) = -8x³
5.
P(x) = 1/4(X + 2) (2x – 3) (4x + 7):
P(x) = 2x³
Therefore, the leading coefficients are 8, 4, 40, -8, and 2 respectively.
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