Question

For the expression (2x – 1) (3x² + 2x – 4) = ar³ + bx² + cx + d, determine the coefficients a, b, c, and d.

a) Determine the value of the coefficient 'a.'
b) Calculate the value of the coefficient 'b.'
c) Find the value of the coefficient 'c.'
d) Solve for the value of the constant 'd.'

Answer 1

The coefficients for the expanded form of (2x - 1)(3x² + 2x - 4) are a = 6, b = 1, c = -10, and d = 4. The values are determined by applying the distributive property (FOIL) to multiply the binomials and then combining like terms.

Step-by-step explanation:

To find the coefficients a, b, c, and d for the given expression (2x - 1)(3x² + 2x - 4) = ar³ + bx² + cx + d, we need to multiply the two binomials using the distributive property also known as the FOIL method (First, Outer, Inner, Last).

• First, we multiply the first terms: 2x · 3x² = 6x³ which implies a = 6.
• Next, we multiply the outer terms: 2x · 2x = 4x² and the inner terms: -1 · 3x² = -3x², combined we get 1x², hence b = 1.
• Then, we multiply the 2x by -4 to get -8x, and the -1 by 2x to get -2x. When we add them, we have -10x, so c = -10.
• Finally, To find d, multiply the last terms: -1 · -4 = 4, so d = 4.