Factoring Quadratics with Leading Coefficients

The video tutorial reviews how to factor polynomials when the leading coefficient is greater than one. It provides two examples of factoring quadratic trinomials. In the first example, the process involves multiplying the leading coefficient by the constant term, finding factors that add up to the middle term, and adjusting the factors accordingly. The second example follows a similar process but with different numbers, demonstrating the method's application. The tutorial emphasizes understanding the steps to achieve the correct factors.

What is the first step in factoring a polynomial with a leading coefficient greater than one?

• Multiply the leading coefficient by the constant term

• Subtract the leading coefficient from the constant term

• Add the coefficients together

• Divide the leading coefficient by the constant term

Which pair of factors adds up to 29 when multiplied to give 28?

• 28 and 1

• 7 and 4

• 29 and 1

• 14 and 2

How do you adjust the factors to avoid fractions when the leading coefficient is 7?

• Multiply one factor by 7 and adjust the other

• No adjustment is necessary

• Divide both factors by 7

• Multiply both factors by 7

What is the correct factorization of the polynomial in the first example?

• (x + 29)(x + 28)

• (x + 28)(x + 1)

• (x + 7)(x + 4)

• (x + 4)(7x + 1)

What is the product of the leading coefficient and the constant term in the second example?

• 40

• 50

• 30

• 60

Which pair of numbers adds up to 22 and multiplies to 40?

• 10 and 12

• 20 and 2

• 22 and 18

• 15 and 7

How is the factor 'x plus five' derived in the second example?

• By dividing 20 by 4

• By multiplying 5 by 4

• By adding 5 to 20

• By subtracting 4 from 20

What adjustment is made to the factor 'two-fourths' in the second example?

• It is left as is

• It is increased to three-fourths

• It is doubled to one

• It is reduced to one-half

In the second example, what role does the number 4 play after factoring?

• It is added to each factor

• It is subtracted from each factor

• It is used to divide the factors

• It is multiplied with each factor

What is the final form of the factors in the second example?

• (x + 5)(x + 1)

• (2x + 1)(x + 2)

• (x + 20)(x + 2)

• (2x + 1)(x + 5)