A.
4x² - 26 x + 42 = 0
We'll factor out and cancel the 2,
2x² - 13x + 21 = 0
We have to factor, so the two constants will multiply to 21. There aren't that many choices, 1*21 and 7*3 and their negatives. We definitely want the negatives because of the minus sign in -13x. Trying a few things gives
Answer: (2x - 7)(x - 3) = 0
Solving,
x = 7/2 or x=3
In complete sentences, this means when we evaluate 4x² - 26 x + 42 at x=7/2 we'll get zero. Same goes for x=3.
B.
(-2x³ + x - 5)(x³ -3x - 4)
By the distributive law,
= -2x³(x³ -3x - 4) + x(x³ -3x - 4) - 5(x³ -3x - 4)
We distribute again, three times,
= -2x⁶ + 6x⁴ + 8x³ + x⁴ - 3x² - 4x - 5x³ + 15x + 20
Then we collect like terms, for example 6x⁴ + x⁴ = 7x⁴.
= -2x⁶ + 7x⁴ + 3x³ - 3x² + 11x + 20
That's it. In complete sentences we multiplied the trinomials by using the distributive law of multiplication over addition four times and then collecting like terms.
C.
(2x - 4)(3x² - x + 4)
= 2x(3x² - x + 4) - 4(3x² - x + 4)
= 6x³ - 2x² + 8x - 12x² + 4x - 16
= 6x³- 14x² + 12x - 16
b. No, not equal, 2x-4 and 4x-2 are two different factors.
