Me answer and explain step by step for
#10 and
#11

10. C, Quadratic trinomial

11. D, (6d - 1) (2d + 1)

Step-by-step explanation:

10. 7x² - 5x + 9 is a quadratic trinomial as there are 3 terms in the expression (trinomial)

11. to factor 12d² + 4d - 1 we can use the quadratic formula, factoring, or completing the square. when the first term is not equal to 1, it may be easier to use the quadratic formula or factoring by grouping. in this example, i will use factoring by grouping which is another way to factor. I will write the middle term (4d) as a subtraction using 2 numbers that when multiplied together give us 12. these 2 numbers are 6 and 2, as 6 x 2 = 12 and 6 - 2= 4

we have the following:

12d² + 6d - 2d - 1 < group 2 factors together

(12d² + 6d) (-2d - 1) < solve for each factor by factoring

to factor 12d² + 6d, we need to find a common factor between the 2 numbers. both have the number 6 in common and the letter d, so we can factor out 6d from the expression

6d(2d + 1)

now we will factor (-2d - 1). we want to get 2d + 1 as a result of the factorization we do, so we need to find a number that gives us that. both -2d and -1 have a -1 in common, so we can factor out a -1 from the expression

-1(2d + 1)

we now have the following:

6d(2d + 1) - 1(2d + 1) < since we have 2 (2d + 1), we only need to write one. we can combine 6d and -1 into one factor

(6d - 1) (2d + 1) is our answer. the answer choice would be D