Factor
c^2+3c-54
v^2-4v-21
(c+9)(c-6)
and
(v-7(v+_)
Fill in the blank
54 = 6*9 differ by three, what we need
(c+9)(c-6)
Oh, see wls has it :)
(v+3)
To factor the quadratic expressions, let's look at each one separately:
For the expression c^2 + 3c - 54:
Step 1: In this case, you want to find two numbers that multiply to -54 and add up to +3 (because the coefficient of c is positive). The numbers that satisfy these conditions are +9 and -6.
Step 2: Rewrite the quadratic expression by splitting the middle term using these two numbers:
c^2 + 9c - 6c - 54
Step 3: Factor by grouping. Group the first two terms together and the last two terms together, then factor each group separately:
c(c + 9) - 6(c + 9)
Step 4: Notice that you now have a common binomial factor of (c + 9). Factor it out:
(c + 9)(c - 6)
Therefore, the factored form of c^2 + 3c - 54 is (c + 9)(c - 6).
Now let's factor the expression v^2 - 4v - 21:
Step 1: Similar to the previous example, you want to find two numbers that multiply to -21 and add up to -4 (because the coefficient of v is negative). The numbers that satisfy these conditions are -7 and +3.
Step 2: Rewrite the quadratic expression by splitting the middle term using these two numbers:
v^2 - 7v + 3v - 21
Step 3: Factor by grouping. Group the first two terms together and the last two terms together, then factor each group separately:
v(v - 7) + 3(v - 7)
Step 4: Notice that you now have a common binomial factor of (v - 7). Factor it out:
(v - 7)(v + 3)
Therefore, the factored form of v^2 - 4v - 21 is (v - 7)(v + 3).