please factor the ff:
1.x^2+16x-36
2.x^4-10x^2+9
3.(4+x)^2-(4+x)-20
4.2-3x^-1+x^-2 (all of the exponent here in number four is negative)
thanks.....
1. can you think of two numbers which when multiplies yields -36 and when added is 16
how about 18 and -2 ????
(x+18)(x-2)
2. can you think of two numbers which when multiplies yields 9 and when added is -10
how about -1 and -9
(x^2 - 1)(x^2 - 9)
now we have the difference of squares for both of them
= (x+1)(x-1)(x+3)(x-3)
3. for this one, let y = 4+x to get
y^2 - y - 20
which is easy ...
(y-5)(y+4), no replace y
= (4+x - 5)(4+x + 4)
= (x-1)(x+8
4.
rewrite it as
(1/x)^2 - 3(1/x) + 2
= (1/x -2)(1/x - 1)
thank you very much..:)
Sure! I'd be happy to help you factor these expressions. Let's tackle them one by one:
1. To factor the expression x^2 + 16x - 36, we need to find two numbers that when multiplied give -36 and when added give 16. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. By trying different combinations, we find that 4 and -9 satisfy the conditions since 4 * (-9) = -36 and 4 + (-9) = 16. So, the factored form of the expression is (x + 4)(x - 9).
2. To factor the expression x^4 - 10x^2 + 9, we can notice that it resembles a perfect square trinomial of the form (a^2 - 2ab + b^2), which can be factored as (a - b)^2. In this case, we can rewrite the expression as (x^2)^2 - 2(x^2)(3) + (3)^2. Now it looks like the perfect square trinomial (x^2 - 3)^2. So, the factored form is (x^2 - 3)(x^2 - 3), or more simply, (x^2 - 3)^2.
3. To factor the expression (4 + x)^2 - (4 + x) - 20, let's simplify it first. Expanding the square, we get (16 + 8x + x^2) - (4 + x) - 20. Combining like terms, we have x^2 + 7x - 8. To find the factors of -8 that add up to 7, we find that 8 and -1 satisfy the condition since 8 * (-1) = -8 and 8 + (-1) = 7. Therefore, we can factor the expression as (x + 8)(x - 1).
4. To factor the expression 2 - 3x^-1 + x^-2, we need to deal with the negative exponents. Firstly, let's rewrite it with positive exponents by taking the reciprocal: 2(1/x^2) - 3(1/x) + 1/(x^2). Now, we can find a common denominator, which is x^2, and simplify: (2x^2 - 3x + 1) / x^2. Since the numerator is a quadratic trinomial, we can factor it as (2x - 1)(x - 1). Therefore, the factored expression is (2x - 1)(x - 1) / x^2.
I hope this helps! Let me know if you have any further questions.