I need some help with a few problems. They are multiple choice but need a breakdown on how I can work the problems. Thanks for your help!
1. Factor the trinomial completely. 10x^2 + 11x-6
a. (2x+3)(5x-2)
b. (2x-3)(5x+2)
c. (10x+3)(x-2)
d. (2x+1)(5x-6)
2. Compute as indicated. Write answers in lowest terms. 9/2s+9/4s^2
a. 9s+9/4s^2
b. 27/2s
c. 18s+9/4s^2
d. 27/4s^2
3. Simplify the expression, assuming that the variable can represent any real number -(8a^3/27)^4/3
a. - 16a^4/81
b. - 81/16a^4
c. 16a^4/81
d. 81/16a^4
4. Use the properties of exponents to simplify the expression. Write the answer using positive exponents only.. (a*b^-4/c^-7)^3
a. ab^12/c^21
b. b^12/a^3c^21
c. b^12c^7/a^3
d. ab^12c^7
5. Reduce to lowest terms x-3/3-x
a. 1
b. -1
c. x/3+3/x
d. x/3-3/x
1.10x^2+15x-4x-6 b should be split in such
a way that the product is equal to ac and the sum should be equal to b.
5x(2x+3)-2(2x+3)
(2x+3)(5x-2)
a
2.Find the LCM
(18s+9)/4s^2
c
3.[(2a/3)^3]^4/3
both 3 s get cancelled and we have 16a^4/81
c
4. Problem is not clear regarding powers and signs.
5.Take out minus sign from Numeratorand we will have -1 while everything gets cancelled
5, Doesn't x-3=-(3-x) ?
4. look at the a term a^3 has to appear in the answer. No answer is correct. Now if the problem is ((ab)^-4)c^-7)^3, then you have to have a^-12 or 1/a^12. Again, no answer is correct.
3. what is -cubrt(8a^3/27) ? now raise that to the 4th power (square it twice).
2. lowest term is 9s/2 (1+s2)
1. Let x=1. compute the trinomial. Now mentally check each answer with x=1. Which is the same?
Sure! Let's break down each problem and go through the steps to find the answers:
1. To factor the trinomial 10x^2 + 11x - 6, we need to find two binomials that, when multiplied together, give us the original expression. First, we look for two numbers whose product is equal to the product of the leading coefficient (10) and the constant term (-6). In this case, the product is -60. We then look for two numbers whose sum is equal to the coefficient of the middle term (11). In this case, the numbers are 15 and -4. Therefore, the factored form is (2x + 3)(5x - 2), so the answer is option a.
2. To compute the expression 9/2s + 9/4s^2, we need to find a common denominator for the fractions. The least common denominator (LCD) in this case is 4s^2. We multiply the first fraction by (2s^2/2s^2) and the second fraction by (4/4) to make the denominators the same. This gives us (18s^2/4s^2) + (18/4s^2). Simplifying further, we have 18s^2 + 18 / 4s^2. Since the numerator and denominator do not share any common factors, we can't reduce it any further. Therefore, the answer is option c.
3. To simplify the expression -(8a^3/27)^4/3, we first raise the fraction to the fourth power: (8a^3/27)^4 = (2^4a^(3*4)) / (3^4). This gives us (16a^12) / (81). Now, we raise the result to the 1/3 power, which is equivalent to finding the cube root: (16a^12)^(1/3) = (16^(1/3)a^(12/3)) = (2a^4). Since the negative sign remains, the final simplified expression is -2a^4. Therefore, the answer is option b.
4. To simplify the expression (a*b^-4/c^-7)^3 using the properties of exponents, we need to apply the rules of multiplying and dividing exponents. We can start by rewriting the expression as (a^1 * b^-4 * c^7)^3, since any number raised to the power of 1 remains unchanged. Taking each factor to the third power, we get a^3 * b^(-4*3) * c^(7*3), which simplifies to a^3 * b^-12 * c^21. Finally, by using the rule that a negative exponent is equivalent to the reciprocal of the positive exponent, b^-12 becomes 1/b^12. So the expression becomes a^3 * (1/b^12) * c^21, which can be written as ab^12c^21. Therefore, the answer is option a.
5. To reduce the fraction (x - 3)/(3 - x) to its lowest terms, we can start by factoring both the numerator and denominator. The numerator is already in factored form. The denominator, however, can be factored as a difference of squares: 3 - x = -(x - 3). Therefore, the expression becomes -(x - 3)/(x - 3). Since the numerator and denominator are the same, they cancel out, leaving us with -1 as the reduced form. Therefore, the answer is option b.
I hope this breakdown helps you understand how to approach each problem and find the correct answers. Let me know if you have any further questions!