To factor the polynomial x3 - 3x2 - 10x, we can factor out an x from each term:
x(x2 - 3x - 10)
To factor the quadratic expression inside the parentheses, we need to find two numbers whose product is -10 and whose sum is -3. The numbers -5 and 2 satisfy these conditions, so we can rewrite the expression as:
x(x - 5)(x + 2)
Therefore, the polynomial x3 - 3x2 - 10x is factored as x(x - 5)(x + 2).
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Write the polynomial in factored form.
x3−3x2−10x
3 answers
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the Remainder Theorem to find the remainder when P(x) = x^4 – 9x^3 – 5x^2 – 3x + 4 is divided by x + 3.
Use the Remainder Theorem to find the remainder when P(x) = x^4 – 9x^3 – 5x^2 – 3x + 4 is divided by x + 3.
To use the Remainder Theorem to find the remainder when P(x) = x^4 - 9x^3 - 5x^2 - 3x + 4 is divided by x + 3, we need to substitute -3 for x in P(x) and calculate the result.
P(-3) = (-3)^4 - 9(-3)^3 - 5(-3)^2 - 3(-3) + 4
= 81 + 243 - 45 + 9 + 4
= 292
Therefore, the remainder when P(x) is divided by x + 3 is 292.
P(-3) = (-3)^4 - 9(-3)^3 - 5(-3)^2 - 3(-3) + 4
= 81 + 243 - 45 + 9 + 4
= 292
Therefore, the remainder when P(x) is divided by x + 3 is 292.