Ill give u a brainliest if u can answer this right
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Answer:
To solve a polynomial inequality, we factor the polynomial into irreducible factors and find all the real _zeros_ polynomial. Then we find the intervals determined by the real _zeros and use test points in each interval to find the_ sign of the polynomial on that interval.
If P(x) = x(x+2)(x-1)
And P(x) ≥ 0
We see that P(x) ≥ 0 on the intervals (-2, 0) and (1, ∞).
Step-by-step explanation:
The complete question is attached to this solution
To solve inequality of a polynomial, we first obtain the solutions of the polynomial. The solutions of the polynomial are called the zeros of the polynomial.
If P(x) = x(x+2)(x-1)
The solutions of this polynomial, that is the zeros of this polynomial are 0, -2 and 1.
To now solve the inequality that arises when
P(x) ≥ 0
We redraw the table and examine the intervals
The intervals to be examined as obtained from the zeros include (-∞, -2), (-2, 0), (0, 1) and (1, ∞)
Sign of | x<-2 | -2<x<0 | 0<x<1 | x>1
x | -ve | -ve | +ve | +ve
(x + 2) | -ve | +ve | +ve | +ve
(x - 1) | -ve | -ve | -ve | +ve
x(x+2)(x-1) | -ve | +ve | -ve | +ve
The intervals that satisfy the polynomial inequality P(x) = x(x+2)(x-1) ≥ 0 include
(-2, 0) and (1, ∞)
Hope this Helps!!!
See attached explanation.: Answer: y=26 or
Step-by-step.<span><span><span><span><span>(<span>−<span>3<span>(<span>y−2</span>)</span></span></span>)</span><span>(2)</span></span>3</span>+29</span>=<span>−19</span></span>
Step 1: Simplify both sides of the equation.<span><span><span><span><span>(<span>−<span>3<span>(<span>y−2</span>)</span></span></span>)</span><span>(2)</span></span>3</span>+29</span>=<span>−19</span></span><span>Simplify: </span><span><span><span><span>−<span>2y</span></span>+4</span>+29</span>=<span>−19 </span></span>(Distribute)<span><span><span>(<span>−<span>2y</span></span>)</span>+<span>(<span>4+29</span>)</span></span>=<span>−19 </span></span>(Combine Like Terms)<span><span><span>−<span>2y</span></span>+33</span>=<span>−19</span></span><span><span><span>−<span>2y</span></span>+33</span>=<span>−19
</span></span>Step 2: Subtract 33 from both sides.<span><span><span><span>−<span>2y</span></span>+33</span>−33</span>=<span><span>−19</span>−33</span></span><span><span>−<span>2y</span></span>=<span>−52
</span></span>Step 3: Divide both sides by -2.<span><span><span>−<span>2y</span></span><span>−2</span></span>=<span><span>−52</span><span>−2</span></span></span><span>y=26</span>Answer: y=26
Step-by-step.<span><span><span><span><span>(<span>−<span>3<span>(<span>y−2</span>)</span></span></span>)</span><span>(2)</span></span>3</span>+29</span>=<span>−19</span></span>
Step 1: Simplify both sides of the equation.<span><span><span><span><span>(<span>−<span>3<span>(<span>y−2</span>)</span></span></span>)</span><span>(2)</span></span>3</span>+29</span>=<span>−19</span></span><span>Simplify: </span><span><span><span><span>−<span>2y</span></span>+4</span>+29</span>=<span>−19 </span></span>(Distribute)<span><span><span>(<span>−<span>2y</span></span>)</span>+<span>(<span>4+29</span>)</span></span>=<span>−19 </span></span>(Combine Like Terms)<span><span><span>−<span>2y</span></span>+33</span>=<span>−19</span></span><span><span><span>−<span>2y</span></span>+33</span>=<span>−19
</span></span>Step 2: Subtract 33 from both sides.<span><span><span><span>−<span>2y</span></span>+33</span>−33</span>=<span><span>−19</span>−33</span></span><span><span>−<span>2y</span></span>=<span>−52
</span></span>Step 3: Divide both sides by -2.<span><span><span>−<span>2y</span></span><span>−2</span></span>=<span><span>−52</span><span>−2</span></span></span><span>y=26</span>Answer: y=26