9:{"metadata":[["$","title","0",{"children":"iimkbmsat0025 - What must be added to x^4+2x^3-2x^2+x-1 so that the result is exactly divisible by x^2+2x-3? | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined To find what must be added so that x^4+2x^3-2x^2+x-1 is exactly divisib<= by x^2+2x-3, we need to perform polynomial long division and find the remainder.

Dividing x^4+2x^3-2x^2+x-1 by x^2+2x-3: First step: x^4 x^2 = x^2 Multiply: x^2(x^2+2x-3) = x^4+2x^3-3x^2 Subtract: (x^4+2x^3-2x^2+x-1) - (x^4+2x^3-3x^2) = x^2+x-1

Second step: x^2 x^2 = 1 Multiply: 1(x^2+2x-3) = x^2+2x-3 Subtract: (x^2+x-1) - (x^2+2x-3) = -x+2 Since the degree of (-x+2) is <=ss than the degree of (x^2+2x-3), we stop.

The remainder is -x+2. For exact divisibility, the remainder must be zero. We need to eliminate this remainder by adding its negative: What to add = -(-x+2) = x-2

Verification: (x^4+2x^3-2x^2+x-1) + (x-2) = x^4+2x^3-2x^2+2x-3 When we divide x^4+2x^3-2x^2+2x-3 by x^2+2x-3, we >=t: x^4+2x^3-2x^2+2x-3x^2+2x-3 = x^2+1 with remainder = 0. Therefore, x-2 must be added."}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"IIM-K (BMSAT),QA,Algebra,Polynomials"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"iimkbmsat0025 - What must be added to x^4+2x^3-2x^2+x-1 so that the result is exactly divisible by x^2+2x-3? | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined To find what must be added so that x^4+2x^3-2x^2+x-1 is exactly divisib<= by x^2+2x-3, we need to perform polynomial long division and find the remainder.

Dividing x^4+2x^3-2x^2+x-1 by x^2+2x-3: First step: x^4 x^2 = x^2 Multiply: x^2(x^2+2x-3) = x^4+2x^3-3x^2 Subtract: (x^4+2x^3-2x^2+x-1) - (x^4+2x^3-3x^2) = x^2+x-1

Second step: x^2 x^2 = 1 Multiply: 1(x^2+2x-3) = x^2+2x-3 Subtract: (x^2+x-1) - (x^2+2x-3) = -x+2 Since the degree of (-x+2) is <=ss than the degree of (x^2+2x-3), we stop.

The remainder is -x+2. For exact divisibility, the remainder must be zero. We need to eliminate this remainder by adding its negative: What to add = -(-x+2) = x-2

Verification: (x^4+2x^3-2x^2+x-1) + (x-2) = x^4+2x^3-2x^2+2x-3 When we divide x^4+2x^3-2x^2+2x-3 by x^2+2x-3, we >=t: x^4+2x^3-2x^2+2x-3x^2+2x-3 = x^2+1 with remainder = 0. Therefore, x-2 must be added."}],["$","meta","9",{"property":"og:url","content":"/iimk-bmsat-past-year-questions/2025/QA/33"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | JIPMAT Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"iimkbmsat0025 - What must be added to x^4+2x^3-2x^2+x-1 so that the result is exactly divisible by x^2+2x-3? | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined To find what must be added so that x^4+2x^3-2x^2+x-1 is exactly divisib<= by x^2+2x-3, we need to perform polynomial long division and find the remainder.

Dividing x^4+2x^3-2x^2+x-1 by x^2+2x-3: First step: x^4 x^2 = x^2 Multiply: x^2(x^2+2x-3) = x^4+2x^3-3x^2 Subtract: (x^4+2x^3-2x^2+x-1) - (x^4+2x^3-3x^2) = x^2+x-1

Second step: x^2 x^2 = 1 Multiply: 1(x^2+2x-3) = x^2+2x-3 Subtract: (x^2+x-1) - (x^2+2x-3) = -x+2 Since the degree of (-x+2) is <=ss than the degree of (x^2+2x-3), we stop.

The remainder is -x+2. For exact divisibility, the remainder must be zero. We need to eliminate this remainder by adding its negative: What to add = -(-x+2) = x-2

Verification: (x^4+2x^3-2x^2+x-1) + (x-2) = x^4+2x^3-2x^2+2x-3 When we divide x^4+2x^3-2x^2+2x-3 by x^2+2x-3, we >=t: x^4+2x^3-2x^2+2x-3x^2+2x-3 = x^2+1 with remainder = 0. Therefore, x-2 must be added."}],"$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20","$L21"],"error":null,"digest":"$undefined"}

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