1.

Find the sum of coefficients of x⁴ and x in the polynomial f(x) = −4x5 + x4 + 2x2 − 7x 8 + 6​

Answer» <html><body><p><strong>Answer:</strong></p><p>First expand the term (1+2x) </p><p>4</p><p> by binomial <a href="https://interviewquestions.tuteehub.com/tag/expansion-980011" style="font-weight:bold;" target="_blank" title="Click to know more about EXPANSION">EXPANSION</a>.</p><p></p><p>(1+2x) </p><p>4</p><p> = </p><p>4</p><p> C </p><p>0</p><p> </p><p> (1) </p><p>4</p><p> (2x) </p><p>0</p><p> + </p><p>4</p><p> C </p><p>1</p><p> </p><p> (1) </p><p>3</p><p> (2x) </p><p>1</p><p> + </p><p>4</p><p> C </p><p><a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a></p><p> </p><p> (1) </p><p>2</p><p> (2x) </p><p>2</p><p> + </p><p>4</p><p> C </p><p>3</p><p> </p><p> (1) </p><p>1</p><p> (2x) </p><p>3</p><p> + </p><p>4</p><p> C </p><p>4</p><p> </p><p> (1) </p><p>0</p><p> (2x) </p><p>4</p><p> </p><p></p><p>=1+8x+24x </p><p>2</p><p> +32x </p><p>3</p><p> +16x </p><p>4</p><p> (1)</p><p></p><p>Now expand the term (2−x) </p><p><a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a></p><p> by binomial expansion,</p><p></p><p>(2−x) </p><p>5</p><p> = </p><p>5</p><p> C </p><p>0</p><p> </p><p> (2) </p><p>5</p><p> (x) </p><p>0</p><p> − </p><p>5</p><p> C </p><p>1</p><p> </p><p> (2) </p><p>4</p><p> (x) </p><p>1</p><p> + </p><p>5</p><p> C </p><p>2</p><p> </p><p> (2) </p><p>3</p><p> (x) </p><p>2</p><p> − </p><p>5</p><p> C </p><p>3</p><p> </p><p> (2) </p><p>2</p><p> (x) </p><p>3</p><p> + </p><p>5</p><p> C </p><p>4</p><p> </p><p> (2) </p><p>1</p><p> (x) </p><p>4</p><p> − </p><p>5</p><p> C </p><p>5</p><p> </p><p> (2) </p><p>0</p><p> (x) </p><p>5</p><p> </p><p></p><p>=<a href="https://interviewquestions.tuteehub.com/tag/32-307188" style="font-weight:bold;" target="_blank" title="Click to know more about 32">32</a>−80x+80x </p><p>2</p><p> −40x </p><p>3</p><p> +10x </p><p>4</p><p> −x </p><p>5</p><p> (2)</p><p></p><p>Multiply the coefficients of those powers which can give the term x </p><p>4</p><p> and then add from equation (1) and (2).</p><p></p><p>=1×10+8(−40)+24(80)+32(−80)+16(32)</p><p></p><p>=−438</p><p></p><p>Therefore, the <a href="https://interviewquestions.tuteehub.com/tag/coefficient-920926" style="font-weight:bold;" target="_blank" title="Click to know more about COEFFICIENT">COEFFICIENT</a> of x </p><p>4</p><p> is −438.</p><p><strong>Step-by-step explanation:</strong></p><p>here is your answer</p></body></html>


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