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Factor each completely, if possible. If the polynomial is not factorable state prime.

4x² + 4x - 15
Final Answer:
Solution:

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Sagot :

Martusjenylynidn

Answer:

To factor the polynomial 4x² + 4x - 15, we can use the method of grouping.

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MrChrisidn

[tex]\underline{\underline{\large{\red{\mathcal{✒GIVEN:}}}}}[/tex]

[tex]\bullet \: \: \rm{4{x}^{2}+4x-15}[/tex]

[tex]\underline{\underline{\large{\red{\mathcal{REQUIRED:}}}}}[/tex]

Factor each completely, if possible. If polynomial is not factorable state prime.

[tex]\underline{\underline{\large{\red{\mathcal{SOLUTION:}}}}}[/tex]

Two numbers that multiply to the product of the coefficient of [tex]\rm{x^{2}}[/tex] term and the constant term [tex]\tt{(4) \times (-15) =-60}[/tex] and add up to the coefficient of the x term 4. These numbers are 10 and -6:

[tex]\tt{10 \times ( - 6) = - 60}[/tex]

[tex]\tt{10 +(-6)=4}[/tex]

Rewrite the middle term using these numbers:

[tex]\small{\tt{ \implies {4x}^{2} + 10x - 6x - 15 = ( {4x}^{2} + 10) + ( - 6x - 15)}}[/tex]

[tex]\tt{ = 2x(2x + 5) - 3(2x + 5)}[/tex]

[tex]\large{\boxed{\tt{\purple{(2x-3)(2x+5)}}}}[/tex]

Final Answer:

The polynomial is factored completed as:

[tex]\large{\rm{\purple{(2x-3)(2x+5)}}}[/tex]

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