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


[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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