type the correct answer in each box. use numerals instead of words. simplify the following polynomial…

Answer:

$5x^{2}-13x - 4-17x^{2}-7x + 19+(5x - 7)(3x + 1)=3x^{2}+4x + 8$ So the blanks should be filled with $3$, $4$, $8$ respectively.

Explanation:

Step1: Expand the product

Expand $(5x - 7)(3x + 1)$ using FOIL method. $(5x - 7)(3x + 1)=5x\times3x+5x\times1-7\times3x - 7\times1=15x^{2}+5x-21x - 7=15x^{2}-16x - 7$

Step2: Remove parentheses

$5x^{2}+13x - 4-17x^{2}-7x + 19+15x^{2}-16x - 7$

Step3: Combine like - terms for $x^{2}$ terms

$(5x^{2}-17x^{2}+15x^{2})=(5 - 17+15)x^{2}=3x^{2}$

Step4: Combine like - terms for $x$ terms

$(13x-7x-16x)=(13 - 7-16)x=4x$

Step5: Combine constant terms

$(-4 + 19-7)=8$