Final answer:
To factor the trinomial x²+10x+16 into two binomials, we can use the method of grouping. By finding two numbers whose product is 16 and sum is 10, we can rewrite the trinomial and factor out the common binomial factor (x+2).
Step-by-step explanation:
To factor the trinomial x²+10x+16 into two binomials, we need to find two numbers whose product is 16 and whose sum is 10. In this case, the numbers are 2 and 8, since 2*8=16 and 2+8=10. Now we can express the middle term of the trinomial, 10x, as the sum of these two numbers: 2x+8x. So, we can rewrite the trinomial as x²+2x+8x+16. Now we group the terms into two pairs: (x²+2x) and (8x+16). We can factor out the greatest common factor from each pair, giving us x(x+2)+8(x+2). Finally, we can factor out the common binomial factor, (x+2), giving us (x+2)(x+8).
Learn more about Factoring trinomials