Explanation:
what is a square ? or is a number or term/expression for which the square root creates a clean result without any endless positions after the decimal point or non-integer exponents.
for the first problem a is already the right answer.
14b⁴ is not a square term, although b⁴ itself is one (= b²×b²), because 14 is not a square (its square root is an endless number).
1 is actually a square (= 1×1).
b² and y⁴ are squares (b×b and y²×y²).
16b² and 49 are squares (4b×4b and 7×7).
(b+1)⁴ and 4b⁶ are squares ((b+1)²×(b+1)² and 2b³×2b³).
factors of x² + 5x - 6
you know how generic factor multiplication works ?
(x + a)(x + b) = x² + ax + bx + ab
so by comparing, we see that
ax + bx is 5x
therefore
a + b = 5
and
ab = -6
now we could solve this ultimately quadratic problem or (much simpler) use the answer options and see which one fits.
and the right answer is c :
-1 + 6 = 5 (that fits)
-1×6 = -6 (that fits too, so this answer is correct).