Margaret shoots an arrow into the air The equation for the h

Margaret shoots an arrow into the air. The equation for the height (in feet) of the tip of the arrow is: h = 16 + 60l - 16t^2 (a) Factor the right side of this equation. (b) Fill in the table for various heights of the arrow, using the factored form of the equation. Factor the following completely. Look first for the greatest common factor. Factor the following completely. Look first for the greatest common factor.

Solution

4(a) h = 16 + 60t - 16t²

h = 16 + 64t - 4t - 16t²

h = 16(1+4t) - 4t(1+4t)

h = (16-4t)(1+4t)

h = 4(4-t)(1+4t)

4(b). for t=0, h = 4(4-0)(1+4×0)

h = 4×4×1

h = 16 ft

for t = 1, h = 4(4-1)(1+4×1)

. h = 4×3×5

. h = 60 ft

for t=2, h = 4(4-2)(1+4×2)

. h = 4×2×9

. h = 72 ft

for t=3, h = 4(4-3)(1+4×3)

. h = 4×1×13

. h = 52 ft

for t=4, h = 4(4-4)(1+4×4)

. h = 4×0×17

. h = 0 ft

(5) 10x³+29x²+10x

first of all x is common to all.

   x{10x²+29x+10}

   x{10x²+25x+4x+10}

   x{5x(2x+5)+2(2x+5)}

   x{(5x+2)(2x+5)}

   x(2x+5)(5x+2)

(6) 2x⁴-14x³+24x²

  first of all 2x² is greatest factor common to all.

   2x²{x²-7x+12}

   2x²{x²-3x-4x+12}

   2x²{x(x-3)-4(x-3)}

   2x²{(x-4)(x-3)}

   2x²(x-3)(x-4)