1)
Let g(j) be the third derivative of -1/960*j**6 + 1/120*j**5 + 6*j**2 - 1/192*j**4 + 6 - 1/8*j**3 + 0*j. Determine z, given that g(z) = 0.
-1, 2, 3
Let z be (2/(-16))/(152/(-19) + -2). Let r(f) be the second derivative of 1/4*f**2 - 1/8*f**3 + z*f**5 + 0 + 0*f**4 - 6*f. Factor r(b).
(b - 1)**2*(b + 2)/4
Let d(q) be the second derivative of -q**5/30 + 2*q**4/3 - 7*q**3/3 - 98*q**2/3 - 3*q + 12. Factor d(n).
-2*(n - 7)**2*(n + 2)/3
Factor -3/7*l**2 + 24/7*l + 27/7.
-3*(l - 9)*(l + 1)/7
Let a(u) be the second derivative of 2*u**6/75 - u**5/5 + 7*u**4/15 - 2*u**3/5 - 4*u + 4. Suppose a(b) = 0. Calculate b.
0, 1, 3
Let z be 12*-3*5/2. Let r be 6/(-8) + z/(-24). What is i in 2*i - 4*i + i**r + 0*i - 2*i**2 + 3*i = 0?
0, 1
Let d(s) be the third derivative of 0 + 2/3*s**3 + 22*s**2 + 2/3*s**4 + 5/12*s**5 + 1/336*s**8 + 1/30*s**7 + 19/120*s**6 + s. Factor d(b).
(b + 1)**3*(b + 2)**2
Let b = 46 + -1884/41. Let k = b + 119/82. Factor k*w + 0 - 6*w**2 + 9/2*w**3.
3*w*(w - 1)*(3*w - 1)/2
Suppose 2*q - 82 = 2*t, 0 = 3*q + 2*t + 9 - 157. Suppose -38 = -b - 4*u, 3*b = u + 29 + q. What is w in w**3 - b*w**2 + 32*w - 9 + 5*w**3 - 2 + 3 = 0?
1/3, 2
Let h(s) be the first derivative of -s**4/6 - 19*s**3/18 + 61*s**2/12 - 7*s/3 + 451. Factor h(g).
-(g - 2)*(g + 7)*(4*g - 1)/6
Let t(b) be the second derivative of b**6/70 + 33*b**5/35 + 219*b**4/14 - 506*b**3/7 + 1587*b**2/14 + 363*b. What is v in t(v) = 0?
-23, 1
Let x(o) be the third derivative of o**9/78624 - o**8/4095 + 19*o**7/10920 - o**6/260 - o**5/12 - 3*o**2. Let z(b) be the third derivative of x(b). Factor z(y).
2*(y - 3)**2*(5*y - 2)/13
Find h, given that 16*h**3 + 12 - 24*h**3 - 16*h**3 - 6*h**3 - 63*h**2 = 0.
-2, -1/2, 2/5
Let m(d) be the third derivative of -d**6/14 + 31*d**5/210 - d**4/84 - 17*d**2 + 3. Determine s so that m(s) = 0.
0, 1/30, 1
Determine m so that -301*m**3 - 3 + 60*m**2 + 36*m + 3*m**4 + 3 + 328*m**3 = 0.
-6, -2, -1, 0
Suppose 4*b + 5*i = -3, 5*i - i + 18 = 2*b. Solve -6*o**2 + 69*o**b - 21*o**4 - 9*o**5 + 53*o**3 - 3*o**4 - 143*o**3 = 0 for o.
-1, -2/3, 0
Suppose 2*q = -8, 0 = a - 5*a - 3*q + 2848. Let 465 - 4*y**3 - 768*y + a + 96*y**2 + 868 = 0. Calculate y.
8
Let -27 + 1/2*h**5 + h**4 - 13*h**3 - 54*h**2 - 135/2*h = 0. What is h?
-3, -1, 6
Let b be (-50)/8 - 3/(-12). Let f(r) = 2*r**4 + r**3 + 5*r**2 - 5*r. Let m(c) = c**4 + 2*c**2 - 2*c. Let j(q) = b*f(q) + 15*m(q). Suppose j(d) = 0. Calculate d.
0, 2
Let x(a) be the third derivative of -a**5/45 - 20*a**4/9 - 800*a**3/9 + 92*a**2. Factor x(m).
-4*(m + 20)**2/3
Let h(o) be the third derivative of -o**9/4536 - o**8/2520 + o**7/1260 + o**6/540 + o**3/3 + 21*o**2. Let m(q) be the first derivative of h(q). Factor m(d).
-2*d**2*(d - 1)*(d + 1)**2/3
Let c = 66031/40359 - -1/3669. Let p be (-131)/(-33) + (-1)/3. Solve p*b**2 + 4/11 + c*b**3 + 26/11*b = 0.
-1, -2/9
Let d(s) be the third derivative of 0*s + 0 + 1/30*s**5 - 1/3*s**4 + 4/3*s**3 - 7*s**2. Factor d(q).
2*(q - 2)**2
Let u(s) be the third derivative of 7*s**5/45 - 5*s**4/24 + s**3/9 + 12*s**2 - 5*s. Suppose u(k) = 0. Calculate k.
1/4, 2/7
Let u(h) be the third derivative of h**8/336 + 2*h**7/105 + h**6/120 - h**5/10 - 3*h**2 + 64. Factor u(i).
i**2*(i - 1)*(i + 2)*(i + 3)
Let o = 26 + -33. Let h(u) = -6*u**2 - 23*u + 13. Let r(b) = -3*b**2 - 11*b + 6. Let y(k) = o*r(k) + 3*h(k). What is t in y(t) = 0?
-3, 1/3
Solve -6*m + 99/4 - 3/4*m**2 = 0.
-11, 3
Let a(p) be the third derivative of 34*p**2 + 1/168*p**7 + 0*p + 7/60*p**5 + 1/12*p**4 + 11/240*p**6 + 0 + 0*p**3. Factor a(l).
l*(l + 2)**2*(5*l + 2)/4
Let x(u) = 8*u**3 - 159*u**2 + 840*u - 1568. Let n(j) = -20*j**3 + 396*j**2 - 2100*j + 3920. Let s(o) = -5*n(o) - 12*x(o). Solve s(i) = 0 for i.
4, 7
Suppose 14/5*n**3 + 2/5*n**4 + 34/5*n + 34/5*n**2 + 12/5 = 0. Calculate n.
-3, -2, -1
Suppose 0 = 3*a + a. Let v be a + (91/140 - (-2)/(-8)). Determine l, given that -18/5 - v*l**2 - 12/5*l = 0.
-3
Factor 27*o - 3*o + 3*o**2 - 9*o.
3*o*(o + 5)
Let n(g) = 22*g**2 + 10*g + 24. Let j(q) = 2*q**2 - q. Let t(r) = -12*j(r) + n(r). Determine m so that t(m) = 0.
-1, 12
Suppose -12*r = -15*r - 18. Let l be (-3)/72*-6*r/(-1). Factor 3/4*d**2 + l*d + 3/4.
3*(d + 1)**2/4
Let m(n) be the third derivative of -n**9/20160 - n**8/1344 + n**7/1680 + n**6/48 - n**5/15 - 20*n**2. Let k(u) be the third derivative of m(u). Factor k(g).
-3*(g - 1)*(g + 1)*(g + 5)
Let w(g) = -11*g**4 + 18*g**3 + 6*g**2 - 18*g + 5. Let m(x) = -6 + 9*x**2 + 24 - 24*x + 27*x**3 - 17*x**4 - 10 - 3*x. Let n(q) = -5*m(q) + 8*w(q). Factor n(f).
-3*f*(f - 3)*(f - 1)*(f + 1)
Let o be (45 - (-1 - -2*2))/2. Let q be 14/o*(-2 - (-69)/30). Factor -q + 3/5*f**3 + f**2 + 1/5*f.
(f + 1)**2*(3*f - 1)/5
Let r(w) = w**3 - 8. Let x(k) = -k**2 + 2*k. Let s(b) = r(b) - 2*x(b). Factor s(t).
(t - 2)*(t + 2)**2
Factor -1 - 3 - 61*k + 5 - 6*k**3 - 5*k**2 + 3*k**3 + 60*k.
-(k + 1)**2*(3*k - 1)
Let p(g) be the third derivative of -g**8/1344 - g**7/84 + 11*g**6/480 + 8*g**2. What is y in p(y) = 0?
-11, 0, 1
Let -81*h**2 + 9996*h + 23*h**3 + 3*h**4 + 8232 + 106*h**3 - 16*h**3 + 1971*h**2 + 16*h**3 = 0. What is h?
-14, -1
Let s(l) = 5*l**4 - 23*l**3 - 17*l**2 - 5*l. Let t(a) = 23*a**4 - 116*a**3 - 85*a**2 - 26*a. Let r(d) = 11*s(d) - 2*t(d). Factor r(m).
m*(m - 3)*(3*m + 1)**2
Let m(v) be the first derivative of 2*v**3/51 - 11*v**2/17 + 20*v/17 - 40. Suppose m(p) = 0. Calculate p.
1, 10
Let x(d) = d**2 - d. Let n = 38 + -35. Let w(a) = -6*a**2. Let c(g) = n*x(g) + w(g). Find o such that c(o) = 0.
-1, 0
Factor -34/3*p**3 + 0 - 4/3*p + 38/3*p**2.
-2*p*(p - 1)*(17*p - 2)/3
Let i(m) = -m**4 - m**3 + m**2 - 2*m. Let s(w) = 12*w**4 + 37*w**3 + 218*w**2 + 802*w + 900. Let y(f) = 44*i(f) + 4*s(f). Determine a, given that y(a) = 0.
-10, -3
Let y(w) be the third derivative of -2*w**7/945 - 19*w**6/270 - 7*w**5/27 - 17*w**4/54 + 235*w**2. Let y(l) = 0. Calculate l.
-17, -1, 0
Let r(y) be the third derivative of -y**6/240 + y**5/20 + 7*y**4/48 + 179*y**2. Determine q, given that r(q) = 0.
-1, 0, 7
Let v(i) be the third derivative of i**8/112 + 2*i**7/105 - i**6/24 - i**5/30 + 16*i**2. Factor v(j).
j**2*(j - 1)*(j + 2)*(3*j + 1)
Let w be 4*52/56 + (10/(-14) - -1). Factor 2/7*h**w - 6/7*h**3 + 0 + 4/7*h**2 + 0*h.
2*h**2*(h - 2)*(h - 1)/7
Suppose 2*x + 30 = 34. Determine k, given that 32*k**4 - 350*k**3 + 5*k**x + 248*k**4 - 100*k**5 + 52*k**4 + 30*k + 83*k**4 = 0.
-1/4, 0, 2/5, 1, 3
Let g(m) = 3*m**2 - 15*m - 12. Let p be g(6). Let r(f) be the first derivative of -3/4*f**2 + 3/8*f**4 + 0*f + 0*f**3 + p. Factor r(d).
3*d*(d - 1)*(d + 1)/2
Let d be (14/7)/((-2)/4). Let b be (4/d*0)/((-4)/4). Factor -2*r**3 - 2/3*r**4 + b - 2*r**2 - 2/3*r.
-2*r*(r + 1)**3/3
Factor 312/5*k - 3/5*k**2 - 8112/5.
-3*(k - 52)**2/5
Let u(h) be the third derivative of 5*h**8/12096 - h**7/252 + h**6/60 - 19*h**5/60 + 9*h**2. Let j(i) be the third derivative of u(i). Factor j(l).
(5*l - 6)**2/3
Suppose -12/5*w**3 + 108/5*w + 162/5 + 0*w**2 - 2/5*w**4 = 0. What is w?
-3, 3
Let q be (-2)/(-1 - 5/(-8)). Suppose 20*b - 14 = -i + 22*b, -b = -3*i + 12. Factor -32/3 + q*o - 2/3*o**i.
-2*(o - 4)**2/3
Let v(m) be the first derivative of -3*m**5/5 - 9*m**4/4 + 23*m**3 - 99*m**2/2 + 42*m + 121. Find c, given that v(c) = 0.
-7, 1, 2
Let l be 12/(-1)*((-27)/(-6) - 4). Let f be ((-4)/l)/((56/36)/7). Solve -417/4*m**f - 24*m - 75/4*m**5 + 285/4*m**4 + 3 + 291/4*m**2 = 0.
2/5, 1
Let f(m) = 1. Let b(q) = -q**2 - 5*q - 11. Let r(t) = -t**2 - t. Let p(o) = b(o) - 3*r(o). Let h(z) = -22*f(z) - 2*p(z). Let h(c) = 0. Calculate c.
0, 1
Let p(w) = -13*w - 71. Let j be p(-6). Let o(h) be the third derivative of 0 + 0*h + 0*h**4 - h**2 + 0*h**3 + 1/10*h**6 - 3/20*h**5 - 1/70*h**j. Factor o(d).
-3*d**2*(d - 3)*(d - 1)
Let a(h) be the first derivative of -h**5/90 + 4*h**4/27 + 19*h**3/27 + 10*h**2/9 - 41*h + 31. Let r(x) be the first derivative of a(x). Solve r(k) = 0.
-1, 10
Suppose 24874*q + 28 = 24888*q. Factor 0 + 2/3*v**5 + 4/3*v**4 + 0*v**3 - 2/3*v - 4/3*v**q.
2*v*(v - 1)*(v + 1)**3/3
Suppose -u = 5*f - 135, 0 = -6*u + 10*u + 20. Suppose -22 + f = 3*v. Factor 2/3*g**v + 4/3 + 2*g.
2*(g + 1)*(g + 2)/3
Let v(u) be the second derivative of u**4 - 152*u**3/3 - 104*u**2 - 486*u. Determine w, given that v(w) = 0.
-2/3, 26
Let r(a) be the second derivative of a**9/5040 -