he second derivative of g*h**2 + 2/75*h**6 + 1/15*h**3 + 0 - 3/20*h**4 - 4*h + 3/100*h**5. Find d such that v(d) = 0.
-2, 0, 1/4, 1
Let z(x) = -4*x + 2. Let p be z(-1). Solve -21*d - 3*d**3 + p - 5*d**2 - 3 + 20*d**2 + 6 = 0.
1, 3
Let h(y) = -2*y**3 - 42*y**2 + 90*y - 46. Let g(a) = -a**2 + 2*a - 1. Let s(f) = 4*g(f) - h(f). Suppose s(j) = 0. What is j?
-21, 1
Let o(b) be the second derivative of 8*b**6/15 - 31*b**5/5 + 20*b**4/3 + 14*b**3/3 + 41*b. Factor o(u).
4*u*(u - 7)*(u - 1)*(4*u + 1)
Factor -65536/9 - 2/9*w**3 - 2048/3*w - 64/3*w**2.
-2*(w + 32)**3/9
Factor 6/5 - 2/5*j**4 + 16/5*j + 0*j**3 + 12/5*j**2.
-2*(j - 3)*(j + 1)**3/5
Let k = 2/363 + 15236/1815. Solve -k*d**3 + 6*d**2 + 12/5*d + 0 = 0 for d.
-2/7, 0, 1
Let o(q) be the first derivative of 1/2*q - 1/2*q**2 + 10 + 1/6*q**3. Factor o(y).
(y - 1)**2/2
Let f(r) = -29*r + 106. Let z(x) = -14*x + 52. Let a(g) = 2*f(g) - 5*z(g). Let w be a(4). Let w*h + 0 - 1/2*h**2 = 0. What is h?
0
Let s(l) = 10*l**2 - 105*l + 510. Let t(d) = 9*d**2 - 104*d + 508. Let v(f) = 4*s(f) - 5*t(f). Determine p, given that v(p) = 0.
10
Let p be (-444)/(-74)*(-1)/(-8). Suppose 3/4*i**4 + 1/4*i**5 + 0*i + p*i**3 + 1/4*i**2 + 0 = 0. Calculate i.
-1, 0
Let k(u) = -u**3 + u - 1. Let d = 4 + -1. Let z(n) = d*n**3 + 0 + n**2 + 1 + 5*n**2 + 6*n - 3*n. Let y(x) = 2*k(x) + 2*z(x). Factor y(t).
4*t*(t + 1)*(t + 2)
Let j = -26 + 36. Suppose -5 - 12*k + 4*k**2 + j + 3 = 0. What is k?
1, 2
Suppose 0 = 4*y - 4*p - p + 356, -2*p = -5*y - 462. Let r = -185/2 - y. Factor -7/6*t + 1/6*t**4 + 1/3 + r*t**2 - 5/6*t**3.
(t - 2)*(t - 1)**3/6
Let a(m) be the third derivative of m**8/2352 + 23*m**7/1470 + m**6/5 + 33*m**5/35 + 7*m**2 - 1. Factor a(s).
s**2*(s + 6)**2*(s + 11)/7
Let c(m) = m**3 + 13*m**2 + 24*m + 24. Let o be c(-11). Let -o*r - 2*r**2 + 13*r**5 + 0*r**5 - 3*r**3 + r**4 - 3*r**2 - 12*r**5 = 0. Calculate r.
-1, 0, 2
Let x(v) be the first derivative of -3*v**4/16 - 9*v**3/4 - 27*v**2/4 - 1. Factor x(y).
-3*y*(y + 3)*(y + 6)/4
Let k(t) be the third derivative of t**5/15 + 5*t**4/6 + 72*t**2. Solve k(w) = 0 for w.
-5, 0
Let t(w) = -w**2 + 5*w + 89. Let i be t(-7). Let k(f) be the second derivative of 0*f**2 + 3/20*f**i + 0 + 0*f**3 + 3*f + 1/4*f**4. Let k(b) = 0. Calculate b.
-1, 0
Suppose -4*n + 2*z + 1 = -1293, -5*z = -5*n + 1615. Factor -18*d - 4*d**2 + 90*d + n + 8*d**2.
4*(d + 9)**2
Let y be 920/25*10/4. Suppose 5*b - n - 264 = 0, 5*b = 3*b - 3*n + y. Let -b*s + 36*s - 4 - 2*s**2 - 28 = 0. Calculate s.
-4
Let u(m) = -m**2 + 7*m - 4. Let r be u(6). Let c = -2/11913 + 95314/59565. Factor -c*p - 8/5 + 6/5*p**r.
2*(p - 2)*(3*p + 2)/5
Let z(p) be the second derivative of 0*p**3 + 1/126*p**7 - 1/12*p**5 + 0*p**2 + 0 - 1/12*p**4 - 8*p - 1/90*p**6. Find b such that z(b) = 0.
-1, 0, 3
Factor -74*t**2 - 1/3*t**4 + 28/3*t**3 - 169/3 + 364/3*t.
-(t - 13)**2*(t - 1)**2/3
Let m(g) be the second derivative of g**5/20 + g**4/3 + g**3/2 - 32*g. Determine w so that m(w) = 0.
-3, -1, 0
Let u = 151 - 91. Factor -11 + 16*i**3 - 8*i**3 - u*i + 8*i**3 + 48*i**2 + 27.
4*(i + 4)*(2*i - 1)**2
Let w be (-10 - 841/(-70)) + -2. Let v(n) be the third derivative of 0*n**5 - w*n**7 + 0*n**3 + 1/40*n**6 + 0*n**4 + 9*n**2 + 0*n + 0. Factor v(b).
-3*b**3*(b - 1)
Solve 13014/13*h**2 - 774/13*h**3 - 45360/13*h + 48600/13 - 2/13*h**5 - 102/13*h**4 = 0 for h.
-30, 3
Let y = -341/4 - -86. Suppose -2*d = 2*f, 5*f + 8 = -d - 4. Factor 3/4*p**d + y*p - 3/2*p**2 + 0.
3*p*(p - 1)**2/4
Let o(j) be the second derivative of 0*j**2 + 0 - 12*j + 1/18*j**3 + 1/36*j**4. Factor o(b).
b*(b + 1)/3
Let q = 3 + 0. Suppose -q = -5*s + 2*s, -3*h - 3*s + 15 = 0. Determine d so that 25 + 6*d - 21*d**5 - 25 + 3*d**2 - 45*d**3 + 57*d**h = 0.
-2/7, 0, 1
Let u be 3/5 - (-17)/5. Suppose u*r + 15 = -5*c - r, -3*r = -4*c + 23. Factor 18*s + 2 - 4 + 6 + 6*s**c - 18*s**3 - 10*s**3.
-2*(s - 1)*(2*s + 1)*(7*s + 2)
Let t(f) be the first derivative of 2*f**5/25 + 3*f**4/10 - 28*f**3/5 + 20*f**2 - 144*f/5 - 443. Factor t(p).
2*(p - 2)**3*(p + 9)/5
Let u(y) = 4*y + 18. Let i be u(-4). Suppose -8 = -i*v - 4. Factor -3/2*n**3 - 1 - n**v + 7/2*n.
-(n - 1)*(n + 2)*(3*n - 1)/2
Factor -12*k**2 + 1/4*k**3 - 49/4*k + 0.
k*(k - 49)*(k + 1)/4
Let c(p) = -3*p - 2. Let f be ((-4)/6)/(10/45). Let x be c(f). Suppose -x*z**2 + z**2 - z + 1 - 1 = 0. Calculate z.
-1/6, 0
Let c(o) be the third derivative of 7*o**6/24 + 13*o**5/6 - 5*o**4/3 - 283*o**2. Factor c(q).
5*q*(q + 4)*(7*q - 2)
Let r(p) be the third derivative of p**5/30 + p**4/6 - p**3 - p**2 + 9*p. Determine l so that r(l) = 0.
-3, 1
Let r be (-184)/(-1725)*15*2/8. Solve -r*s**2 + 12/5*s - 18/5 = 0.
3
Let u(a) be the second derivative of 3*a**6/10 - 3*a**5/10 - 3*a**4/4 + a**3 - 62*a. Let u(y) = 0. Calculate y.
-1, 0, 2/3, 1
Let y(r) = 11*r + 21. Let c be y(-1). Suppose c*a - 8 = 6*a. Factor -4*f**a - 2/5*f**5 - 2*f**4 - 2/5 - 4*f**3 - 2*f.
-2*(f + 1)**5/5
Let y = 23 - 21. Factor -6*h**2 + 15*h - 19*h + y*h**2.
-4*h*(h + 1)
Let o(c) be the first derivative of -41*c**3 + 231/4*c**4 + 5 - 12*c - 48*c**2. Suppose o(l) = 0. Calculate l.
-2/7, -2/11, 1
Let i = 1772 - 12398/7. Find f, given that i*f**2 - 2/7*f + 0 = 0.
0, 1/3
Let z be (-2)/(12/(-9)) - 84/56. Let q(h) be the second derivative of z*h**3 + 0*h**2 - 2/33*h**4 + 10*h - 1/165*h**6 + 2/55*h**5 + 0. Factor q(s).
-2*s**2*(s - 2)**2/11
Let d(n) be the second derivative of 0*n**3 + 0 + 1/2*n**2 + 0*n**4 + 1/20*n**5 + 3*n. Let c(y) = 7*y**3 - 2*y + 5. Let h(g) = c(g) - 5*d(g). Factor h(i).
2*i*(i - 1)*(i + 1)
Let k(d) = -80*d**2 + 128*d + 197. Let y(c) = -9*c**2 + 14*c + 22. Let w(o) = -6*k(o) + 57*y(o). Factor w(x).
-3*(x - 2)*(11*x + 12)
Let v = -1306 + 6532/5. Determine p so that 6/5*p + 0 - v*p**2 = 0.
0, 3
Let r(p) be the third derivative of -p**7/42 - p**6/6 - p**5/3 + 32*p**2 + 2*p. Factor r(f).
-5*f**2*(f + 2)**2
Let f be (81 - 90)*(-1)/12. Factor 27/4*q**2 + 81/4 - 81/4*q - f*q**3.
-3*(q - 3)**3/4
Let a(y) = 4*y - 34. Let r be a(10). Solve -46*z - 8 - 15*z**2 + r*z - 9 - 3 = 0 for z.
-2, -2/3
Let k(c) be the second derivative of -1/42*c**7 + 1/10*c**5 + 1/15*c**6 + 0 + 21*c - 1/3*c**4 + c**2 - 1/6*c**3. Factor k(t).
-(t - 2)*(t - 1)**2*(t + 1)**2
Let k(j) = -5*j**3 - 96*j**2 + 6*j. Let h(r) = -10*r**3 - 191*r**2 + 11*r. Let n(a) = -6*h(a) + 11*k(a). Factor n(s).
5*s**2*(s + 18)
Let w(p) be the first derivative of -2*p**2 - 16*p - 10 + p**4 + 16/3*p**3. Factor w(x).
4*(x - 1)*(x + 1)*(x + 4)
Let t = -67 - -65. Let w(m) = m**3 + 3*m**2 + 4*m + 4. Let o be w(t). Factor 1/2*v + 1/2*v**2 + o.
v*(v + 1)/2
Let x be (-1)/(-6)*((-87)/48 - -2). Let y(w) be the third derivative of 1/20*w**5 + 0 + 5*w**2 - 1/12*w**3 + 7/480*w**6 + 0*w + x*w**4. What is m in y(m) = 0?
-1, 2/7
Let q = -967 - -23209/24. Let l(u) be the second derivative of -11*u + 0*u**2 + 0 + q*u**4 + 0*u**3 - 1/20*u**5 + 1/60*u**6. Solve l(n) = 0 for n.
0, 1
Let w(n) = -n**2 - 8*n + 1. Let i be w(-10). Let g = i + 21. Factor -2*d**3 + d**4 - 20 - g*d**5 + 3*d**4 + 20.
-2*d**3*(d - 1)**2
Suppose 4 = v + 5, -3*q + 12 = 3*v. Suppose 5*p = -5*i + 60, 0 = 2*i - 3*i - q*p. Factor 24*b**3 - 4*b**4 + 30*b - 37*b**2 - i*b**2 + 0*b**4 + 18*b - 16.
-4*(b - 2)**2*(b - 1)**2
Let 7*u**4 - 5*u + 5*u**2 - 60*u**5 + 13*u**3 - 12*u**4 + 52*u**3 = 0. Calculate u.
-1, -1/3, 0, 1/4, 1
Suppose 0*c - 5*m + 18 = 4*c, m = 5*c - 8. Let j(u) be the second derivative of -1/6*u**3 - 1/12*u**4 - 4*u + u**c + 0. Factor j(s).
-(s - 1)*(s + 2)
Solve m**5 + 204 - 155*m - 165 + 4*m**4 - 53*m**3 - 97*m**3 + 25*m**4 + 6*m**4 + 230*m**2 = 0.
-39, 1
Let j(x) be the first derivative of 16/5*x**5 - 7 - 2*x**2 + x**4 - 28/3*x**3 + 12*x. Factor j(u).
4*(u - 1)*(u + 1)**2*(4*u - 3)
Let z(n) be the third derivative of -5*n**8/168 - 7*n**7/30 + 67*n**6/120 + n**5/15 - n**4/2 - 7*n**2 + 12. Suppose z(k) = 0. Calculate k.
-6, -2/5, 0, 1/2, 1
Let g(m) = -m**3 + 55*m**2 - 664*m - 72. Let b be g(37). Factor 0*v**b - 1/3*v**3 + 0 + 0*v - 1/3*v**4.
-v**3*(v + 1)/3
Factor -441/5 - 1/5*u**2 + 42/5*u.
-(u - 21)**2/5
Let z(r) be the third derivative of r**7/168 + r**6/18 + 5*r**5/24 + 5*r**4/12 - 5*r**3/6 + 2*r**2. Let s(p) be the first derivative of z(p). Factor s(w).
5*(w + 1)**2*(w + 2)
Let z(j) = -5*j + 23. Let g be z(4). Let i = g + 2. Let 1/3*n**i - 1/3*n**2 + 1/3*n**4 + 0*n - 1/3*n**