+ 16. Determine a so that 0 + 0*a**2 + 1/2*a**3 + 0*a - 2*a**j = 0.
0, 1/4
Let j(s) be the third derivative of s**11/554400 - s**9/100800 - s**5/15 + 5*s**2. Let o(y) be the third derivative of j(y). Factor o(g).
3*g**3*(g - 1)*(g + 1)/5
Let q(d) be the second derivative of -3*d**5/40 + d**3 + 2*d. Determine j so that q(j) = 0.
-2, 0, 2
Let n(f) = -6 + 3*f**2 + 2*f**2 - 5*f - 3 - 4*f**2. Let b be n(7). Factor 4/3*a**4 - 4/3*a**2 + 2/3*a + 0 - 2/3*a**b + 0*a**3.
-2*a*(a - 1)**3*(a + 1)/3
Let w(g) be the second derivative of g**4/3 - 8*g**3 + 72*g**2 + 3*g. Factor w(y).
4*(y - 6)**2
Suppose 4*y + 4 = 4*s + 3*y, -s = -2*y + 6. Let o(j) = j**3 + 4*j**2 + 3*j + 2. Let w be o(-3). Factor 5/4*z**s - 1/4*z**3 - w*z + 1.
-(z - 2)**2*(z - 1)/4
Let p(d) be the second derivative of -d**6/480 + d**5/120 - d**4/96 - 3*d**2/2 + 4*d. Let t(k) be the first derivative of p(k). Factor t(j).
-j*(j - 1)**2/4
Factor 9*u**3 + 2*u**2 + 6*u**3 - 2*u**4 - 2*u - 13*u**3.
-2*u*(u - 1)**2*(u + 1)
Let k(w) be the second derivative of -1/30*w**6 + 0 - 7*w + 0*w**4 - 1/3*w**3 + 1/10*w**5 + 1/2*w**2. What is n in k(n) = 0?
-1, 1
Suppose -3/8*k**2 + 0*k + 0 + 3/8*k**3 = 0. Calculate k.
0, 1
Let z(b) be the first derivative of b**6/2 + 3*b**5/2 + 3*b**4/2 + b**3/2 + 3. Determine k so that z(k) = 0.
-1, -1/2, 0
Let a(n) be the first derivative of 14*n**3/3 - 19*n**2 - 12*n - 4. Solve a(l) = 0 for l.
-2/7, 3
Determine k so that 0 + 0*k + 1/2*k**2 - 1/2*k**5 + 3/2*k**4 - 3/2*k**3 = 0.
0, 1
Suppose 0*c = 5*c - 10. Suppose -8 = -2*j - c*j. Factor -1/2*d**4 + 0*d**3 + 1/2*d**j + 0*d + 0.
-d**2*(d - 1)*(d + 1)/2
Factor 0 + 1/3*a**2 + 0*a + 2/3*a**3 + 1/3*a**4.
a**2*(a + 1)**2/3
Let t be (4/2)/(2/8). Suppose 0*a - t = -4*a. Factor 4*d**5 - 3*d - 2*d**5 - 7*d + 8*d**4 - 8*d**2 + a*d + 6*d**3.
2*d*(d - 1)*(d + 1)*(d + 2)**2
Let n(b) = -5*b**5 + 4*b**4 - b**3 + 2. Let z(o) = -6*o**5 + 3*o**4 + 3. Let s(v) = 3*n(v) - 2*z(v). Factor s(j).
-3*j**3*(j - 1)**2
Let g = -1/7 - -16/63. Let o(p) be the second derivative of 4*p + 0*p**2 - 1/36*p**4 + g*p**3 + 0. Suppose o(q) = 0. What is q?
0, 2
Let a(v) be the third derivative of v**6/140 - 2*v**5/35 - 5*v**4/28 - 15*v**2. Suppose a(r) = 0. What is r?
-1, 0, 5
Let k(u) be the third derivative of -u**8/1176 + u**7/245 - u**6/140 + u**5/210 + 11*u**2. Solve k(r) = 0.
0, 1
Let b(q) be the second derivative of 0 - 1/10*q**5 + 1/12*q**4 + 2/3*q**3 + q**2 + 2*q. Let m(z) be the first derivative of b(z). Factor m(x).
-2*(x - 1)*(3*x + 2)
Let p(c) be the second derivative of -c**7/63 + 2*c**6/15 - 13*c**5/30 + 2*c**4/3 - 4*c**3/9 - 6*c. Let p(d) = 0. Calculate d.
0, 1, 2
Let c(y) be the third derivative of 5/96*y**4 + 1/480*y**6 - 1/60*y**5 + 0 - 1/12*y**3 + 4*y**2 + 0*y. Suppose c(k) = 0. Calculate k.
1, 2
Let p(k) be the first derivative of 4 + 0*k**4 + 0*k + 0*k**2 - 2/45*k**5 + 2/27*k**3. Factor p(v).
-2*v**2*(v - 1)*(v + 1)/9
Let s = -74 + 74. Factor s*l**2 - 1/2*l**3 + 0*l + 0.
-l**3/2
Suppose -6*a - 1 + a**2 - 3*a**2 - 8 + 5 = 0. What is a?
-2, -1
Let a(p) be the second derivative of p**4/28 + p**3/14 - 5*p. Find b, given that a(b) = 0.
-1, 0
Let w = 3 - 1. Suppose 5*b = -5*p + 20, b + b - 3*p = -w. Factor 0*a + 3*a**3 + b*a - a**3 - 2*a**2 - 4*a + 2.
2*(a - 1)**2*(a + 1)
Let w = -7 - -9. Suppose 0 = -0*u + 3*u + 3*h - 6, -9 = -w*u + 3*h. Find k such that 0 + k**u + 1/2*k**2 - k - 1/2*k**4 = 0.
-1, 0, 1, 2
Suppose 0 = -3*s - 2*s + 2*y + 25, 15 = 3*s - y. Let i = s - 3. Factor 0 + 2 - i + 3*t**2.
3*t**2
Let g be -4*(1 + 3/(-4)). Let a be g/2 - (-44)/56. Find t such that 2/7 - a*t**2 + 0*t = 0.
-1, 1
Let j(q) = -2*q + 2. Let r be j(-4). Let f = 13 - r. Determine s, given that 5*s**f - 2*s**2 + s**2 + 0*s**2 - 4*s**3 = 0.
0, 1
Let x(z) be the third derivative of -z**6/160 + z**4/8 - 9*z**2. Find c such that x(c) = 0.
-2, 0, 2
Let o(y) = 3*y**2 - 16*y + 8. Let d(n) = -4*n**2 + 24*n - 12. Let u(f) = -5*d(f) - 8*o(f). Let u(a) = 0. Calculate a.
1
Let j(d) be the third derivative of -d**6/80 - 7*d**5/40 - 15*d**4/16 - 9*d**3/4 + 2*d**2. Factor j(b).
-3*(b + 1)*(b + 3)**2/2
Let v(f) be the first derivative of -2/35*f**5 + 0*f + 0*f**2 - 2/21*f**3 + 1/7*f**4 - 4. Factor v(j).
-2*j**2*(j - 1)**2/7
Let q = 4 - -2. Let a be 2 + -2 + q/21. Suppose a*d**2 + 8/7*d + 8/7 = 0. Calculate d.
-2
Let f(i) be the first derivative of 4*i**3/3 - 20*i**2 + 100*i + 11. Suppose f(b) = 0. What is b?
5
Let p be ((-1)/2)/((-1)/(-40)). Let l be ((-2)/4)/(2/p). Determine j so that 0*j**2 + 0 - 1/4*j**3 + 0*j + 0*j**4 + 1/4*j**l = 0.
-1, 0, 1
Suppose -5*v + j + 9 = -28, -j - 16 = -2*v. Let z = 7 - v. Factor 0*a + z*a**3 + 2/3*a**4 - 2/3*a**2 + 0.
2*a**2*(a - 1)*(a + 1)/3
Let n be 744/360 + 10/(-6). Let -2/5*g**2 + 0 - n*g**3 + 0*g = 0. What is g?
-1, 0
Suppose -2 = -14*r + 26. Factor 7/5*y**r + 2/5 + 11/5*y - 4*y**3.
-(y - 1)*(4*y + 1)*(5*y + 2)/5
Factor 2*c**2 - 29*c + 37*c + 2*c**3 + 6*c**2.
2*c*(c + 2)**2
Let o(t) = -t + 8. Let p(u) = 2*u - 17. Let i(j) = -5*o(j) - 2*p(j). Let r be i(8). Factor 2/5*w**4 - 2/5*w**r + 0*w - 2/5*w**5 + 2/5*w**3 + 0.
-2*w**2*(w - 1)**2*(w + 1)/5
What is y in 3/4*y**2 + 9/8*y**3 + 0 + 0*y**4 - 3/8*y**5 + 0*y = 0?
-1, 0, 2
Let h(k) be the first derivative of k**3/6 + 3*k**2/4 - 7. Factor h(z).
z*(z + 3)/2
Let d = 27 - 22. Let m be -1*3 + 42/12. Suppose 0 - m*g**3 - 1/2*g**4 + 0*g + 1/2*g**2 + 1/2*g**d = 0. Calculate g.
-1, 0, 1
Let y(g) be the third derivative of -7*g**6/80 - g**5/120 + g**4/24 + 27*g**2. Factor y(b).
-b*(3*b + 1)*(7*b - 2)/2
Suppose -g - 1 = -3. Let r be ((-40)/30)/(8/(-18)). Suppose s**2 - g*s + 6*s - r*s - 2 = 0. What is s?
-2, 1
Let d(y) be the third derivative of -1/20*y**6 - 3*y**2 + 0 - 1/2*y**3 + 1/4*y**4 + 0*y**5 + 0*y + 1/70*y**7. Factor d(n).
3*(n - 1)**3*(n + 1)
Solve -2/17*w**5 - 4/17*w**2 - 8/17*w**3 + 10/17*w - 4/17 + 8/17*w**4 = 0.
-1, 1, 2
Let b be (-2)/(7/(42/4)). Let f be 1 + (24/15 - b). Suppose 8/5*n + f*n**3 - 6/5*n**4 - 38/5*n**2 + 8/5 = 0. Calculate n.
-1/3, 1, 2
Let s = 3294 - 1363717/414. Let p = s + 2491/2898. Determine j, given that p*j**2 + 4/7 + 10/7*j = 0.
-1, -2/3
Let d(j) = j**2 + 6*j + 5. Suppose 8 = 4*t - 0*t, 2*t + 11 = -3*q. Let s be d(q). Let 2/9*f**2 + 2/9*f + s = 0. What is f?
-1, 0
Let p(h) be the third derivative of -h**5/15 - h**4/6 - h**2. Factor p(u).
-4*u*(u + 1)
Let l = -17 + 20. Factor z - z**l + 3*z**3 - 7*z + 4.
2*(z - 1)**2*(z + 2)
Let k(b) be the third derivative of 3*b**2 + 0*b**5 + 0*b + 0*b**3 + 0 + 0*b**4 - 1/300*b**6. Factor k(f).
-2*f**3/5
Let s = 1/168 - -95/168. Let s*p**3 - 2/7 - 2/7*p**4 - 2/7*p - 2/7*p**5 + 4/7*p**2 = 0. Calculate p.
-1, 1
Let c(y) = 4*y**3 - 3*y**2 - 3*y - 2. Let k(v) = 5*v**3 - 4*v**2 - 3*v - 2. Let d(z) = 4*c(z) - 3*k(z). Let p(q) be the first derivative of d(q). Factor p(s).
3*(s - 1)*(s + 1)
Let w = 208 - 206. Factor -18/11*o - 12/11*o**4 - 28/11*o**3 - 4/11 - 32/11*o**w - 2/11*o**5.
-2*(o + 1)**4*(o + 2)/11
Let s(w) be the first derivative of -2*w**5/5 + w**4 - 2*w**2 + 2*w - 1. Find c, given that s(c) = 0.
-1, 1
Let t(w) = w**2 + w - 27. Let k be t(-6). Factor -5/4*j + 1/2 + 1/4*j**k + 3/4*j**2 - 1/4*j**4.
-(j - 1)**3*(j + 2)/4
Let p(g) be the third derivative of g**8/5880 - g**6/630 + g**4/84 + g**3/6 + 3*g**2. Let f(w) be the first derivative of p(w). Suppose f(d) = 0. Calculate d.
-1, 1
Suppose 1/4*a**2 - 1/4*a - 1/2 = 0. Calculate a.
-1, 2
Factor 16/15*h + 6/5 - 2/15*h**2.
-2*(h - 9)*(h + 1)/15
Let r(w) be the third derivative of w**5/30 + w**4/6 + w**3/3 + 6*w**2. Factor r(m).
2*(m + 1)**2
Let o(c) be the second derivative of -27*c**7/280 - c**6/10 - c**5/30 - 2*c**3/3 + 2*c. Let x(j) be the second derivative of o(j). Factor x(i).
-i*(9*i + 2)**2
Let x(a) be the first derivative of -3/8*a**2 - 1/4*a**3 - 2 - 1/16*a**4 - 1/4*a. Factor x(b).
-(b + 1)**3/4
Let p(c) be the second derivative of -c**5/10 - c**4 - 4*c**3 - 8*c**2 + c. Determine z, given that p(z) = 0.
-2
Let t be (-1 + 6)/(2 - 1). Let m(n) be the second derivative of -1/10*n**2 + 0 + 7/60*n**4 + 1/25*n**t - 2*n + 1/15*n**3. Factor m(k).
(k + 1)**2*(4*k - 1)/5
Let h(i) be the first derivative of -i**4/36 - 2*i**3/27 + 8. Factor h(m).
-m**2*(m + 2)/9
Let r(d) be the first derivative of d**5/5 + d**4/3 + 8*d - 5. Let o(k) be the first derivative of r(k). Determine s, given that o(s