33*n**3. Solve j(a) = 0.
1
Let a(k) be the second derivative of 0*k**2 - 7/20*k**4 + 3/10*k**3 + 3/20*k**5 + 8*k - 1/50*k**6 + 0. Factor a(i).
-3*i*(i - 3)*(i - 1)**2/5
Let g be (1603/(-28))/(35/(-24)). Let o = -139/7 + g. Factor -139/5*z**3 + 4/5 + 19*z**4 - 32/5*z - 5*z**5 + o*z**2.
-(z - 1)**3*(5*z - 2)**2/5
Let s = 0 + 4. Suppose -6*j = -49 + 37. Factor 0*x**5 + j*x**2 + 5*x + x**4 - 4*x**s - x**4 + 2 - x**5 - 4*x**3.
-(x - 1)*(x + 1)**3*(x + 2)
Factor 2/5*j + 1/10*j**3 + 0 - 2/5*j**2.
j*(j - 2)**2/10
Let t(i) be the second derivative of 0 + 2/3*i**3 - 2/3*i**4 + 0*i**2 - 3*i + 1/5*i**5. Factor t(a).
4*a*(a - 1)**2
Factor -3*a**2 - 6*a**4 + 0*a**4 + 5*a**5 - 4*a**4 - 20*a**3 + 15*a + 13*a**2.
5*a*(a - 3)*(a - 1)*(a + 1)**2
Let r(i) be the first derivative of -3*i**4/4 + 4*i**3 - 9*i**2/2 - 30. Factor r(s).
-3*s*(s - 3)*(s - 1)
Suppose z - 2*z + 6 = 3*i, -2*z + 30 = -3*i. Factor -16 - 10*a + 4*a - z*a**2 + 14*a + 2*a**3 + 16*a.
2*(a - 2)**3
Find z, given that 5/4*z**2 - 17/4*z + 3/2 = 0.
2/5, 3
What is w in 0 + 4/5*w - 3*w**3 + 4/5*w**2 = 0?
-2/5, 0, 2/3
Let w(k) be the first derivative of -k**3 - 9. Find q, given that w(q) = 0.
0
Let g = -5 - -2. Let o be (-149)/g - (-3 + 6). Factor 8/3 + o*u**3 - 2*u**2 - 40/3*u + 98/3*u**4.
2*(u + 1)**2*(7*u - 2)**2/3
Let g(c) be the first derivative of 6*c + 0*c**3 - 9/2*c**2 + 7 + 3/4*c**4. Let g(n) = 0. Calculate n.
-2, 1
Suppose -o = f - 14 + 9, 0 = -o - 3*f + 11. Determine g so that 2 - 2/3*g**o - 4/3*g = 0.
-3, 1
Let i(m) be the second derivative of m**4/12 + m**3/3 + m**2/2 + 11*m. Factor i(d).
(d + 1)**2
Let p(g) be the third derivative of 1/18*g**3 + 0*g**4 + 0*g + 0 + 2*g**2 - 1/180*g**5. Solve p(t) = 0 for t.
-1, 1
Let l(w) be the second derivative of 1/10*w**5 + 5*w + 1/10*w**6 + 1/3*w**3 - 7/12*w**4 + 0*w**2 + 0. Factor l(q).
q*(q - 1)*(q + 2)*(3*q - 1)
Let b(m) = -m**2 - 7*m + 5. Let n be b(-6). Suppose 4*l - n = 5. Determine q so that -4*q**3 + 2*q**2 + 8*q**l + 2*q - 10*q**2 + 6*q**5 - 4*q = 0.
-1, -1/3, 0, 1
Determine f so that -f + 6 + 0*f**3 - 8*f + 3*f**3 = 0.
-2, 1
Let v(f) be the third derivative of f**5/12 + 5*f**4/3 + 40*f**3/3 - 29*f**2. Determine u, given that v(u) = 0.
-4
Let p(j) be the third derivative of j**8/6720 + j**7/840 + j**5/60 - 11*j**2. Let h(u) be the third derivative of p(u). Solve h(v) = 0 for v.
-2, 0
Let f be ((-2)/(-116))/((-2)/4). Let t = f + 33/116. Factor 3/4*p**2 + 1/4*p**3 + t + 3/4*p.
(p + 1)**3/4
Let k(g) be the third derivative of -g**7/840 - g**6/80 - 3*g**5/80 - g**4/24 - 4*g**2 - 4. Factor k(l).
-l*(l + 1)**2*(l + 4)/4
Let w(g) = g**2 - 9*g + 23. Let i be w(6). What is l in -8/7*l**2 + 6/7*l**4 + 0*l**3 + 2/7*l**i + 0 + 0*l = 0?
-2, 0, 1
Let -1/10*p**2 + 1/5*p - 1/10 = 0. What is p?
1
Let b be -1 - (0 + -2 + 2 + -3). Determine i, given that -8/3*i + 0 - 2/3*i**b = 0.
-4, 0
Let n be 9 + 22/(-6) - 5. Suppose -3*a - 5*y + 6 = 0, -4*a - 3*y + 0*y + 8 = 0. Factor 1/3 + n*s**a + 2/3*s.
(s + 1)**2/3
Suppose 2*h - 2 = 3*w - 7, -3 = -3*h + w. Factor -5*y**2 + 6*y**h + y + 0*y**2.
y*(y + 1)
Let z = 5 - 10. Let m be 9/15 - (-3)/z. Determine a so that -4/5*a**2 + 0 + m*a**3 - 2/5*a**5 + 4/5*a**4 + 2/5*a = 0.
-1, 0, 1
Let m(x) be the third derivative of x**10/45360 - x**8/5040 + x**6/1080 + 5*x**4/24 + 5*x**2. Let w(d) be the second derivative of m(d). Factor w(v).
2*v*(v - 1)**2*(v + 1)**2/3
Let p(y) = 16*y. Let o be p(0). Find w such that 1/3*w**2 + 2/3*w**3 + o + 0*w + 1/3*w**4 = 0.
-1, 0
Let v be ((332/(-7))/(-2))/6. Let i = 30/7 - v. Solve -i*j**2 - 1/3*j + 0 = 0.
-1, 0
Let j = 65/7 - 9. Suppose 0 - j*l + 2/7*l**2 = 0. Calculate l.
0, 1
Let z be 1/(-1 + 8/7). Let y = z + -3. Factor -2*r**4 + y*r**3 + 3*r**4 - 6*r**3 + r**2.
r**2*(r - 1)**2
Let c(l) be the third derivative of l**9/80640 - l**8/26880 + l**5/12 - 2*l**2. Let k(j) be the third derivative of c(j). Factor k(g).
3*g**2*(g - 1)/4
Solve 2/5 + 8/15*x + 2/15*x**2 = 0.
-3, -1
Let q(l) be the second derivative of l**7/56 - 7*l**6/120 + l**5/40 + l**4/8 - 5*l**3/24 + l**2/8 + 8*l. Factor q(r).
(r - 1)**3*(r + 1)*(3*r - 1)/4
Let x(l) be the first derivative of -l**3/3 - 2*l**2 - 3*l - 4. Factor x(u).
-(u + 1)*(u + 3)
Let g(b) be the third derivative of -b**5/36 + 12*b**2. Factor g(i).
-5*i**2/3
Suppose 128*p + 9 = 131*p. Let 3/4*x - 9/4*x**2 + 3/2*x**p + 0 = 0. Calculate x.
0, 1/2, 1
Let c(s) = s**2 + 36*s + 35. Let b be c(-35). Suppose 1/5*i**5 - 2/5*i**3 + b + 0*i**4 + 1/5*i + 0*i**2 = 0. Calculate i.
-1, 0, 1
Let g be 12 - (8/2 - 2). Factor -5*t**4 + 7*t**2 + 0*t**4 - 12 + g + 3*t - 3*t**3.
-(t - 1)*(t + 1)**2*(5*t - 2)
Let g(a) = a**4 - 4*a**3 + 4*a + 5. Suppose -2*b = b - 6. Let o(p) = 5 - 2 - 2 + 4*p + 5 + b*p**4 - 4*p**3. Let x(v) = 4*g(v) - 3*o(v). Factor x(s).
-2*(s - 1)*(s + 1)**3
Suppose 0 - 3/5*z**2 - 1/5*z**3 - 2/5*z = 0. What is z?
-2, -1, 0
Let a = 919/7 - 131. Factor 2/7 + a*n**2 + 4/7*n.
2*(n + 1)**2/7
Let w(l) = -2*l + l + 0 - 1. Let u(i) = -i**2 + 1. Let d be (-1)/(2/24*3). Let o(s) = d*w(s) - 2*u(s). Factor o(n).
2*(n + 1)**2
Let t(k) = -2*k**2 + 6*k - 2. Let r(n) = -9*n**2 + 24*n - 9. Let l(g) = -5*r(g) + 21*t(g). Factor l(m).
3*(m + 1)**2
Let r = -7 - -12. Find y such that 2*y**4 - 8*y**2 + 0*y**4 + 3*y**3 - 2 - 5*y**3 + y**r - 2*y - 5*y = 0.
-1, 2
Suppose -5*b + 4*b = -2. Factor d**4 - d**2 - b*d - d + 2*d + d**3.
d*(d - 1)*(d + 1)**2
Suppose 0 = -9*i + 39 + 6. Determine d, given that -4/3*d**i + 1/3*d + 1/3 + 8/3*d**4 - 5/3*d**2 - 1/3*d**3 = 0.
-1/2, 1
Let z(u) be the second derivative of -u**6/10 + 2*u**5/5 + 7*u**4/12 + 8*u. Let t(n) = 3*n**4 - 9*n**3 - 8*n**2. Let s(y) = -6*t(y) - 7*z(y). Factor s(h).
h**2*(h - 1)*(3*h + 1)
Find f, given that -2/7*f + 2/7*f**3 - 2/7*f**2 + 2/7*f**4 + 0 = 0.
-1, 0, 1
Let m(q) = -q**2 + 14*q + 13. Let h be m(13). Let g = h - 23. Factor 2/7*u**g - 2/7*u**2 + 2/7*u**4 - 2/7*u + 0.
2*u*(u - 1)*(u + 1)**2/7
Let h be -1 + 3 + (-12 - -5 - -5). Factor 0*q - 2/9*q**3 + 2/9*q**2 + h.
-2*q**2*(q - 1)/9
Let b(m) = 5*m**2 + 4*m + 8. Let a(j) = 4*j**2 + 4*j + 7. Let o(r) = -4*a(r) + 3*b(r). Determine g so that o(g) = 0.
-2
Let l(r) be the first derivative of -2*r**5/15 + r**4/6 + 2*r**3/3 - r**2/3 - 4*r/3 - 8. Let l(o) = 0. Calculate o.
-1, 1, 2
Let t(h) be the third derivative of h**7/1155 - h**5/165 + h**3/33 - 18*h**2. Factor t(f).
2*(f - 1)**2*(f + 1)**2/11
Let s(k) be the first derivative of -196*k**3/3 - 56*k**2 - 16*k + 18. Solve s(z) = 0 for z.
-2/7
Let x(u) be the second derivative of -u**6/30 - u**5/4 - u**4/4 + 5*u**3/6 + 2*u**2 + 5*u. Factor x(j).
-(j - 1)*(j + 1)**2*(j + 4)
Let v = 2 + -1. Let y be 0 + 1 - (v + -3). Factor -3*o**y + o**5 + o**2 - 2*o**3 + 4*o**3 - o**4.
o**2*(o - 1)**2*(o + 1)
Let j(q) be the first derivative of 3*q**5/35 - q**3/7 - 11. Factor j(n).
3*n**2*(n - 1)*(n + 1)/7
Let a(x) be the second derivative of x - 1/21*x**4 + 0*x**2 - 1/70*x**5 + 0 + 0*x**3. Factor a(c).
-2*c**2*(c + 2)/7
Let q = -8 + 10. Solve v - 8*v**2 - 11*v - 6 + 2 - q*v**3 = 0 for v.
-2, -1
Let c(p) be the first derivative of p**4/4 + 2*p**3 + 9*p**2/2 + 11. Suppose c(i) = 0. Calculate i.
-3, 0
Suppose -12 = 4*r, -f + 6*r + 17 = r. Let b(j) be the first derivative of 7/18*j**6 - 14/9*j**3 - 11/6*j**f + 16/15*j**5 - 2/3*j + 1/3*j**4 + 1. Factor b(k).
(k - 1)*(k + 1)**3*(7*k + 2)/3
Let h(i) be the third derivative of i**8/13440 - i**7/3360 - i**6/240 - 3*i**5/20 - i**2. Let w(p) be the third derivative of h(p). Suppose w(y) = 0. What is y?
-1, 2
Factor 1/5*d**5 + 0*d + 0 - 1/5*d**4 - 1/5*d**3 + 1/5*d**2.
d**2*(d - 1)**2*(d + 1)/5
Let c = 25 + -23. Let u(y) be the second derivative of 1/24*y**3 - 1/48*y**4 + 1/4*y**c - 2*y + 0. Factor u(f).
-(f - 2)*(f + 1)/4
Suppose 4*j + 0 + 4 = 0, 9 = l - 5*j. Suppose -4*a = -4*i, i = -0*i - l*a. Let i + 2*w**3 - 10/3*w**5 + 4/3*w - 14/3*w**2 + 14/3*w**4 = 0. Calculate w.
-1, 0, 2/5, 1
Suppose 3*b - 4 = 3*j + 11, 7 = -4*b - 5*j. Solve -d**3 - d**b + 3*d**4 - 2*d**2 + 6*d**2 + 7*d**3 = 0 for d.
-1, 0
Let s be 68/14 - 2 - 2/(-14). Factor 0 - 4/7*x**s - 2/7*x**2 + 2/7*x.
-2*x*(x + 1)*(2*x - 1)/7
Let j be (-35 + 5)*(-2)/4. Suppose -2*k + j = 3*k. Solve -8/7*o**2 + 0*o - 130/7*o**4 + 0 + 100/7*o**5 + 8*o**k = 0 for o.
0, 2/5, 1/2
Let -183 - 6*o - 11*o**2 + 183 - 2*o**3 + 2*o**4 + o**2 = 0. What is o?
-1, 0, 3
Factor 6 + 2*z*