1)**2*(q + 1)**2/5
Find w such that 8/3*w + 0 - 2/3*w**3 + 0*w**2 = 0.
-2, 0, 2
Let o be (9/(-216)*-3)/((-2)/(-4)). Let s(c) be the first derivative of -1/6*c - o*c**2 - 1/24*c**4 - 1/6*c**3 + 1. Factor s(f).
-(f + 1)**3/6
Let l(s) be the first derivative of 2*s**6/9 - 4*s**5/15 - s**4/3 + 4*s**3/9 - 16. Solve l(f) = 0 for f.
-1, 0, 1
Let u(r) be the third derivative of -1/70*r**7 + 0 + 1/112*r**8 + 1/20*r**5 + 0*r**3 - 1/40*r**6 + 0*r**4 + 0*r - 5*r**2. Determine x, given that u(x) = 0.
-1, 0, 1
Let x be (-4)/14*(-1)/((-5)/(-10)). Factor 2/7*n**2 + 2/7 + x*n.
2*(n + 1)**2/7
Let b be (-400)/(-504) - (-12)/(-21). Factor b*c**2 - 2/9*c + 0.
2*c*(c - 1)/9
Let s(i) be the second derivative of 0 - 3/20*i**5 + 3/2*i**4 - 6*i**3 + 2*i + 12*i**2. Solve s(p) = 0 for p.
2
Let q(d) be the second derivative of -d**6/30 + 3*d**5/20 - d**4/6 + 31*d - 2. Factor q(w).
-w**2*(w - 2)*(w - 1)
Let w(g) = 10*g**3 - 11*g**2 + 10*g + 9. Let k(p) = p**3 - p**2 + p + 1. Let f(u) = -18*k(u) + 2*w(u). What is i in f(i) = 0?
0, 1
Let j be (4*-1)/2 - 48/(-18). Factor -j*a**2 + 4/3*a + 0 - 2/3*a**3.
-2*a*(a - 1)*(a + 2)/3
Let k(n) be the first derivative of -n**2 - 6*n + 5. Let s be k(-3). Factor -c - 1/2*c**2 + s.
-c*(c + 2)/2
Suppose -3*u + 3*w = -6, -5*w + 8 = 2*u - u. What is k in -14/3*k**u - 2/3*k - 2/3*k**5 - 3*k**4 + 0 - 3*k**2 = 0?
-2, -1, -1/2, 0
Let j(l) be the first derivative of 2*l**3/33 - l**2/11 - 6. Solve j(a) = 0.
0, 1
Let o(u) = -17 - 21*u - 21*u**3 + 31*u + 29*u - 1. Let y(l) = -6*l**3 + 11*l - 5. Let k(n) = -5*o(n) + 18*y(n). Determine p, given that k(p) = 0.
-1, 0, 1
Let b(x) be the first derivative of -2*x**2 + x + 2. Let m be b(-1). What is i in -m*i + i**5 + 5*i + i**2 - i**3 - i**4 = 0?
-1, 0, 1
Suppose -34 + 2*u**4 + 34 - 4*u**3 + 2*u**2 = 0. What is u?
0, 1
Let u(l) = -2*l**3 - 2*l**2 + 2. Let n be 1*-2*45/18. Let y(m) = 4*m**3 + 5*m**2 - 5. Let r(q) = n*u(q) - 2*y(q). Factor r(h).
2*h**3
Let t be (-68)/(-12) + -3 + 6/(-9). Factor -10/3*f - 14/3*f**t + 4/3.
-2*(f + 1)*(7*f - 2)/3
Let g(z) be the first derivative of z**5/10 + z**4/2 + z**3 + z**2 + 2*z + 1. Let i(y) be the first derivative of g(y). Suppose i(d) = 0. Calculate d.
-1
Let v(u) = u**4 + 5*u**3 + 3*u**2 + 5*u - 9. Let b(t) = t**4 + 3*t**3 + t**2 + 3*t - 5. Let q(j) = -5*b(j) + 3*v(j). Factor q(z).
-2*(z - 1)**2*(z + 1)**2
Let h = -14 - -20. Let i(l) be the second derivative of -l + 0*l**3 + 1/3*l**4 + 7/5*l**5 + 49/30*l**h + 0 + 0*l**2. Factor i(q).
q**2*(7*q + 2)**2
Let h(v) = 2*v + 2. Let b be h(2). Let a be 3/(-6) - (-3)/b. Find z such that 2/7*z + a - 4/7*z**2 - 6/7*z**3 = 0.
-1, 0, 1/3
Let a(p) be the third derivative of p**5/12 - 5*p**4/24 - 5*p**3/3 + 12*p**2. Factor a(c).
5*(c - 2)*(c + 1)
Let u(o) be the first derivative of -4*o**3/3 + 16*o**2 - 28*o - 13. Find j such that u(j) = 0.
1, 7
Let s(l) be the second derivative of 0 - 1/8*l**4 + 0*l**3 + 1/40*l**6 + 3/8*l**2 - l + 0*l**5. Factor s(m).
3*(m - 1)**2*(m + 1)**2/4
Let o(f) be the first derivative of -f**6/2 - 8*f**5/5 - 3*f**4/4 + 2*f**3/3 + 5. Let o(l) = 0. What is l?
-2, -1, 0, 1/3
Let v(j) = -2*j**2 + 46*j - 242. Let x(s) = 2*s**2 - 47*s + 242. Let d(p) = 6*v(p) + 4*x(p). Suppose d(r) = 0. What is r?
11
Let q(m) be the third derivative of m**7/420 + m**6/120 - m**4/24 - m**3/12 + 3*m**2. Factor q(o).
(o - 1)*(o + 1)**3/2
Let b(k) = -3*k**2 - 4*k + 0*k**2 + 3*k + 4*k**2. Let f(p) = 2*p**2 - p. Let c(i) = -3*b(i) + f(i). Factor c(o).
-o*(o - 2)
Factor -9/10 - 7/10*h**2 + 3/2*h + 1/10*h**3.
(h - 3)**2*(h - 1)/10
Find b, given that 4/7*b + 4/7*b**2 + 0 = 0.
-1, 0
Factor 8/9*f + 0 - 2/9*f**2.
-2*f*(f - 4)/9
Let c(o) = 2*o - 30. Let d be c(16). Determine j, given that 2/7*j - 2/7*j**d + 2/7*j**4 + 0 - 2/7*j**3 = 0.
-1, 0, 1
Suppose -2*k + h + 3 = 0, 12*k + h = 11*k + 6. Solve 4/9*w**2 + 2/9*w**k + 0*w - 2/9*w**4 + 0 = 0.
-1, 0, 2
Find y such that 2/3*y + 1 - 1/3*y**2 = 0.
-1, 3
Let d(u) be the second derivative of u**7/378 + u**6/270 + 2*u. Factor d(w).
w**4*(w + 1)/9
Let j(f) be the second derivative of f**5/90 - 7*f**4/144 - f**3/18 - f**2/2 + 3*f. Let n(m) be the first derivative of j(m). Let n(i) = 0. Calculate i.
-1/4, 2
Let q(g) = -3*g**3 - 3*g**2 + 12*g. Let h(v) = v**3 - v**2 - v. Let k(w) = 6*h(w) + q(w). Factor k(s).
3*s*(s - 2)*(s - 1)
Let y(k) be the first derivative of -28*k**3/3 - 8*k**2 + 3. Factor y(q).
-4*q*(7*q + 4)
Suppose 2*f = 0, -f = 2*w + 2*f. Factor -3*s**2 + w + 0 + 2*s + s**2.
-2*s*(s - 1)
Let h(a) be the third derivative of -a**7/105 - a**6/300 - 3*a**2. Factor h(i).
-2*i**3*(5*i + 1)/5
Let x(t) be the second derivative of 1/21*t**3 + 0*t**2 + 0 + 4/35*t**6 + 4/147*t**7 + 1/7*t**4 + 13/70*t**5 - 3*t. Factor x(z).
2*z*(z + 1)**2*(2*z + 1)**2/7
Let x(m) = 15*m**2 - 21*m - 27. Let j(b) be the second derivative of 7*b**4/12 - 5*b**3/3 - 13*b**2/2 + 3*b. Let y(r) = 9*j(r) - 4*x(r). Factor y(o).
3*(o - 3)*(o + 1)
Suppose -3/5*y**5 + 0*y**2 + 3/5*y**3 + 0 + 0*y + 0*y**4 = 0. Calculate y.
-1, 0, 1
Let q(n) be the first derivative of 2*n**5/35 + 3*n**4/14 + 4*n**3/21 - 6. Factor q(s).
2*s**2*(s + 1)*(s + 2)/7
Determine c so that -3*c**2 + 4*c**2 + 4*c**2 - 16*c**3 + 11*c**3 = 0.
0, 1
Let u be 10/4*48/(-340). Let c = 86/51 + u. Factor c + 2/3*o**2 - 2*o.
2*(o - 2)*(o - 1)/3
Let w = -1/188 + 1511/1316. Suppose -2/7*p**3 + 0 - w*p**2 - 8/7*p = 0. Calculate p.
-2, 0
Suppose 0*n - 8/13 - 2/13*n**3 + 6/13*n**2 = 0. Calculate n.
-1, 2
Let u be (-8)/(-20) + 28/5. Let d be -4 + 16/u - -3. Factor 0 - 2/3*q + d*q**2 + 1/3*q**4 - 4/3*q**3.
q*(q - 2)*(q - 1)**2/3
Let j be 1/2 + 7/42. Let g be (-2 - -5) + 7/(-3). Factor g*l - 4/3 + j*l**2.
2*(l - 1)*(l + 2)/3
Let c(k) be the third derivative of -k**6/240 + k**5/60 + k**4/48 - k**3/6 - 5*k**2. Solve c(a) = 0 for a.
-1, 1, 2
Let i(b) be the second derivative of -b**7/14 - 17*b**6/30 - 37*b**5/20 - 13*b**4/4 - 10*b**3/3 - 2*b**2 - 4*b. Suppose i(s) = 0. What is s?
-2, -1, -2/3
Let d(s) = -s + 1. Let p be d(-4). Suppose p*t = o - 0*o - 1, 0 = -4*o + 4. Solve t*i + 0 + 0*i**2 + 1/3*i**3 = 0.
0
Factor -3/4*o**2 - o**3 + 1/4*o + 0.
-o*(o + 1)*(4*o - 1)/4
Find k, given that -1/8*k**4 - 1/8*k**2 + 3/8*k**3 - 3/8*k + 1/4 = 0.
-1, 1, 2
Solve 108/13*o + 72/13*o**2 + 54/13 + 16/13*o**3 = 0.
-3/2
Let h(o) be the third derivative of -o**8/1008 - o**7/630 + o**6/120 + o**5/180 - o**4/36 + 18*o**2. What is f in h(f) = 0?
-2, -1, 0, 1
Suppose 0 = n + v, n - 2*v - 20 = -n. Let d = n + 0. Factor -p**5 + 2*p**d - 8*p**3 + 7*p**3.
p**3*(p - 1)*(p + 1)
Let d be ((-3 - -2)*4)/(-1). Suppose 0 = -d*z - 3*v + 20, 4*v + 15 = 3*z + 2*v. Factor -12*n**2 + 14*n**3 - 2*n + 3*n - z*n + 2*n**2.
2*n*(n - 1)*(7*n + 2)
Let r(n) be the first derivative of n - 1/18*n**3 + 0*n**2 + 1/60*n**5 + 0*n**4 - 2. Let t(v) be the first derivative of r(v). Factor t(s).
s*(s - 1)*(s + 1)/3
Let o(x) be the first derivative of -x**5/40 - 3*x**4/16 - 13*x**3/24 - 3*x**2/4 - x/2 - 42. Let o(f) = 0. What is f?
-2, -1
Let u(s) = -5*s**2 - 35*s + 3. Let d be u(-7). Factor -3/2*r**d + 3/4*r**2 + 0*r + 3/4*r**4 + 0.
3*r**2*(r - 1)**2/4
Suppose -5*q + 16 = -4*f, q - 3 = -q + 5*f. Suppose -4 + q - 3*b**3 + 3*b**2 = 0. What is b?
0, 1
Suppose 0 - d + 1/2*d**3 - 1/2*d**2 = 0. What is d?
-1, 0, 2
Let l(p) be the first derivative of p**5/5 + p**4/2 + p**3/3 + 3. Determine i so that l(i) = 0.
-1, 0
Let b(j) be the third derivative of j**7/490 + j**6/280 - j**5/140 - j**4/56 - 6*j**2. Determine n, given that b(n) = 0.
-1, 0, 1
Let z(v) = 4*v**2 - 3*v. Suppose -3*d = -d - 4. Let i be z(d). Solve 2*u**3 + 10 - i + 2*u**2 = 0.
-1, 0
Suppose -3*b + 3*q + 9 = -0*b, b + 2 = -4*q. Let o(n) be the first derivative of 2 + 1/7*n**b + 1/14*n**4 + 0*n - 4/21*n**3. Find f, given that o(f) = 0.
0, 1
Let p(z) be the second derivative of -z**5/60 - z**4/12 - z**3/6 + z**2/2 - 3*z. Let i(h) be the first derivative of p(h). Factor i(a).
-(a + 1)**2
Let 0 + 0*h**2 - 1/5*h**4 - 3/5*h**3 + 0*h = 0. Calculate h.
-3, 0
Suppose 0 = -0*w + 3*w - 6. Suppose -3*o - 2*u = -8*o, -w*o + 14 = 2*u. Factor -2*j - j**o - 3*j**2 + 2*j**2 + 4.
-2*(j - 1)*(j + 2)
Let v(z) = 4*z**4 - 4*z**2. Suppose -5*r = -39 + 4. Let j(o) = 5*o**4 - 5*o**2. Let l(a) = r*v(a) - 6*j(a). Factor l(q).
-2*q**2*(q - 1)*(q + 1)
Let s be (((-15)/(-6))/1 - 1) + 0. Factor 0 + 0*j + 0*j**3 - 3