5 - k**5/28 + 5*k**4/42 + 3*k**3/14 + k**2/7 - k. Determine s so that d(s) = 0.
-2, -1, -1/2, 1
Let d be (-6)/8 + (-129)/(-12). Let h(s) = 2*s**2 - 19*s - 5. Let y be h(d). Suppose 0*j - 1/4*j**y + 0 + 1/4*j**2 + 1/4*j**3 - 1/4*j**4 = 0. What is j?
-1, 0, 1
Let r(l) = 6*l**5 + 12*l**4 - 3*l**3 - 9*l**2. Let c(o) = -3*o**5 - 6*o**4 + o**3 + 4*o**2. Let m(u) = -9*c(u) - 4*r(u). Suppose m(a) = 0. Calculate a.
-1, 0
Suppose 0 + 4 = -4*h. Let w(m) = -m**3 - m**2 - 1. Let g(k) = k**3 + 4*k**2 - k + 2. Let p(x) = h*g(x) - 2*w(x). Find r, given that p(r) = 0.
0, 1
Let i(q) be the second derivative of -q**5/100 + q**4/20 - q**3/10 + q**2/10 + 7*q. Factor i(v).
-(v - 1)**3/5
Determine m, given that 8*m + 9*m**3 + 13*m**3 - 6*m**3 - 20*m**2 + 0*m - 4*m**4 = 0.
0, 1, 2
Let b(r) be the second derivative of 1/24*r**4 + 0*r**2 + 1/80*r**5 + 0 - 3*r + 1/24*r**3. What is n in b(n) = 0?
-1, 0
Suppose -4*b + 6*v - 3*v + 112 = 0, -b + 9 = 4*v. Let t = -99/4 + b. Solve 0 - t*z - 1/4*z**5 + 0*z**2 + 1/2*z**3 + 0*z**4 = 0.
-1, 0, 1
Let h(o) be the third derivative of -o**6/240 - o**5/160 + o**4/32 + o**3/2 - 3*o**2. Let y(w) be the first derivative of h(w). Factor y(c).
-3*(c + 1)*(2*c - 1)/4
Solve 6/7*z**2 + 26/7*z + 8/7 = 0.
-4, -1/3
Suppose -4*y + 2*c - 8 = -34, 5*c + 21 = -y. Let t be (4/(-8))/((-2)/y). Find o such that 5/2*o - 3/2*o**2 - t = 0.
2/3, 1
Let t(n) be the third derivative of 2*n**7/735 + n**6/70 - 4*n**5/105 - 30*n**2. Factor t(y).
4*y**2*(y - 1)*(y + 4)/7
Let f(l) = l**3 - 2*l**2 - 6*l - 8. Let o be f(4). Let 0*k**3 + 0*k + 0 + o*k**2 - 1/4*k**4 = 0. Calculate k.
0
Suppose -2*i = 2*i - 68. Suppose 5*c**4 - i*c**3 + 21*c**2 + 0 + 2 - 11*c - 4*c**2 + 4*c**2 = 0. Calculate c.
2/5, 1
Let a(v) be the second derivative of -v**6/480 + v**5/80 - v**4/32 + v**3/3 - 11*v. Let l(f) be the second derivative of a(f). What is p in l(p) = 0?
1
Let q(z) be the first derivative of 20*z**4 + 4 + 4*z + 17*z**2 + 92/3*z**3. Determine n, given that q(n) = 0.
-1/2, -2/5, -1/4
Let i(q) be the first derivative of -3*q**5/25 - 3*q**4/20 + q**3/5 + 3*q**2/10 - 8. Factor i(u).
-3*u*(u - 1)*(u + 1)**2/5
Suppose 1 = 3*g - 8. Factor -5*v**g + 3*v**3 + v**3 - v**2 + 2*v**2.
-v**2*(v - 1)
Let w(n) be the first derivative of 1/3*n**3 + 3/2*n**2 + 2*n + 3. Determine a so that w(a) = 0.
-2, -1
Let x(j) be the first derivative of j**6/288 - j**5/160 - j**4/48 + j**3/3 + 6. Let r(o) be the third derivative of x(o). Factor r(d).
(d - 1)*(5*d + 2)/4
Suppose 5*o + s = -s + 67, s - 1 = 0. Suppose 3 - o = -5*i. Find p, given that 2*p - i*p**3 + p**4 - 1 + p - p = 0.
-1, 1
Let w(a) = -4*a - 2*a**2 - 1 + a**3 + 8*a - 2*a**2. Let g be w(3). Suppose -o**g - 3*o + 3*o + o = 0. Calculate o.
0, 1
Let k(x) be the third derivative of x**6/360 + x**5/240 - x**3/3 - 4*x**2. Let a(b) be the first derivative of k(b). Factor a(s).
s*(2*s + 1)/2
Let o = 45 + -9. Let s be 176/18 - (-8)/o. Factor -a + a**5 + s*a**3 + 2*a - 12*a**3.
a*(a - 1)**2*(a + 1)**2
Let t(v) be the third derivative of v**2 + 0*v**4 + 1/30*v**5 - 1/30*v**6 + 0*v + 0 + 0*v**3 + 1/105*v**7. Factor t(k).
2*k**2*(k - 1)**2
Let c(u) be the third derivative of -u**8/1176 + u**7/245 - u**6/210 - u**5/105 + u**4/28 - u**3/21 + 9*u**2. Suppose c(y) = 0. What is y?
-1, 1
Let y be 7/(-4) - 1/4. Let c = y + 2. Factor -2*d**2 + d**3 + c*d**2 - 2*d + 2*d**4 + d**3.
2*d*(d - 1)*(d + 1)**2
Suppose 2*g - 12 = -4*b, -b + 3*g - 7 = 4*b. Factor b - 5/2*f**3 - 1/2*f - 4*f**2.
-(f + 1)**2*(5*f - 2)/2
Factor -6*m**2 - 6*m**2 - 6 - 3*m**3 + 15*m + 6*m**3.
3*(m - 2)*(m - 1)**2
Let f be (-16)/(-20)*(-10)/(-4). Let k(d) be the third derivative of -1/240*d**6 + 1/48*d**4 + 0*d + 0*d**3 + 0 + 1/420*d**7 + 2*d**f - 1/120*d**5. Factor k(h).
h*(h - 1)**2*(h + 1)/2
Let f(v) be the first derivative of v**5/5 + v**4 + v**3 - 2*v**2 - 4*v - 4. Factor f(c).
(c - 1)*(c + 1)*(c + 2)**2
Let p(a) be the first derivative of -a**4/2 + 8*a**3/3 - a**2 - 12*a + 30. Find m such that p(m) = 0.
-1, 2, 3
Factor 2/5*y**2 - 3/5*y + 1/5*y**3 + 0.
y*(y - 1)*(y + 3)/5
Suppose -2/11*b**5 - 4/11*b**2 - 18/11*b + 10/11 + 20/11*b**3 - 6/11*b**4 = 0. What is b?
-5, -1, 1
Let l(v) = v**3 + 6*v**2 - 6*v + 7. Let g be l(-7). Suppose -2*u + g*u + 4 = 0. Find i, given that u*i - 1 + 14*i**2 + 0*i - 12*i - 3 = 0.
-2/7, 1
Factor -2*z**2 + 2*z - 2/3 + 2/3*z**3.
2*(z - 1)**3/3
Find l, given that -7*l + 12*l + 16 - 20*l**2 + 24*l + 3*l = 0.
-2/5, 2
Let t(i) = 5*i**2 - 7*i. Let w(d) = 35*d**2 - 50*d. Let q(j) = -20*t(j) + 3*w(j). Let q(m) = 0. Calculate m.
0, 2
Let o(m) be the third derivative of 0*m - 1/60*m**6 - 1/105*m**7 + 1/12*m**4 - 3*m**2 + 0*m**3 + 0 + 1/30*m**5. Suppose o(j) = 0. What is j?
-1, 0, 1
Let p(z) be the first derivative of -z**6/9 - z**5/5 + z**4/12 + z**3/3 + z**2/6 - 3. Suppose p(r) = 0. What is r?
-1, -1/2, 0, 1
Let t(d) = -d**2 + 1. Let p(m) = -10*m**2 - 9*m + 10. Let c(v) = p(v) - 4*t(v). Let c(w) = 0. Calculate w.
-2, 1/2
Let c be (2 + 23/(-4))*-4. Suppose 3*t + v + 2 = -0, -c = 5*t + 4*v. Determine k, given that k**2 - 2*k**2 - 2*k**2 - 4*k - t = 0.
-1, -1/3
Let n(c) = c**4 + 9*c**3 - 5*c**2 - 9*c + 4. Let r(v) = v**4 + v**3 - v**2 - v. Let u(k) = -n(k) + 3*r(k). Factor u(d).
2*(d - 2)*(d - 1)**2*(d + 1)
Let a(j) = 4*j**4 - 18*j**3 + 32*j**2 - 16*j + 2. Let l(n) = -8*n**4 + 35*n**3 - 64*n**2 + 32*n - 5. Let u(w) = -5*a(w) - 2*l(w). Find b, given that u(b) = 0.
0, 1, 2
Let y(p) be the third derivative of -1/735*p**7 - 1/1176*p**8 + 0*p**4 + 0*p**3 - 2*p**2 + 0*p + 0*p**6 + 0 + 0*p**5. Factor y(l).
-2*l**4*(l + 1)/7
Let x(l) be the first derivative of 2*l**6/3 + 18*l**5/5 + 13*l**4/2 + 10*l**3/3 - 3*l**2 - 4*l + 7. Solve x(t) = 0.
-2, -1, 1/2
Suppose -2*f = -2*n - 4, 5*n = 5*f - f - 5. Let x be 6/2 + (n - 6). Factor -1/4*b**5 + 3/4*b**4 + 1/4*b**2 + 0*b + x - 3/4*b**3.
-b**2*(b - 1)**3/4
Let g(o) be the third derivative of -o**9/4320 - o**8/2016 + 2*o**7/315 - o**6/90 + o**5/20 - 8*o**2. Let k(d) be the third derivative of g(d). Factor k(y).
-2*(y - 1)*(y + 2)*(7*y - 2)
Let b = -1 + 2. Factor -j**2 - 2*j - b + 0*j + 0*j**2.
-(j + 1)**2
Let d = -99 + 299/3. Suppose -d*p**5 + 0*p - 2/3*p**2 + 2/3*p**3 + 0 + 2/3*p**4 = 0. Calculate p.
-1, 0, 1
Suppose -2*b - 28*t = -24*t - 8, t = 2. Find h, given that b + 0*h**3 + 2/5*h**2 - 2/5*h**4 - 1/5*h + 1/5*h**5 = 0.
-1, 0, 1
Let z(p) be the second derivative of -p**4/48 + p**3/12 - 8*p. Factor z(n).
-n*(n - 2)/4
Factor 6/7*c + 0 - 2/7*c**2.
-2*c*(c - 3)/7
Let b = -108 + 542/5. Let z be -4*15/10 + (-1 - -9). Determine v, given that 0*v - b*v**z - 1/5*v**3 + 0 = 0.
-2, 0
Let y(u) be the second derivative of u**7/12600 - u**6/900 + u**5/150 - u**4/6 + 4*u. Let k(l) be the third derivative of y(l). Factor k(g).
(g - 2)**2/5
Determine z so that 2/7*z**3 - 2/7*z**2 - 4/7*z + 0 = 0.
-1, 0, 2
Let p = 20/71 - -326/355. Solve p + 3/5*r**2 - 9/5*r = 0 for r.
1, 2
Suppose -3*d - d = -9*d. Factor t**4 - 1/2*t**3 - t**2 + 1/2*t**5 + 0*t + d.
t**2*(t - 1)*(t + 1)*(t + 2)/2
Let o(l) = 18*l**3 - 12*l**2 + 5*l + 3. Let a(x) = 18*x**3 - 12*x**2 + 4*x + 2. Let f(d) = 3*a(d) - 2*o(d). Determine i, given that f(i) = 0.
0, 1/3
Let q(n) be the third derivative of -n**8/1176 - n**7/735 + n**6/420 + n**5/210 + 4*n**2. Factor q(s).
-2*s**2*(s - 1)*(s + 1)**2/7
Factor -4/13 + 2/13*c + 2/13*c**2.
2*(c - 1)*(c + 2)/13
Let j(m) = -m**2 + 8*m + 6. Let k be j(8). Solve -7*c**4 + c**4 + c**2 + 9*c - 9*c**3 + 3 - 4*c**2 + k*c**2 = 0.
-1, -1/2, 1
Let t = 8/6193 + 166475/569756. Let c = -1/23 + t. Solve -c*r**2 + 1/4*r + 1/2 = 0.
-1, 2
Let a(c) = c**5 + 4*c**3 - 4*c + 4. Let z(t) = -t**5 - 5*t**3 + 5*t - 5. Let q(o) = 5*a(o) + 4*z(o). Determine f, given that q(f) = 0.
0
Let y(u) = -6*u**5 + 3*u**4 + 2*u**3 + 9*u**2 - 6*u + 3. Let l(b) = -b**5 + b**4 + b**2 - b + 1. Let c(h) = -20*l(h) + 4*y(h). What is s in c(s) = 0?
-2, -1, 1
Find j, given that -4/5*j + 0 + 4*j**2 - 9/5*j**3 = 0.
0, 2/9, 2
Let z = 1569/4 + -392. Factor 0 - z*c + 1/4*c**2.
c*(c - 1)/4
Let n be (5 - 46/10)/1. Factor 0 + m**2 + n*m.
m*(5*m + 2)/5
Let h(c) be the second derivative of -c**4/108 - c**3/3 - 9*c**2/2 + 23*c. Factor h(g).
-(g + 9)**2/9
Let -21/5*r**2 + 0 + 6/5*r = 0. What is r?
0, 2/7
Let g(w) be the first derivative of w**6/27 - 4*w**5/45 - 5*w**4/18 + 20*w**3/27 + 4*w**2/9 - 16*w/9 - 63. Solve