 Determine a so that 4/9*a + 32/9*a**3 - 14/9*a**q + 0 - 22/9*a**2 = 0.
0, 2/7, 1
Let w(l) be the third derivative of l**5/20 + l**4/4 + 8*l**2. Determine b so that w(b) = 0.
-2, 0
Let z(b) be the third derivative of b**8/840 + b**7/140 + b**6/180 - b**4/24 - 2*b**2. Let l(u) be the second derivative of z(u). Factor l(q).
2*q*(q + 2)*(4*q + 1)
Let x(b) be the first derivative of b**7/210 - b**6/45 + b**5/30 - 5*b**3/3 - 3. Let h(a) be the third derivative of x(a). Factor h(s).
4*s*(s - 1)**2
Let s(p) be the third derivative of -p**5/360 + p**4/144 + p**3/18 - 5*p**2. Factor s(t).
-(t - 2)*(t + 1)/6
Let b(j) be the third derivative of j**5/60 - j**4/6 + 2*j**3/3 + 13*j**2. Determine v, given that b(v) = 0.
2
Suppose 13*a = 8*a. Let t(k) be the third derivative of 0*k + a*k**5 + 0 - 1/32*k**4 - 1/12*k**3 + 1/480*k**6 + k**2. Factor t(p).
(p - 2)*(p + 1)**2/4
Let z(m) be the second derivative of m**4/48 + 5*m**3/24 + m**2/2 - 14*m. Factor z(h).
(h + 1)*(h + 4)/4
Let j(r) = r**3 - 8*r**2 + 3. Let d be j(8). Suppose -2*z + 4*c + 4 = 0, 0*c - 3*c + 2 = z. Let 0*q**z + 0*q + 0 + 2/3*q**d = 0. What is q?
0
Let g(o) = -8*o**4 + 10*o**3 + 6*o**2 + 2*o + 2. Let q(h) = -15*h**4 + 19*h**3 + 11*h**2 + 3*h + 4. Let v(z) = 11*g(z) - 6*q(z). Factor v(k).
2*(k - 1)**3*(k + 1)
Let d(s) = -s**3 - 3*s**2 + s + 3. Let n be d(-3). Suppose n - 2 = -p. Factor 0 + 4/7*o**p + 0*o - 6/7*o**3.
-2*o**2*(3*o - 2)/7
Solve 5/4*g - 7/4*g**2 + 1/2 = 0.
-2/7, 1
Let l(q) be the third derivative of q**5/24 + q**4/96 - 23*q**2. Determine r, given that l(r) = 0.
-1/10, 0
Let u be -1 + 3/((-9)/(-87)). Suppose -3*y - s - 3*s + u = 0, 0 = 5*y + 5*s - 40. Suppose 8*b**2 + 0 - y - b - 6*b**3 + 3*b = 0. Calculate b.
-2/3, 1
Let k(u) be the third derivative of u**6/60 + 7*u**5/60 + u**4/6 + u**3/2 - 4*u**2. Let f(a) be the first derivative of k(a). Solve f(x) = 0.
-2, -1/3
Suppose 1/4*r + 0 + 3/8*r**2 + 1/8*r**3 = 0. What is r?
-2, -1, 0
Let h(q) be the third derivative of -q**6/360 + q**5/60 + q**3/3 + q**2. Let d(m) be the first derivative of h(m). Factor d(w).
-w*(w - 2)
Let p(q) = 2*q - 16. Let z be p(9). Let -1/5*h**z - 2/5*h - 1/5 = 0. Calculate h.
-1
Let r = 39 - 37. Let v(o) be the second derivative of -1/189*o**7 + 0*o**r - 2*o + 0*o**4 + 0 + 0*o**6 - 1/27*o**3 + 1/45*o**5. Find k, given that v(k) = 0.
-1, 0, 1
Let m(s) be the second derivative of -1/6*s**3 - 1/24*s**4 - 1/4*s**2 + 0 - 3*s. Let m(l) = 0. Calculate l.
-1
Let v(o) be the first derivative of 2*o**5/5 + 11*o**4/8 + 5*o**3/6 - o**2/2 + 5. Factor v(x).
x*(x + 1)*(x + 2)*(4*x - 1)/2
Let s(y) = -290*y**4 + 50*y**3 + 290*y**2 - 120*y. Let b(d) = 17*d**4 - 3*d**3 - 17*d**2 + 7*d. Let n(c) = 35*b(c) + 2*s(c). Solve n(v) = 0 for v.
-1, 0, 1/3, 1
Let i = -19/12 - -9/4. Factor -i*y**3 + 2/9*y**4 + 0 - 2/9*y + 2/3*y**2.
2*y*(y - 1)**3/9
Let v(j) = j**3 - j**2 - j + 1. Let f(n) = -4*n**3 + 2*n**2 + 7*n + 1. Let u(z) = -f(z) - 3*v(z). What is i in u(i) = 0?
-2, -1, 2
Let c(s) = 6*s**5 + 4*s**4 - 8*s**2 - 2*s - 4. Let b(q) = q**5 - q**2 - 1. Let f(y) = -4*b(y) + c(y). Factor f(x).
2*x*(x - 1)*(x + 1)**3
Suppose -3 + 0*x**2 - 3*x + x**2 + 0*x**2 + 5 = 0. What is x?
1, 2
Suppose -3*t = -2*n + 6, -4*n - 4 = t + t. Let v(d) be the first derivative of 0*d**3 + 1/21*d**6 - 1/14*d**4 + 1 + 0*d**2 + 0*d + n*d**5. Factor v(y).
2*y**3*(y - 1)*(y + 1)/7
Let g(p) be the second derivative of p**6/165 + 2*p**5/55 - p**4/11 - 4*p**3/33 + 5*p**2/11 - 20*p. Let g(s) = 0. Calculate s.
-5, -1, 1
Let -31/4*n - 3 + 19/4*n**3 + 21/4*n**2 + 3/4*n**4 = 0. What is n?
-4, -3, -1/3, 1
Suppose -z - 3*z - 2 = -2*n, -5*n + 3*z = -12. Solve -6*b**4 + 12*b - 4*b**4 + n + 14*b**4 + 12*b**3 - b**4 + 18*b**2 = 0.
-1
Let d = 1550/3 + -515. Solve -1/3*p**3 + 4/3*p**2 - d*p + 2/3 = 0 for p.
1, 2
Let o(u) = u**2 - 1. Let k be (-2)/(1/(-1 + -1)). Suppose -3*g + 1 = k. Let v(i) = -11*i**2 + 10*i + 1. Let f(s) = g*v(s) - 3*o(s). Find h such that f(h) = 0.
1/4, 1
Let h be (2 - 3)*(22 + 0). Let k be (-3)/h*(-52)/(-39). Determine t so that -2/11*t**2 + k*t**3 + 0*t - 2/11*t**5 + 2/11*t**4 + 0 = 0.
-1, 0, 1
Let l be (2 - (1 - -7))/1. Let i be (-32)/120 + (-4)/l. Suppose 2/5 + 12/5*s**2 + 8/5*s**3 + 8/5*s + i*s**4 = 0. Calculate s.
-1
Let u = 148 + -148. Factor 1/2*s**3 - 1/2*s**2 + u + 0*s.
s**2*(s - 1)/2
Let s(w) be the third derivative of -w**7/420 - w**6/120 - w**5/120 + 23*w**2. Factor s(g).
-g**2*(g + 1)**2/2
Let u(r) be the first derivative of -2*r**5/5 - 3*r**4/2 + 4*r**2 + 3. Factor u(i).
-2*i*(i - 1)*(i + 2)**2
Suppose -3*s = -2*c - 0*c - 19, -3*s = -3*c - 24. Suppose 12*o**s - 4*o**3 - o**2 - 4*o**3 = 0. What is o?
0, 1/4
Let o(b) = -5*b**3 - 4*b. Let p(r) = -r**3 + r**2. Let x(u) = -o(u) + 4*p(u). Factor x(c).
c*(c + 2)**2
Let n(c) = -11*c**2 - c - 17. Let s(m) = -5*m**2 - m - 8. Let z(r) = 4*n(r) - 9*s(r). Let z(b) = 0. Calculate b.
-4, -1
Let x(y) be the second derivative of 1/225*y**6 + 0*y**3 - 1/315*y**7 + 1/75*y**5 + 0 + 0*y**2 + 0*y**4 - 2*y. Suppose x(i) = 0. Calculate i.
-1, 0, 2
Factor 3*r**3 - r**3 + 10*r**3 - 44*r**2 - 18 + 4*r**3 + 48*r - 2*r**4.
-2*(r - 3)**2*(r - 1)**2
Let m(k) be the second derivative of 2*k**4 + 11*k**3/6 + k**2/2 - 7*k. Let z(q) = -q**2 + q. Let r(i) = 3*m(i) - 3*z(i). Determine t, given that r(t) = 0.
-1/5
Let i be 1*(-4)/(-12)*3. Suppose -t = -3 + i. Factor 0*y**t + 0 - 2/3*y + 2/3*y**3.
2*y*(y - 1)*(y + 1)/3
Let l(y) = -y**3 + 1. Let u(q) = 6*q**3 - 15*q - 11. Let i(h) = -l(h) - u(h). Suppose i(p) = 0. Calculate p.
-1, 2
Let j be -10 + 10 + 4/(-1). Let o be (-2 - 1) + (-20)/j. Factor -2/5*q + 0*q**o + 2/5*q**3 + 0.
2*q*(q - 1)*(q + 1)/5
Let h(x) = x**2 + 3*x - 6. Let g be h(-5). Let l be g/7*(-21)/(-6). Factor 2/3*z + 0 + 2/3*z**l.
2*z*(z + 1)/3
Let f = 3676 - 77149/21. Let y = f - -3/7. Factor -8/3 + 26/3*n**2 + y*n + 10/3*n**3.
2*(n + 1)*(n + 2)*(5*n - 2)/3
Let z(r) = r**2 - 2*r + 4. Let k be z(3). Let p be (14/(-18))/(k/(-42)). Solve p*t**3 - 4/3*t**2 + 0*t - 10/3*t**4 + 0 = 0.
0, 2/5, 1
Let p be (-4 + 3)*(1 - -3). Let k be -3 + (-17)/p + -1. Factor 0*j + 0 - k*j**2.
-j**2/4
Find w such that -16/3*w + 2/3*w**4 + 16/3*w**3 - 20/3*w**2 + 6 = 0.
-9, -1, 1
Let -50/3 - 20/3*j - 2/3*j**2 = 0. What is j?
-5
Let k(t) be the third derivative of 1/36*t**6 + t**2 + 0 + 0*t + 3/2*t**3 + 3/4*t**4 + 1/5*t**5 + 1/630*t**7. Factor k(g).
(g + 1)*(g + 3)**3/3
Let o(x) be the first derivative of -2/15*x**5 + 1 - 1/3*x**2 + 1/6*x**4 + 2/9*x**3 + 0*x. Factor o(k).
-2*k*(k - 1)**2*(k + 1)/3
Let x(k) be the first derivative of -k**4/24 - k**3/18 + k**2/6 - 11. Factor x(o).
-o*(o - 1)*(o + 2)/6
Factor 0*y - 1/2 + 1/2*y**2.
(y - 1)*(y + 1)/2
Let w = -14 - -16. Factor w*k**3 + k - 8 + 2*k**3 + 2*k + 5*k + 14*k**2.
2*(k + 2)**2*(2*k - 1)
Suppose 4*a + 85 = -83. Let y be 28/a - 16/(-15). What is j in -2/5 + y*j**3 + 2/5*j**2 - 2/5*j = 0?
-1, 1
Let d(t) = -t**2 - 9*t - 4. Let n be d(-9). Let p = 4 + n. Suppose 40/3*c**2 - 8/3*c - 50/3*c**3 + p = 0. What is c?
0, 2/5
Let w(x) = -x**2 + 2. Let h be w(-2). Let g be (-52)/(-30) + h/5. Solve -14/3*s**3 - 2*s - g + 8*s**2 = 0.
-2/7, 1
Let v = 4 + 0. Factor 2*a + 0 + v - a**2 - 5.
-(a - 1)**2
Suppose -2*h = 2*f - 8, 2*f + 5*h = h + 6. Factor r + f*r**2 - 6*r**2 - 2*r.
-r*(r + 1)
Let d(i) be the second derivative of i**7/126 - i**6/30 + i**5/60 + i**4/12 - i**3/9 - 36*i. Determine p, given that d(p) = 0.
-1, 0, 1, 2
Let q(d) be the third derivative of d**6/30 + 2*d**5/15 - d**4/6 - 4*d**3/3 - d**2. Factor q(m).
4*(m - 1)*(m + 1)*(m + 2)
Let b(j) be the third derivative of 0 - 1/20*j**5 + 1/4*j**4 - 1/2*j**3 + 2*j**2 + 0*j. Solve b(o) = 0.
1
Let z = -53/39 - -438/13. Let h = -32 + z. Factor 2/3*k**4 + 2/3*k**3 + 1/6*k**5 - 1/3 - 5/6*k - h*k**2.
(k - 1)*(k + 1)**3*(k + 2)/6
Let g = 18 + -18. Factor 2/11 + g*j**3 - 4/11*j**2 + 0*j + 2/11*j**4.
2*(j - 1)**2*(j + 1)**2/11
Let g be -1*2*2/(-20). Let k = 19 - 17. Factor 2/5*a + g*a**k + 1/5.
(a + 1)**2/5
Let i(j) be the first derivative of 0*j**2 - 1/30*j**6 - 1 - 1/42*j**7 + 2*j + 0*j**3 + 0*j**5 + 0*j**4. Let q(v) be the first derivative of i(v). Factor q(w).
-w**4*(w + 1)
Let c be (-6)/(-21) + (-3213)/4214. Let m = 1/43 - c. Factor -m*r**5 - 1/2 + r**3 + r**2 - 1/2*r**4 - 1/2*r.
-(r - 1)**2*(r + 1)**3/2
Let r = 9 - 6. Determine k so that -3*k**r + 2*k**5 + 6*k*