Solve -2/11*w**4 + 2/11*w**3 + 6/11*w + 10/11*w**2 + 0 = 0.
-1, 0, 3
Suppose 35*z = 28*z. Factor z - 1/4*f + 1/4*f**2.
f*(f - 1)/4
Determine r so that -67*r**4 + 6*r**3 + 51*r**4 + 20*r**2 - 10*r**5 + 2*r - 4 + 2*r**3 = 0.
-1, 2/5, 1
Solve 0 - 2/9*f**3 + 8/9*f - 2/3*f**2 = 0 for f.
-4, 0, 1
What is l in -5/3*l**2 + 1/3*l**3 + 7/3*l - 1 = 0?
1, 3
Let o(h) be the first derivative of 0*h + 0*h**2 + 5 - 1/15*h**3 + 1/30*h**6 + 3/20*h**4 - 3/25*h**5. Factor o(v).
v**2*(v - 1)**3/5
Let t(m) = m**3 - 4*m**2 + 4*m. Let u be t(3). Factor 12*r**3 - 2 - u*r**4 + 6*r**2 + 2 - 18*r**2.
-3*r**2*(r - 2)**2
Let i(q) be the third derivative of q**6/540 + 2*q**5/45 + 4*q**4/9 + 64*q**3/27 - 9*q**2. Factor i(r).
2*(r + 4)**3/9
Let i = -1144769/40 + 28621. Let b = -11/8 + i. Factor -b*y + 2/5*y**2 + 0.
2*y*(y - 1)/5
Let a(n) be the second derivative of n**5/5 + n**4/12 - 5*n**2/2 + n. Let t(o) = -o**3 + 1. Let z(b) = -a(b) - 5*t(b). Suppose z(y) = 0. What is y?
0, 1
Let s(m) be the first derivative of 25*m**5 - 75*m**4/4 + 10*m**3/3 + 2. Factor s(h).
5*h**2*(5*h - 2)*(5*h - 1)
Let r(i) = 9*i**5 + 6*i**4 - 6*i**3 - 3*i - 6. Let u(y) = y**5 + y**4 - y - 1. Let f(o) = o + 5. Let p be f(-4). Let j(n) = p*r(n) - 6*u(n). Factor j(s).
3*s*(s - 1)**2*(s + 1)**2
Let t(z) = -3*z**4 - 5*z**3 - 7*z**2 - 7*z. Let q(x) = -10*x**4 - 15*x**3 - 20*x**2 - 21*x + 1. Let y(k) = -6*q(k) + 21*t(k). Factor y(j).
-3*(j + 1)**3*(j + 2)
Determine x, given that 3/5*x**4 + 0 - 6/5*x**2 + 0*x + 3/5*x**3 = 0.
-2, 0, 1
Let d(s) be the third derivative of 0*s + 0*s**4 + 0*s**3 + 4*s**2 + 0 - 1/40*s**6 - 1/10*s**5. What is m in d(m) = 0?
-2, 0
Let w = -9/77 + 113/308. Suppose 0*d + w - 1/4*d**2 = 0. What is d?
-1, 1
Let t = -291/14 - -149/7. Solve 3/2*k**4 - k**2 - 3/2*k + 1/2*k**5 + k**3 - t = 0 for k.
-1, 1
Let s(m) be the first derivative of -m**6/48 + 3*m**5/40 - m**4/16 - 30. What is v in s(v) = 0?
0, 1, 2
Suppose 0 + 0*w**3 + 0*w + 1/3*w**5 + 0*w**2 - 1/3*w**4 = 0. Calculate w.
0, 1
Let v(n) be the second derivative of n**7/70 - n**6/25 - 3*n**5/50 + n**4/5 + n**3/10 - 3*n**2/5 - 2*n. Determine a so that v(a) = 0.
-1, 1, 2
Let y(k) = 13 + 5*k**3 - 6*k**3 + 2*k**3 - 24*k + 9*k**2. Let n(h) = -h**3 - 19*h**2 + 48*h - 27. Let c(q) = 3*n(q) + 5*y(q). Let c(r) = 0. What is r?
2
Let o(y) = y**5 + y**4 - y**3 + y + 1. Let z(r) = -3*r**5 - 9*r**4 + 6*r**2 - 3*r - 9. Suppose -12 = 2*k - 0. Let p(d) = k*o(d) - z(d). Solve p(x) = 0 for x.
-1, 1
Let c(w) be the second derivative of -1/80*w**5 + 0 - 1/120*w**6 + 1/48*w**4 + 0*w**2 + 1/24*w**3 + 3*w. Let c(z) = 0. What is z?
-1, 0, 1
Let o(w) be the second derivative of 8*w**6/3 + 6*w**5 + 15*w**4/4 + 5*w**3/6 - 13*w. Factor o(k).
5*k*(k + 1)*(4*k + 1)**2
Suppose -7*y = -12*y. Let m be -2 + (-27)/(-6) + -2. Determine z, given that m*z**2 + y + 1/2*z - 1/2*z**3 - 1/2*z**4 = 0.
-1, 0, 1
Solve 12/7 + 2/7*i**2 - 10/7*i = 0 for i.
2, 3
Suppose -12*q = 10*q. Determine t, given that -4/7 + q*t + 4/7*t**2 = 0.
-1, 1
Let k = -8 - -6. Let i be k - 1/(12/(-27)). Factor i*y**4 - 1/2*y**3 + 1/4*y**2 + 0 + 0*y.
y**2*(y - 1)**2/4
Let y(h) be the third derivative of -h**7/630 + h**6/1080 + h**5/90 - h**4/72 - 2*h**3/3 - h**2. Let i(c) be the first derivative of y(c). Factor i(v).
-(v - 1)*(v + 1)*(4*v - 1)/3
Let d be (-6)/27 - (-280)/693. Solve d*c**2 + 2/11 - 4/11*c = 0 for c.
1
Let b(s) be the third derivative of 1/20*s**6 + 0*s + 0 - 1/2*s**4 - 1/70*s**7 + 3/20*s**5 - 4*s**2 - 2*s**3. Factor b(p).
-3*(p - 2)**2*(p + 1)**2
Let j(r) be the third derivative of r**8/40320 - r**6/1440 + r**5/30 - r**2. Let i(c) be the third derivative of j(c). Factor i(q).
(q - 1)*(q + 1)/2
Suppose 3*w - 18 = -2*s, 2 + 9 = s + 2*w. Find z, given that 4*z - s*z**2 - 1 + 3*z - 4*z + z**3 = 0.
1
Solve -1/3*o**5 - 1/3*o + 1/3*o**4 - 2/3*o**2 + 2/3*o**3 + 1/3 = 0.
-1, 1
Let h(p) = -3*p + 4 + 1 + 2*p - 10. Let d be h(-7). Factor 1/2*v**d + 1/2 + v.
(v + 1)**2/2
Let d(m) be the second derivative of 0*m**2 + 1/8*m**4 + 1/2*m**3 + 0 + 10*m. What is u in d(u) = 0?
-2, 0
Let y(m) be the second derivative of -m**5/50 - m**4/15 + m**3/15 + 2*m**2/5 + 5*m. Let y(r) = 0. What is r?
-2, -1, 1
Let x = 67/155 + -1/31. Factor 6/5*w + x*w**3 + 2/5 + 6/5*w**2.
2*(w + 1)**3/5
Let s(j) = -j + 1. Let t(l) = l**2 - 5*l + 4. Let w(d) = 6*s(d) - t(d). Factor w(v).
-(v - 1)*(v + 2)
Let z(k) = -k**3 + 5*k**2 + 8*k - 6. Let h be z(6). Let -h*g**2 - 4*g**3 + 6*g**2 + 6*g**2 - 4*g + 1 + g**4 = 0. What is g?
1
Let x(q) be the first derivative of -8*q**5/55 - 4*q**4/11 - 10*q**3/33 - q**2/11 + 12. Let x(v) = 0. What is v?
-1, -1/2, 0
Let l(p) = 3*p**3 + p**2 - 5. Let h = -2 + 6. Let g(f) = -f**3 + 2. Let x(d) = h*l(d) + 10*g(d). Factor x(j).
2*j**2*(j + 2)
Suppose -w**5 + 0*w**4 - w**3 + 0*w**2 - w**2 + 2*w**5 + w**4 = 0. What is w?
-1, 0, 1
Let v(j) be the third derivative of -j**8/168 - j**7/21 - 7*j**6/60 + j**5/30 + 2*j**4/3 + 4*j**3/3 + 4*j**2. Solve v(n) = 0 for n.
-2, -1, 1
Let c(v) be the third derivative of 0*v + 1/90*v**6 + 0*v**5 + 0*v**3 + 0 + 1/105*v**7 + 4*v**2 + 0*v**4. Factor c(g).
2*g**3*(3*g + 2)/3
Suppose -4*r + 12 = u, -5*u + 3*r + 10 = -u. Let o be 38/9 + 7/(63/(-2)). Factor u*i**5 - 7*i**4 + i**o - 31*i**5.
-3*i**4*(9*i + 2)
Let s(h) = h**4 - h**3 + h**2 + h. Let u(q) = -q**4 + 5*q**3 - 5*q**2 + 3*q. Let l(p) = s(p) - u(p). Factor l(m).
2*m*(m - 1)**3
Let q(b) be the first derivative of -b**6/27 + 2*b**5/15 - b**4/9 - 4. Factor q(k).
-2*k**3*(k - 2)*(k - 1)/9
Let s be (-440)/924 - 8/(-6). Suppose 2/7*r**2 + s*r + 0 = 0. What is r?
-3, 0
Let h(z) be the first derivative of 0*z + 1/3*z**3 - 1 - z**2. What is c in h(c) = 0?
0, 2
Let a(r) = r**3 - 12*r**2 - 3*r. Let s(b) = 75*b**2 + 12*b - 15*b**2 - 4*b**3 + 4*b. Let p(c) = -24*a(c) - 5*s(c). What is k in p(k) = 0?
-2, -1, 0
Let r(k) be the second derivative of 5*k**4/12 - 5*k**3/6 + 3*k. Factor r(f).
5*f*(f - 1)
Factor 0 - 4/3*i - 6*i**2 - 14/3*i**3.
-2*i*(i + 1)*(7*i + 2)/3
Let r(j) be the third derivative of -j**6/720 - j**5/240 + j**3/2 - 3*j**2. Let g(s) be the first derivative of r(s). Factor g(v).
-v*(v + 1)/2
Let q = 179/282 + 3/94. Factor 0 - g**2 - q*g.
-g*(3*g + 2)/3
Factor 2/11*z**2 + 10/11*z + 8/11.
2*(z + 1)*(z + 4)/11
Suppose 4*x = 11 - 3. Factor 2*t**x + 5/4*t + 1/4 + t**3.
(t + 1)*(2*t + 1)**2/4
Let w be -1 + 5 - (2 + -1). Suppose -u - 4*p - 13 = -3, -4*p - 16 = -2*u. Let o**4 - w*o**3 + 3*o**2 + 5*o - 4*o - u*o = 0. What is o?
0, 1
Let b be (-2)/7 - (-1564)/2093. Determine o, given that 4/13*o + 2/13*o**2 - b = 0.
-3, 1
Let r be (-6)/(-5)*15/3. Suppose 0 = -r*h + 4*h. Factor h*s**2 + 4*s**2 + s**4 - s + 0*s**2 + s**3 - 5*s**2.
s*(s - 1)*(s + 1)**2
Let r(k) be the second derivative of 2*k**7/77 + 3*k**6/55 - 3*k**5/110 - 3*k**4/22 - k**3/11 - 24*k. Solve r(o) = 0.
-1, -1/2, 0, 1
Let m = 2446/45 - 163/3. Let z(t) be the second derivative of -2*t + 1/27*t**3 + 1/9*t**2 + 1/135*t**6 + 1/189*t**7 + 0 - m*t**5 - 1/27*t**4. Factor z(u).
2*(u - 1)**2*(u + 1)**3/9
Factor 0*m - 4/7*m**3 + 0 + 4/7*m**2.
-4*m**2*(m - 1)/7
Let z(h) be the third derivative of 3/20*h**5 + 1/2*h**3 - 1/40*h**6 + 0*h - 4*h**2 + 0 - 3/8*h**4. Find x such that z(x) = 0.
1
Let f be 7/2 - (-15)/(-10). Factor -r**2 + f*r**2 - 1 - r**3 + r + 0*r**3 + 0.
-(r - 1)**2*(r + 1)
Let i(u) be the second derivative of 3*u + 0*u**2 - 1/6*u**4 + 0 - 2/3*u**3 + 1/5*u**5 + 1/15*u**6. Factor i(o).
2*o*(o - 1)*(o + 1)*(o + 2)
Let p(x) be the second derivative of -x**7/98 + x**6/70 + 9*x**5/140 - 5*x**4/28 + x**3/7 + 4*x. Solve p(t) = 0.
-2, 0, 1
Let l = 7 - 6. Let r = 5 - l. Factor -2*o**4 + 4*o**2 + 2 - r - 3*o**4 + 3*o**4.
-2*(o - 1)**2*(o + 1)**2
Let m(j) be the second derivative of -j**6/345 - 3*j**5/230 - j**4/69 + 22*j. Factor m(n).
-2*n**2*(n + 1)*(n + 2)/23
Let r = 7 - 47/7. Let h(w) be the first derivative of 8/35*w**5 - 11/14*w**4 - 1/7*w**2 - r*w + 6/7*w**3 - 1. Suppose h(n) = 0. What is n?
-1/4, 1
Suppose -15 = -4*m + m. Let r(o) = o**4 + o**3 - o + 1. Let j(h) = -4*h**4 - 5*h**3 - 2*h**2 + 5*h - 4. Let l(i) = m*r(i) + j(i). What is s in l(s) = 0?
-1, 1
Suppose 0 = -3*a - 0*a + 6. Factor 9*y + y**a + y**2 + 0*y**2 + 6 + y**2.
3*(y + 1)*(y + 2)
Find h, given that -1/5*h + 0 - 1/5*h**3 - 3/5*h**4 + 2/5*h**5 + 3/5*h**2 = 0.
-1, 0, 1/2, 1
Suppose 2*w - 16 = -2*w. Factor -7*j**