x) + 2*w(x). Solve m(y) = 0.
-1, 0
Let y(x) = 2*x**2 + 22*x + 63. Let d be y(-5). Factor 14/3*r**d - 2/3 + 1/3*r**5 - 2*r**4 - 16/3*r**2 + 3*r.
(r - 2)*(r - 1)**4/3
Let u = -43 - -43. Let m(o) be the third derivative of 1/60*o**5 + o**2 + 0 + 0*o**3 + 1/24*o**4 + u*o. Factor m(f).
f*(f + 1)
Suppose 5*p - 2*p + 6 = 0. Let d be p/(-3)*36/8. Factor -2*b**d + 3*b**2 - 4*b**2 - b**4 + 3 - 3.
-b**2*(b + 1)**2
Let l(y) be the second derivative of y**6/10 + 9*y**5/20 + 12*y. Suppose l(f) = 0. Calculate f.
-3, 0
Find h such that 2*h**3 - 24*h**2 + 17*h + 31*h + h**3 = 0.
0, 4
Determine n, given that 3/5*n**5 - 3/5*n**3 - 9/5*n**4 + 21/5*n**2 - 12/5 + 0*n = 0.
-1, 1, 2
Determine s so that -1/2*s**3 + 2/3*s + 0*s**2 - 1/6*s**4 + 0 = 0.
-2, 0, 1
Let q(a) be the first derivative of -a**6/21 + 4*a**5/35 + 3*a**4/14 - 8*a**3/21 - 4*a**2/7 - 3. What is x in q(x) = 0?
-1, 0, 2
Suppose 104 = 2*h + 20. Let p = h - 167/4. Factor p*u**2 + 1/4*u + 0.
u*(u + 1)/4
Let p(x) be the third derivative of 1/42*x**4 + 4*x**2 + 0 + 0*x + 1/210*x**5 + 1/21*x**3. Suppose p(s) = 0. What is s?
-1
Determine x so that 6*x - x - 3*x + 2*x**5 - 2*x**2 + 2*x**4 + 2*x - 6*x**3 = 0.
-2, -1, 0, 1
Let p be (2 - 8)/(3/9). Let z be p/12*(-16)/6. Determine o so that 1 + 2*o**2 + 2*o - z*o - o**2 = 0.
1
Suppose -2/7 + 2*x**2 - 12/7*x = 0. What is x?
-1/7, 1
Suppose 2*j + 10 - 18 = 0. Determine y so that -58/9*y**j - 8/3*y**5 + 4/9*y - 2/9*y**2 + 0 - 40/9*y**3 = 0.
-1, -2/3, 0, 1/4
Let x(u) = 5*u**3 + u + 6. Let z(i) = -9*i**3 - i**2 - 3*i - 11. Let w(k) = -7*x(k) - 4*z(k). Factor w(j).
(j + 1)**2*(j + 2)
Let -27/2*n + 63/2*n**2 + 9/2*n**4 + 0 + 51/2*n**3 = 0. What is n?
-3, 0, 1/3
Let y(k) be the third derivative of 1/24*k**4 + 0 + 2*k**2 + 7/360*k**6 - 1/9*k**3 + 0*k + 1/15*k**5. Factor y(c).
(c + 1)**2*(7*c - 2)/3
Let -3*j - 2*j**2 + 1 - 9 - 8*j + 3*j = 0. Calculate j.
-2
Let v(o) = -o**3 - o**2 - 6*o - 8. Let r be v(-3). Solve -17/4*f - 64*f**5 + r*f**2 + 1/4 + 128*f**4 - 88*f**3 = 0.
1/4, 1
Let d(r) be the first derivative of 2 + 2/3*r**2 + 0*r - 2*r**3. Factor d(l).
-2*l*(9*l - 2)/3
Let i(y) be the third derivative of -y**7/840 + y**6/160 - y**5/80 + y**4/96 + 7*y**2. Factor i(g).
-g*(g - 1)**3/4
Factor 15*m + 4 + 2*m**3 - 17*m + 2*m**4 + 4*m**2 - 10*m**2.
2*(m - 1)**2*(m + 1)*(m + 2)
Let r = 71 - 39. Suppose -5*m = t + 25, -r = t + 4*m - 12. Find v, given that 6/5*v**4 + 0*v + t*v**2 + 0 - 4/5*v**3 = 0.
0, 2/3
Suppose -3*p + 35 = 29. Find n, given that n**3 - 1/2 + 1/2*n**4 + 0*n**p - n = 0.
-1, 1
Suppose -3*t = -5*d + 22, 4*t - 8 - 1 = -d. Find p such that -2*p**3 - p**4 - 1 + t - p**4 = 0.
-1, 0
Let v(r) be the first derivative of -9 + 2/5*r**3 - 3/10*r**4 - 1/5*r**2 + 2/25*r**5 + 0*r. Factor v(a).
2*a*(a - 1)**3/5
Let m(k) = -k. Let y be m(3). Let p = y + 6. Let -4/3*j**2 - 2/3 - 5/3*j - 1/3*j**p = 0. Calculate j.
-2, -1
Suppose 5*x - 16 = x, h - x = 0. Suppose 7*n - b - 10 = 2*n, n + 17 = h*b. Solve -d**2 + 3*d + 2*d**2 - 1 + n = 0.
-2, -1
Let q(b) be the first derivative of 2*b**3/27 + 4*b**2/9 + 8*b/9 - 23. Factor q(o).
2*(o + 2)**2/9
Suppose -3*p + 41 = 4*g, -2*g = -p - 0*p + 17. Suppose -2*c - 3*j = -p, 3*c + 0*j = -j + 5. Let 4/9*b + 2/9*b**2 + c = 0. Calculate b.
-2, 0
Suppose -5*h = n + 8, -2*n + 8 = -5*h - 6. Factor -2*s - 4 - s**n + 4*s + 2*s.
-(s - 2)**2
Let j(d) be the second derivative of -2/15*d**5 - 3*d + 1/9*d**4 + 2/45*d**6 + 0 + 0*d**2 + 0*d**3. Factor j(b).
4*b**2*(b - 1)**2/3
Let s be 5/(-40)*-20 + 3/(-6). Determine r so that -8/11 + 38/11*r**s + 14/11*r**3 + 16/11*r = 0.
-2, -1, 2/7
Let v(l) be the third derivative of -l**6/480 + l**5/120 + l**4/96 - l**3/12 - 25*l**2. Determine k, given that v(k) = 0.
-1, 1, 2
Let y(g) = 68*g**3 + 266*g**2 + 240*g - 34. Let z(s) = 68*s**3 + 267*s**2 + 240*s - 35. Let v(c) = 3*y(c) - 2*z(c). Factor v(j).
4*(j + 2)**2*(17*j - 2)
Suppose 0*f - 2*f + 26 = 0. Let b = f - 8. Factor -4*w**3 - b*w**3 + w**2 - 4*w + 11*w**2.
-w*(3*w - 2)**2
Let i(g) be the first derivative of -4*g**3/9 + 49*g**2/6 - 4*g - 3. Factor i(r).
-(r - 12)*(4*r - 1)/3
Let y(q) be the second derivative of -q**7/280 - q**6/60 - q**5/40 + 2*q**3/3 + 7*q. Let v(w) be the second derivative of y(w). Factor v(k).
-3*k*(k + 1)**2
Factor -2/3*k**2 + 0 + 2/3*k.
-2*k*(k - 1)/3
Suppose 0 = 2*a + 43 - 53. Let s(w) be the third derivative of 0 - 1/480*w**6 - 2*w**2 + 1/840*w**7 + 1/96*w**4 + 0*w**3 + 0*w - 1/240*w**a. Factor s(r).
r*(r - 1)**2*(r + 1)/4
Let x(n) be the third derivative of 1/9*n**3 - 1/90*n**6 - 1/9*n**4 + 0*n + 1/18*n**5 - 3*n**2 + 0. Factor x(j).
-2*(j - 1)**2*(2*j - 1)/3
Let k(u) = 168*u**3 + u**2 - 1. Let d be k(-1). Let m = 844/5 + d. Let -14/5*w**2 - 6/5*w**4 + m*w + 0 + 16/5*w**3 = 0. Calculate w.
0, 2/3, 1
Let s(g) = g**2 + 9*g - 4. Let r(i) = 8*i - 24. Let a(f) = -1. Let z(k) = -20*a(k) + r(k). Let x(p) = -4*s(p) + 6*z(p). Solve x(m) = 0.
1, 2
Let x(v) = 5 + 6*v**2 + 13*v + 10*v + 12. Let y(b) = 9*b**2 + 34*b + 25. Let r(h) = 7*x(h) - 5*y(h). Factor r(p).
-3*(p + 1)*(p + 2)
Let z = 8208 - 4506194/549. Let p = 3280/3843 - z. Solve 2/7*a**3 + p*a - 6/7*a**2 - 2/7 = 0.
1
Let w be (-3)/36 - 1/(-6). Let r(o) be the third derivative of -1/3*o**3 - 1/120*o**5 - w*o**4 + 0*o - 2*o**2 + 0. Solve r(l) = 0.
-2
Let u(p) be the third derivative of p**2 + 3/20*p**5 + 0 + 0*p - 3/40*p**6 + 0*p**3 - 1/8*p**4 + 1/70*p**7. Find f such that u(f) = 0.
0, 1
Let q(r) = 7*r**2 + 2*r + 1. Let z(a) = 6*a**2 + 2*a + 1. Let u(y) = -5*q(y) + 6*z(y). What is j in u(j) = 0?
-1
Let l be (2/6)/((-2)/(-6)). Let f be 3 + (-2 + l - -3). Factor 0 + 0*t**4 - t**3 + 1/2*t + 1/2*t**f + 0*t**2.
t*(t - 1)**2*(t + 1)**2/2
Let u(b) = b**3 + 2*b + 14. Let o be u(0). Let a be (-8)/(-16) - 3/o. Factor -a*i**2 + 2/7*i + 0.
-2*i*(i - 1)/7
Let y be (-4)/(-10)*(1 - 6). Let l be -2 - y - (0 + -4). Factor -2/3*x**l + 0 + 0*x + 2/3*x**2 + 0*x**3.
-2*x**2*(x - 1)*(x + 1)/3
Suppose 10 = 2*w + 3*a, -3*a = 4*w + 2*a - 18. Solve j**2 + j**w - 4*j + 2*j = 0 for j.
0, 1
Let t = -23 + 28. Let p(m) be the first derivative of 1/20*m**t - 3 - 1/12*m**3 - 1/24*m**6 + 0*m**2 + 0*m + 1/16*m**4. Suppose p(f) = 0. What is f?
-1, 0, 1
Suppose -1172 - 3*t**3 + 2*t + 1172 + t**2 = 0. Calculate t.
-2/3, 0, 1
Let d be (-2)/(-8) - (-69)/12. Let t be ((-9)/d)/((-3)/6). Let u(p) = -p - 1. Let n(c) = -c**2 - 5*c - 3. Let l(a) = t*u(a) - n(a). Suppose l(m) = 0. What is m?
-2, 0
Suppose -2*j = 2*d - 12, 2*d - d = -5*j + 18. Factor 1/2*c**j - 1/2 - 1/2*c + 1/2*c**2.
(c - 1)*(c + 1)**2/2
Let g(z) be the second derivative of -121*z**4/15 + 44*z**3/15 - 2*z**2/5 - 35*z. Factor g(f).
-4*(11*f - 1)**2/5
Let d(j) be the third derivative of 1/90*j**6 + 0*j + 0*j**3 + 1/90*j**5 + 0 + j**2 + 0*j**4. Find a, given that d(a) = 0.
-1/2, 0
Let y(m) be the third derivative of -m**5/30 + m**4/2 - 3*m**3 - 2*m**2. Factor y(s).
-2*(s - 3)**2
Suppose -g + 6*g - 28 = -t, -5*g = -4*t - 13. Determine w, given that 6/5*w**2 + 0 - 3/5*w**t + 0*w = 0.
0, 2
Let g = 37 + -19. Suppose 4*v - 2*r = g, -r - 3 = 2. Determine q so that -2*q + 5*q - 3*q - 2 - v*q**4 + 4*q**2 = 0.
-1, 1
Let w(f) = 7*f**2 - 5*f - 15. Let u(b) = -8*b**2 + 4*b + 16. Let h(g) = -3*u(g) - 4*w(g). Factor h(q).
-4*(q - 3)*(q + 1)
Suppose -s - 4*s + 10 = 0. Factor -t - 4*t - 3*t + 3 + 3*t**2 + s*t.
3*(t - 1)**2
Let w be (-8)/(-9) + (-4)/(-12)*-2. Factor -w*x**2 + 0 + 0*x + 2/9*x**4 - 2/9*x**5 + 2/9*x**3.
-2*x**2*(x - 1)**2*(x + 1)/9
Let y = 7 - 3. Let a be 12/18*(2 - -1). Factor y - 5 + t**4 - a*t**2 + 2.
(t - 1)**2*(t + 1)**2
Let h(v) be the first derivative of 2*v**6/21 + 2*v**5/35 - 3*v**4/7 + 2*v**3/21 + 2*v**2/7 - 10. Find i, given that h(i) = 0.
-2, -1/2, 0, 1
Let o(m) be the first derivative of -m**3/9 + 4*m/3 - 6. Suppose o(z) = 0. What is z?
-2, 2
Let a(y) = 2*y**2 - 14*y + 8. Let z(g) = -5*g**2 + 43*g - 24. Let s(v) = 7*a(v) + 2*z(v). Factor s(f).
4*(f - 2)*(f - 1)
Factor 2*x**2 + 29*x**4 + 40*x**4 + 20*x**3 + 0*x**3 - 19*x**4.
2*x**2*(5*x + 1)**2
Let u(r) = 3*r**2 + 5*r - 5. Let p(b) = -15*b + 2. Let q(v) = -7*v + 1. Let s(f) = 6*p(f) - 13*q(f). Let z(a) = -5*s(a) + u(a). Suppose z(j) = 0. What is j?
0
Let l(f) be the second derivative of f**6/90 + f**5/30 - f**3/9 - f**2/6 - 11*f. Find u, given that l(u) = 0.
-1, 1
Factor 16*g + 3 - 2 - 9 - 6*g**2.
-2*(g - 2)*(3*g - 2)
Le