*5 + 0. Factor n(r).
-2*r**2/5
Find o, given that 68*o**3 + 62*o**3 - 26244 + 11664*o + 14*o**3 - 6*o**4 - 1944*o**2 + 2*o**4 = 0.
9
Let d(o) = o**3 - 3*o**2 + 2*o - 3. Let a be d(3). Let v(w) be the first derivative of -2/5*w + 1 - 2/5*w**2 - 2/15*w**a. Factor v(r).
-2*(r + 1)**2/5
Let x(c) be the first derivative of c**6/120 - c**5/60 - c**4/12 - c**2 - 3. Let o(n) be the second derivative of x(n). Factor o(b).
b*(b - 2)*(b + 1)
Let m(r) be the second derivative of -r**5/20 - r**4 - 8*r**3 - 32*r**2 - 7*r. Find z, given that m(z) = 0.
-4
Let v(z) be the first derivative of -5*z**6/6 + 9*z**5 - 75*z**4/2 + 230*z**3/3 - 165*z**2/2 + 45*z + 2. Find i such that v(i) = 0.
1, 3
Factor -58*g + 36*g**4 - 108*g**2 + 7 + 9 - 8*g**3 + 10*g.
4*(g - 2)*(g + 1)**2*(9*g - 2)
Let s(m) = -2*m**4 - 6*m**3 - 8*m**2 + 4*m. Let a(d) = -3*d**4 - 7*d**3 - 9*d**2 + 5*d. Let z(n) = -4*a(n) + 5*s(n). Factor z(x).
2*x**2*(x - 2)*(x + 1)
Let y(m) = 2*m**4 + 3*m**3 - 3*m**2 - 7*m - 3. Let x(z) = -3*z**4 - 5*z**3 + 6*z**2 + 15*z + 7. Let t(n) = -2*x(n) - 5*y(n). Factor t(a).
-(a - 1)*(a + 1)**2*(4*a + 1)
Let g(u) = -15*u**2 - 15*u + 9. Let v(w) be the third derivative of -7*w**5/60 - 7*w**4/24 + 2*w**3/3 + 4*w**2. Let t(x) = -4*g(x) + 9*v(x). Factor t(k).
-3*k*(k + 1)
Let z(s) be the third derivative of s**5/390 + s**4/156 - 2*s**3/39 + 5*s**2. Factor z(v).
2*(v - 1)*(v + 2)/13
Let -3/2*c**3 + 3/2*c**2 + 3/2*c - 3/2 = 0. What is c?
-1, 1
Let d(s) be the second derivative of s**9/6048 + s**8/1920 - s**7/630 - s**6/360 - s**4/12 + s. Let x(k) be the third derivative of d(k). Factor x(n).
n*(n - 1)*(n + 2)*(5*n + 2)/2
Let u(j) = -j - 7. Let d be u(-9). Let p be (d/44)/(16/64). Factor -2/11*o**5 - 2/11*o**2 + 0 + p*o**4 + 2/11*o**3 + 0*o.
-2*o**2*(o - 1)**2*(o + 1)/11
Let z(c) = -c**4 + 3*c**3 - c**2 + c + 4. Let m(k) = -6*k**4 + 16*k**3 - 4*k**2 + 6*k + 21. Let d(w) = -6*m(w) + 33*z(w). Factor d(p).
3*(p - 1)**2*(p + 1)*(p + 2)
Let u(r) be the second derivative of r**7/315 + r**6/180 - r**5/120 - r**4/72 + r**3/36 + 7*r**2/2 - 3*r. Let z(x) be the first derivative of u(x). Factor z(p).
(p + 1)**2*(2*p - 1)**2/6
Let t(f) = -f - 1. Let k(j) = j**3 - j. Let w(g) = k(g) + 6*t(g). Find b, given that w(b) = 0.
-2, -1, 3
Let v(t) be the second derivative of -2*t**7/21 + t**5/5 + 6*t. Let v(w) = 0. Calculate w.
-1, 0, 1
Let 1/5*p**4 - 2/5*p**2 + 0*p + 0*p**3 + 1/5 = 0. What is p?
-1, 1
Let s = -43/6 + 15/2. Let o = -3/25 + 34/75. Factor s*r**3 - 1/3*r**5 + o*r**4 + 0 - 1/3*r**2 + 0*r.
-r**2*(r - 1)**2*(r + 1)/3
Suppose v - 2 = -u, -4*v + v - 9 = 0. Suppose -2/5*q**u + 6/5*q**4 - 6/5*q**3 + 0*q + 0 + 2/5*q**2 = 0. Calculate q.
0, 1
Let h(v) = -15*v - 6 + 16*v + 3. Let m be h(6). Find k such that 0*k**m - 4/5*k**2 - 2/5*k**5 + 0 + 2/5*k + 4/5*k**4 = 0.
-1, 0, 1
Let m(b) = b**2 + 16*b + 18. Let f be m(-15). Let z be (-10)/(-75)*(f + 7). Factor -2/3*x**2 - z + 2*x.
-2*(x - 2)*(x - 1)/3
Let a = 45094/45 - 1002. Let t(w) be the second derivative of -13/24*w**4 - w + 17/36*w**3 + 1/15*w**5 - 1/6*w**2 + 0 + a*w**6. Suppose t(k) = 0. What is k?
-2, 1/4, 1
Let c(a) be the second derivative of -a**6/105 - 3*a**5/35 - a**4/42 + 8*a**3/7 - 16*a**2/7 + 10*a. Solve c(m) = 0.
-4, 1
Let v(g) be the first derivative of -5*g**4/4 - 5*g**3 + 5*g**2/2 + 15*g + 26. Factor v(x).
-5*(x - 1)*(x + 1)*(x + 3)
Let j = 8 - -2. Factor 6*z**3 - 2 + j*z**2 + 2*z**3 + 8*z - 22*z**2 - 2*z**4.
-2*(z - 1)**4
Let d be 172/360 - 4/10. Let r(p) be the second derivative of 11/27*p**3 - 8/27*p**4 + d*p**5 + 0 - 3*p - 2/9*p**2. Factor r(g).
2*(g - 1)**2*(7*g - 2)/9
Suppose -5*q = -5*i, -2*i - i = 4*q - 21. Suppose 3*k - 3 + 0 = 0, -q*p = k - 10. Factor 0*h + 3/4*h**3 + 0 + 0*h**2 - p*h**5 - 9/4*h**4.
-3*h**3*(h + 1)*(4*h - 1)/4
Let a = -20 + 23. Determine f, given that 14*f**3 - 2*f**4 + 5*f**2 - f**4 + a*f - 12*f**5 - 2*f**4 - 5*f = 0.
-1, -2/3, 0, 1/4, 1
Let r = 3 + -2. Let v = r - -3. Factor v*m - 2 + 2*m**2 - 1 + 5.
2*(m + 1)**2
Suppose -22 - 41 = -3*a. Let r be 1/63 - (-9)/a. Factor r - 2/9*c**2 + 2/9*c.
-2*(c - 2)*(c + 1)/9
Let j(q) be the second derivative of q**6/30 - q**5/20 - 5*q**4/6 - 4*q**3/3 - 7*q - 1. Factor j(k).
k*(k - 4)*(k + 1)*(k + 2)
Let y = -3/502 - -517/2510. Factor -y*a**2 + 1/5*a + 0.
-a*(a - 1)/5
Let n(p) be the first derivative of -p**8/280 + p**7/42 - 7*p**6/135 + 2*p**5/45 - 2*p**3 - 6. Let f(j) be the third derivative of n(j). Factor f(x).
-2*x*(x - 2)*(3*x - 2)**2/3
Let m be (1 - (-27)/(-24))/(45/(-120)). Factor -1/3 + 10/3*w**3 - 5/3*w**4 + m*w**5 + 5/3*w - 10/3*w**2.
(w - 1)**5/3
Suppose 0 = 4*b - 7*b - 6. Let t(p) = -4*p**2 - 2*p - 2. Let v(z) = -3*z**2 - 2*z**2 - 3*z + z - 3. Let x(w) = b*v(w) + 3*t(w). Solve x(i) = 0 for i.
-1, 0
Let 11/6*q + 7/6*q**2 + 5/6 + 1/6*q**3 = 0. Calculate q.
-5, -1
Let s = 5 - 2. Factor -9*i**2 + 0*i**s + 3*i - 3*i**3 - 9*i.
-3*i*(i + 1)*(i + 2)
Let x = 17 - 14. Suppose -23*b**x - 57*b**3 + 12*b**2 + 4*b - 170*b**4 - 22*b**4 + 256*b**5 = 0. Calculate b.
-1/4, 0, 1/4, 1
Find w such that 48*w**2 + 15*w**3 + 9 + 23 + 3*w**3 - 88*w = 0.
-4, 2/3
Let m(f) = f**2 - f - 1. Let w(z) = z**3 + 4*z**2 - 6*z - 4. Let b = 0 + 2. Suppose -b*u + u = 2. Let y(j) = u*w(j) + 10*m(j). Suppose y(l) = 0. What is l?
-1, 1
Let b(f) be the first derivative of 4*f**4/9 + 44*f**3/27 + 10*f**2/9 - 8*f/9 + 8. Suppose b(s) = 0. Calculate s.
-2, -1, 1/4
Let q = 6 + -4. Suppose -7*y + 15 = -q*y. Factor 0 - 1/2*i - 6*i**3 + 5*i**4 - 3/2*i**5 + y*i**2.
-i*(i - 1)**3*(3*i - 1)/2
Let u(c) be the second derivative of 1/12*c**4 - 2*c + c**2 - 1/2*c**3 + 0. Factor u(d).
(d - 2)*(d - 1)
Let c(i) be the third derivative of i**8/168 - 2*i**7/105 + i**5/15 - i**4/12 - i**2. Solve c(w) = 0 for w.
-1, 0, 1
Let q(g) = 6*g - 5*g - 6*g. Let m be q(-1). Factor 0*u + 0*u**2 + 1/2*u**m + 1/2*u**3 + 0 - u**4.
u**3*(u - 1)**2/2
Let q be (4 + 11/(-2))*8/(-30). Solve -4/5*f - 2/5*f**2 - q = 0.
-1
Let g(v) be the second derivative of 21*v**5/10 + 67*v**4/18 - 4*v**2/3 - 17*v. Solve g(r) = 0 for r.
-1, -2/7, 2/9
Let w be 2 + 17 + 1 - 1. Factor 27*k**4 + 71*k**2 - w*k + 40*k**2 + 90*k**3 + 79*k + 12.
3*(k + 1)**2*(3*k + 2)**2
Let v(p) = p**3 - 5*p**2 + 3*p + 2. Let w be v(4). Let z = w - -4. Factor -2/7 - 4/7*r**z - 6/7*r + 2/7*r**5 + 6/7*r**4 + 4/7*r**3.
2*(r - 1)*(r + 1)**4/7
Let x = 22 - 20. Let y(j) be the second derivative of -1/9*j**3 + 2/9*j**x + 0*j**4 + 2*j + 0 + 1/90*j**5. Factor y(q).
2*(q - 1)**2*(q + 2)/9
Let n(f) be the third derivative of -1/60*f**6 - 1/3*f**3 + 1/30*f**5 + 0*f - 2*f**2 + 0 + 1/12*f**4. Determine h so that n(h) = 0.
-1, 1
Let f(y) be the third derivative of y**8/504 - 6*y**2. Find i, given that f(i) = 0.
0
Let 24*n**2 - 5*n - 15*n**3 - 16*n + 9*n + 3*n**4 = 0. Calculate n.
0, 1, 2
Let u(q) = 5*q**3 - 20*q**2 - 15*q + 15. Let y(b) = -b**2 - b + 1. Let r(h) = -u(h) + 15*y(h). Let r(f) = 0. What is f?
0, 1
Let m(c) be the second derivative of c**6/70 - c**4/28 - 4*c. Suppose m(w) = 0. Calculate w.
-1, 0, 1
Suppose -5*k + c = -8, 0 = 2*c - 4. Let g(w) = w**3 + w**2 + 2. Let d be g(0). Factor -d*t**2 + 1 + 5*t**k - 13*t + 4*t + 5.
3*(t - 2)*(t - 1)
Suppose 0 = 2*i + 5*q - 1 + 12, 22 = i - 3*q. Suppose -4*b = -4*j, 0 = -3*b - 1 + i. Find a such that 1/2*a**3 - 1/2*a**4 + 0 + 0*a + 0*a**j = 0.
0, 1
Let b(o) = o**2 - 6*o - 9. Let n be ((-24)/(-30))/((-4)/30). Suppose -10 - 4 = -2*m. Let p(u) = u**2 - 5*u - 8. Let w(q) = m*p(q) + n*b(q). Factor w(t).
(t - 1)*(t + 2)
Let w be (-2)/10 + 34/(-140)*-2. Let 4/7*y**2 - 4/7 + w*y - 2/7*y**3 = 0. What is y?
-1, 1, 2
Let h(g) = -g**3 - 2*g**2 + 7*g. Let f be h(3). Let y = 26 + f. Factor -9/2*z**y + 3/2*z**3 + 3*z + 0.
3*z*(z - 2)*(z - 1)/2
Let n(f) = 3*f**4 + 14*f**3 + 13*f**2 + 6*f. Let s(i) = -6*i**4 - 29*i**3 - 25*i**2 - 12*i. Let z(d) = 5*n(d) + 2*s(d). Suppose z(k) = 0. Calculate k.
-2, -1, 0
Let i(v) be the first derivative of 3*v**5/10 - 3*v**3/2 - 3*v**2/2 - 6. Find n, given that i(n) = 0.
-1, 0, 2
Let v be ((-36)/(-24))/(-2 - 39/(-19)). Determine q so that 0*q + v*q**2 - 9/2*q**4 - 6 - 15/2*q**5 + 51/2*q**3 = 0.
-1, 2/5, 2
Let b(z) be the first derivative of -z**3/3 - z**2/2 + z + 3. Let w(y) = -2*y**2 - 3*y + 2. Let p(m) = 3*b(m) - w(m). Factor p(s).
-(s - 1)*(s + 1)
Solve 3/8*l**5 - 3/4*l**4 + 0*l**3 + 0 - 3/8*l + 3/4*l**2 = 0.
-1, 0, 1
