k).
3*k*(2*k - 1)**2
Let b(g) be the second derivative of g**6/3 - 7*g**5/10 - g**4/2 + 7*g**3/3 - 2*g**2 + 46*g. Factor b(z).
2*(z - 1)**2*(z + 1)*(5*z - 2)
Let w(u) be the first derivative of 0*u**2 + 2/27*u**3 + 0*u + 2. Let w(x) = 0. What is x?
0
Suppose -z - 13 = 4*g, -2*z = 10 - 0. Let s = g + 2. Find d, given that -4/5*d**3 + 0*d**2 + s + 0*d**4 + 2/5*d**5 + 2/5*d = 0.
-1, 0, 1
Let f(h) = h + 7. Let u be f(-9). Let b = u + 6. Solve 0*k**3 - 4/9*k**2 + 2/9*k - 2/9*k**5 + 4/9*k**b + 0 = 0.
-1, 0, 1
Let k(y) be the second derivative of -y**5/40 - y**4/8 + 12*y. Factor k(r).
-r**2*(r + 3)/2
Let i(u) be the third derivative of -u**6/180 + u**5/15 - u**4/3 + 8*u**3/9 - 33*u**2. Find z, given that i(z) = 0.
2
Suppose 3*j - 9 = -2*f + 6, -4*f - 3*j + 39 = 0. Suppose -f - 8 = -4*v. Factor -v*g**4 - 3*g**3 - 2*g**5 - g**2 + 5*g**4 + g**5 - 3*g**4.
-g**2*(g + 1)**3
Let v(r) = r + 6. Let o be v(0). Suppose 2*y - o + 2 = 0. Factor -j + y*j + j - 2*j**2.
-2*j*(j - 1)
Factor 7/11*r**2 + 0 + 1/11*r**4 + 3/11*r + 5/11*r**3.
r*(r + 1)**2*(r + 3)/11
Let w(g) = -4*g**3 - 11*g**2 + 135*g. Let o(u) = u**3 + 4*u**2 - 45*u. Let h(l) = -11*o(l) - 4*w(l). Factor h(n).
5*n*(n - 3)*(n + 3)
Let b(p) = -p**3 + 6*p**2 - 5*p + 3. Let q be b(4). Suppose q = 3*r + 2*r. What is a in -6*a**3 + 2 + 2*a**3 - r*a + 3*a**3 + 6*a = 0?
-1, 2
Let o(k) be the second derivative of -k**4/4 - 3*k**3/2 - 3*k**2 - 8*k. Determine h so that o(h) = 0.
-2, -1
Let p(a) = 16*a**4 - 29*a**3 + 27*a**2. Let s(o) = 5*o**4 - 10*o**3 + 9*o**2. Let i(u) = 2*p(u) - 7*s(u). Solve i(t) = 0.
0, 1, 3
Suppose 1 = 5*s - 4*s - 2*h, 0 = 2*s + 4*h - 18. Find l such that 0*l**2 + 0*l + 6/5*l**4 + 3/5*l**s + 0 + 3/5*l**3 = 0.
-1, 0
Let t(h) = 6*h**3 - 11*h**2 - 5*h + 9. Let b(o) = o**3 - o**2 + 1. Let y(w) = -3*b(w) + t(w). Suppose y(v) = 0. Calculate v.
-1, 2/3, 3
Let w(d) be the second derivative of 3*d + 1/27*d**4 + 0 - 1/45*d**6 + 2/45*d**5 + 1/9*d**2 - 4/27*d**3. Suppose w(m) = 0. What is m?
-1, 1/3, 1
Suppose -1/8*v**2 - 1/4 - 3/8*v = 0. Calculate v.
-2, -1
Find i such that 10*i**2 + 3*i + 15*i**3 - 5 - 5*i**2 - 2*i - 16*i**3 = 0.
-1, 1, 5
Let z(l) be the first derivative of -3*l**4/8 + l**3 + 34. Find h, given that z(h) = 0.
0, 2
Solve 2*d**2 + 3*d**3 + 0*d - 11*d**2 + 22 - 25 + 9*d = 0.
1
Suppose -5*i + 13 + 2 = 5*f, 2*i = 4*f + 12. Let w(l) be the third derivative of -1/60*l**5 - 1/24*l**i - 3*l**2 + 1/3*l**3 + 0 + 0*l. Factor w(a).
-(a - 1)*(a + 2)
Let q = 3277/2 + -1637. Suppose 0 - q*r**2 - 3/2*r**3 - 1/2*r**4 - 1/2*r = 0. Calculate r.
-1, 0
Suppose 0 = -2*k - 0*k + x + 196, -5*k + 5*x = -490. Let u = -3 - -10. Determine g so that -5*g**4 - g - 90*g**3 + k*g**5 - 51*g**4 + 56*g**2 - u*g = 0.
-1, 0, 2/7, 1
Let r(h) = h - 4. Let m be r(4). Let y(a) be the third derivative of 0 + m*a + 3/10*a**5 + a**2 - 7/12*a**4 - 2/3*a**3. Factor y(n).
2*(n - 1)*(9*n + 2)
Let m(i) = i**3 - 6*i**2 + i - 6. Let n be m(6). Factor 1/4*r**4 + 0*r**2 + r + n - 3/4*r**3.
r*(r - 2)**2*(r + 1)/4
Let y(i) be the second derivative of -i**7/315 + i**6/90 + i**5/90 - i**4/18 + 3*i**2/2 + 2*i. Let s(q) be the first derivative of y(q). Factor s(f).
-2*f*(f - 2)*(f - 1)*(f + 1)/3
Let g(u) = u**2 - 2*u. Let n be g(3). Let f(r) be the first derivative of 3*r - 3/4*r**4 + 17/4*r**n - 15/2*r**2 + 3. Solve f(k) = 0 for k.
1/4, 2
Find m, given that 6/7*m**3 + 0*m + 0 - 4/7*m**2 + 24/7*m**4 + 2*m**5 = 0.
-1, 0, 2/7
Let y be (0 + 0)/((-1)/(-1)). Let l(n) = n - 3. Let m be l(6). Suppose 0*u + 0*u**m + 2/9*u**5 + 0 - 2/9*u**4 + y*u**2 = 0. What is u?
0, 1
Let x(o) = -o**2 + 7*o - 8. Let k be x(6). Let w be (-13 - -3)/(2/k). Find r such that -32*r + 12*r**2 - 8 + 70*r**5 + 178*r**3 + 202*r**4 + 0 + w*r**2 = 0.
-1, -2/7, 2/5
Factor 3*q**4 + 10*q**3 + 11*q + 3 + 46/3*q**2 + 1/3*q**5.
(q + 1)**3*(q + 3)**2/3
Let z(c) be the first derivative of c**5 - 15*c**4/4 + 10*c**3/3 + 1. Factor z(o).
5*o**2*(o - 2)*(o - 1)
Let f(y) be the second derivative of y**8/3360 + y**7/630 + y**6/360 - y**4/12 - y. Let c(n) be the third derivative of f(n). Suppose c(o) = 0. What is o?
-1, 0
Suppose 14*d - 9*d - 45 = 0. Factor -3*c**3 - 4*c**3 + d*c**3.
2*c**3
Let b(o) be the third derivative of o**9/60480 - o**8/20160 - o**5/30 - 5*o**2. Let q(u) be the third derivative of b(u). Factor q(n).
n**2*(n - 1)
Let o(d) be the third derivative of d**8/448 - d**7/56 + 3*d**6/160 + 9*d**5/80 - 5*d**2 + 8. Let o(q) = 0. What is q?
-1, 0, 3
Let p(i) be the second derivative of 0 - 7*i + 0*i**2 + 2/5*i**6 + 2/21*i**7 + 0*i**3 + 1/3*i**4 + 3/5*i**5. Factor p(a).
4*a**2*(a + 1)**3
Let b(k) = k**2 + 2*k + 2. Let r(v) = -v**2 - 3*v - 3. Let p(l) = -2*b(l) - 3*r(l). Let z(m) = -2*m - 2. Let h(f) = 2*p(f) + 5*z(f). Factor h(y).
2*y**2
Let m(z) = 4*z**5 + 4*z**4 + 3*z**3 + 10*z**2 - 7*z + 7. Let j(c) = c**5 + c**4 + c**3 + 3*c**2 - 2*c + 2. Let s(h) = 7*j(h) - 2*m(h). Factor s(g).
-g**2*(g - 1)*(g + 1)**2
Let j(x) = 4*x - 3. Let r be j(2). Let f(h) = 2*h - 6. Let c be f(r). Determine y, given that 0*y**3 - 2*y**3 + y**5 + 2*y**c - 2*y**2 + y**5 = 0.
-1, 0, 1
Let i(o) be the third derivative of 11*o**6/960 - 13*o**5/480 - 5*o**4/48 + o**3/12 - o**2 + 3*o. Solve i(p) = 0 for p.
-1, 2/11, 2
Let x(w) be the third derivative of w**10/75600 + w**9/15120 - w**5/12 - 4*w**2. Let a(j) be the third derivative of x(j). Factor a(c).
2*c**3*(c + 2)
Let m(u) = -2*u - 2. Let q be m(-2). Suppose -2*d + 14 = 10. Find y such that 2*y**q - d*y**4 + 0 + 2/3*y**3 + 2/3*y - 4/3*y**5 = 0.
-1, -1/2, 0, 1
Let p(f) be the second derivative of -2*f**6/15 - 3*f**5/5 + 44*f. Factor p(x).
-4*x**3*(x + 3)
Suppose 270 = 5*t - 60. Factor 82*i + t*i**2 - 1029*i**3 + 228*i**2 - 21 - 3 + 2*i.
-3*(7*i - 2)**2*(7*i + 2)
Let b(f) be the second derivative of f**6/60 + f**5/10 + f**4/4 + f**3/3 + f**2 - 3*f. Let s(d) be the first derivative of b(d). Factor s(l).
2*(l + 1)**3
Solve 41*o**2 + 35*o**2 + 13 - 73*o**2 + 15*o - 31 = 0 for o.
-6, 1
Factor 3/2*w**4 + 13/6*w**2 - 1/3*w - 4*w**3 + 0.
w*(w - 2)*(3*w - 1)**2/6
Suppose 4*p - 2 - 10 = 0. Suppose p*m - h = 0, 4*h + 0*h = -3*m. Let 0*i + 0 - 1/4*i**5 + 1/4*i**3 + m*i**2 + 0*i**4 = 0. Calculate i.
-1, 0, 1
Let l(c) = c**2 - 2*c + 3. Let w be l(2). Let k(v) be the first derivative of 1/2*v**2 + 2*v - 3 - 1/3*v**w. Factor k(x).
-(x - 2)*(x + 1)
Let n = 14561/4155 - -8/277. Let v = n + -16/5. Let b**2 - 4/3 + 0*b + v*b**3 = 0. What is b?
-2, 1
Let v(s) = -3*s**2 + 7*s + 6. Let m be v(3). Solve m + 1/3*h**2 - 1/3*h = 0 for h.
0, 1
Solve -16/7*k + 36/7*k**2 + 0 + 10/7*k**3 = 0.
-4, 0, 2/5
Let m(b) be the third derivative of b**5/15 + b**4/3 + b**3 - b**2. Let t(d) = 1. Let p(f) = -m(f) + 2*t(f). Factor p(w).
-4*(w + 1)**2
Let x(q) be the second derivative of q**7/14 + q**6/40 - 3*q**5/10 - q**4/8 + q**3/2 + 3*q**2/8 - 15*q. Let x(a) = 0. Calculate a.
-1, -1/4, 1
Let s(j) be the first derivative of 2*j**5/25 + j**4/2 + 6*j**3/5 + 7*j**2/5 + 4*j/5 + 14. Factor s(g).
2*(g + 1)**3*(g + 2)/5
Let z(y) be the third derivative of -1/10*y**5 + 4*y**2 + 0*y**4 + 0*y**3 + 0*y + 0 + 6/35*y**7 + 1/16*y**8 + 3/40*y**6. Solve z(d) = 0.
-1, 0, 2/7
What is g in 1 - 7*g + 11 + 3*g**2 - 5*g = 0?
2
Suppose -3*d = -d - 22. Factor -2*l**3 + 11*l - d*l.
-2*l**3
Suppose -5*y + 8*y = 9. Suppose 0 = t + y*z + 4, -z - 1 + 8 = 2*t. Factor -t*m**2 + 10*m**4 + 19*m**2 - 5*m**5 - 18*m**3 + 2*m - 6*m + 3*m**5.
-2*m*(m - 2)*(m - 1)**3
Let r(z) be the first derivative of 32/3*z**3 - 1 - 8*z**2 - 36/5*z**5 + 3*z**4 + 0*z. Find p such that r(p) = 0.
-1, 0, 2/3
Let s be ((20/(-15))/((-4)/6))/2. Find w, given that -1/2*w**3 + 3/2*w + 0*w**2 - s = 0.
-2, 1
Let y = 10 + -8. Let h = -45 - -137/3. Factor h*r - 1/3 + r**y.
(r + 1)*(3*r - 1)/3
Let m be (9/6)/3*6. Factor -4*j**2 + m*j**3 + 5*j**4 - 9*j**4 - 11*j**3.
-4*j**2*(j + 1)**2
Let f be (0 + -1)*14/(-28). Let l(v) be the first derivative of f*v**4 + 1 - v**2 + 0*v + 0*v**3. Factor l(g).
2*g*(g - 1)*(g + 1)
Let s(t) = -3*t**3 + 3*t. Suppose -26 = 5*z + 9. Let u(f) = -3*f**3 + f**2 + 3*f - 1. Let y(r) = z*s(r) + 6*u(r). Determine l, given that y(l) = 0.
-2, -1, 1
Let o(n) = -4*n**3 - 4*n**2 + 7*n + 1. Let a(b) = -16*b**3 - 15*b**2 + 27*b + 4. Let w(q) = -6*a(q) + 22*o(q). Factor w(v).
2*(v - 1)*(v + 1)*(4*v + 1)
Find z such that -80*z**2 - 5*z**4 - 5*z**3 + 30*z