1/20*a**5 + 0*a**3 - 1/8*a**4 + 0 - 6*a**2 + 0*a. Factor m(k).
3*k*(k - 1)
Let h(x) be the first derivative of 1/2*x**3 - 3/2*x - 3/4*x**2 + 8 + 3/8*x**4. Let h(w) = 0. What is w?
-1, 1
Let r(x) be the first derivative of -x**4/8 + 2*x**3 - 12*x**2 + 32*x + 1. What is v in r(v) = 0?
4
Let k(w) = w**3 + 7*w**2 - 9*w - 6. Let v be k(-8). Factor -i**3 - 3*i**v - i**3 + 5*i**3.
3*i**2*(i - 1)
Let u(h) be the third derivative of -h**6/30 - h**5/15 + h**4/3 - 7*h**2. Factor u(z).
-4*z*(z - 1)*(z + 2)
Let o(x) be the third derivative of x**5/60 + x**4/24 - x**3/6 - x**2. Let n(c) = -11*c**2 - 13*c + 4. Let f(r) = -n(r) - 6*o(r). Factor f(u).
(u + 1)*(5*u + 2)
Let r = -199 - -997/5. Let 2/5*b - 4/5 + r*b**2 = 0. Calculate b.
-2, 1
Let p(m) be the second derivative of m**4/42 - m**2/7 + 6*m. Let p(c) = 0. What is c?
-1, 1
Let f be (2/(-5))/((-2)/10). Factor -f*r - 10*r**3 + 4*r**4 - r**2 + 12*r**3 - 3*r**2 - 2*r**2 + 2.
2*(r - 1)*(r + 1)**2*(2*r - 1)
Determine u so that -u + 3/4*u**2 + 1/4*u**4 - 1 + u**3 = 0.
-2, -1, 1
Let b be ((-6)/36)/((-1)/9). Let p(t) be the first derivative of b*t**2 - 2*t**3 + 3*t + 2. Factor p(r).
-3*(r - 1)*(2*r + 1)
Let h be 36/(-21)*(-14)/4. Factor 15*s - 20*s**2 + 4*s**2 - 10*s**2 + h + 5*s**2.
-3*(s - 1)*(7*s + 2)
Factor -9 - 3*c**4 + 99*c**2 - 30*c - 80*c**2 - 55*c**2 - 18*c**3.
-3*(c + 1)**3*(c + 3)
Let b(n) be the second derivative of -n**5/70 - 2*n**4/63 + 5*n**3/63 + 2*n**2/21 - 9*n. Solve b(m) = 0.
-2, -1/3, 1
Suppose -8*n + 10 = -3*n. Determine i, given that 2*i + 3*i**2 + 0*i**n + 2*i**2 - 1 - 6*i**2 = 0.
1
Let k(m) be the first derivative of m**5/40 + 5*m**4/48 + m**3/6 + m**2/8 - m - 3. Let i(g) be the first derivative of k(g). Determine w, given that i(w) = 0.
-1, -1/2
Suppose -6 - 8*p**2 + 6 + 22*p**3 - 2*p**3 = 0. What is p?
0, 2/5
Let v(r) be the third derivative of r**5/270 - r**4/108 - 4*r**2. Factor v(y).
2*y*(y - 1)/9
Let u(h) be the second derivative of h**5/150 - h**4/60 - 2*h**3/15 + 2*h**2 - 3*h. Let t(p) be the first derivative of u(p). Factor t(b).
2*(b - 2)*(b + 1)/5
Factor 0 - 6/5*w - 15*w**3 - 9*w**2.
-3*w*(5*w + 1)*(5*w + 2)/5
Let i(y) = -y**2 - 9*y + 2. Let m be i(-9). Suppose -58*f - 2*f**m - f**2 + 61*f = 0. Calculate f.
0, 1
Let d(t) = -2*t**2 - 7*t + 3. Let v be d(9). Let g = v + 1558/7. Factor 0*i - g*i**5 - 2/7*i**2 + 6/7*i**4 + 0*i**3 + 0.
-2*i**2*(i - 1)**2*(2*i + 1)/7
Let x(i) be the first derivative of -1/15*i**6 - 1/2*i**4 + 0*i**2 - 8/25*i**5 - 4/15*i**3 + 0*i - 3. Factor x(p).
-2*p**2*(p + 1)**2*(p + 2)/5
Suppose -g = -2*g + 2. Find n, given that -8 + 64*n - 190*n**4 - 250*n**g + 24*n**5 + 104*n**3 + 174*n**3 + 56*n**2 + 26*n**5 = 0.
2/5, 1
Let -15 - 10*t - 35*t**2 - 38*t**2 + 78*t**2 = 0. Calculate t.
-1, 3
Let n be (-85)/(-25) - 10/75*3. Determine f, given that 0*f - 11/2*f**4 + f**n - 6*f**5 + 0 + 1/2*f**2 = 0.
-1, -1/4, 0, 1/3
Let u(g) be the third derivative of g**5/150 - g**4/60 - 3*g**2. Factor u(r).
2*r*(r - 1)/5
Solve -65*p**4 + 62*p**4 + 6*p**3 - 3*p**3 = 0.
0, 1
Let b(u) = u**3 + 4*u**2 - 3*u + 6. Let m be b(-5). Let j be -1 + 3 - (m + 4). Factor -j*g**5 - g**3 - g**3 - 4*g**4 + 0*g**4.
-2*g**3*(g + 1)**2
Let w be ((-3)/3)/((-2)/(-12)). Let j = w + 11. Find p such that -3*p**3 - p**j + 3*p**3 - p**3 + 2*p**4 = 0.
0, 1
Let b(s) be the third derivative of -s**6/1080 + s**5/360 - s**3/6 - 3*s**2. Let t(o) be the first derivative of b(o). Factor t(a).
-a*(a - 1)/3
Let t = 67/2 - 33. Let l be (-1)/(-1) + -1*(-6)/(-8). Factor 0 - t*w**3 - l*w**4 + 0*w - 1/4*w**2.
-w**2*(w + 1)**2/4
Suppose 4*p + 18 = 10*p. Let t(l) be the first derivative of -1/4*l**4 - 1/5*l**5 + 0*l + 0*l**2 + 1/3*l**3 + 1/6*l**6 - p. Let t(m) = 0. Calculate m.
-1, 0, 1
Let r(a) = a**2 - 29*a. Let w(u) = -2*u**2 + 88*u. Let f(t) = 17*r(t) + 6*w(t). Factor f(n).
5*n*(n + 7)
Let q = 3/2 - -3/4. What is g in 9/4*g**2 - q + 3/4*g**3 - 3/4*g = 0?
-3, -1, 1
Let p = -47 + 71. Let y(m) = 7*m + 42. Let v be y(-6). Factor 75/2*k**5 + 15/2*k**4 + 0*k + 6*k**2 - p*k**3 + v.
3*k**2*(k + 1)*(5*k - 2)**2/2
Let d(i) be the third derivative of -i**5/15 + i**4/2 + 8*i**3/3 - 11*i**2. Suppose d(s) = 0. Calculate s.
-1, 4
Suppose -2*i + 92 = 4*b - 0*i, 0 = 4*i - 8. Let q(k) = k**2 - k + 1. Let n(v) = v**3 - 8*v**2 + 14*v - 10. Let p(w) = b*q(w) + 2*n(w). Factor p(a).
2*(a + 1)**3
Let w(j) = j**2 - j + 1. Suppose 2*q = 2*t + 8, -2*q - 2*t = t + 17. Suppose -s - 3 = 3. Let b(a) = -7*a**2 + 6*a - 5. Let k(g) = q*b(g) + s*w(g). Factor k(d).
(d - 1)*(d + 1)
Suppose o - k = 4*k + 25, -3*o = -3*k - 15. Suppose 2*v + v - 6 = o. Factor -6*a + 3*a**2 + 4*a**3 - a**3 + 0*a**v.
3*a*(a - 1)*(a + 2)
Let v(w) be the third derivative of w**8/1344 - w**7/840 - w**6/240 + w**5/120 + w**4/96 - w**3/24 + 9*w**2. Let v(l) = 0. What is l?
-1, 1
Let k(l) = -l**5 + l**3 - l - 1. Let w(c) = -3*c**5 - 2*c**4 - c**3 + 10*c**2 - 9*c - 5. Let f(t) = -10*k(t) + 2*w(t). Factor f(a).
4*a*(a - 1)**3*(a + 2)
Suppose -8*h + 23 + 1 = 0. Factor 0 - 4/7*p**h + 2/7*p**4 + 2/7*p**2 + 0*p.
2*p**2*(p - 1)**2/7
Let f(w) be the first derivative of w**3/2 - 9*w**2/4 + 3*w + 7. Suppose f(r) = 0. What is r?
1, 2
Let u(p) = 3*p**3 - p**2 - 11*p - 2. Let f(z) = z**3 - z**2 - 5*z - 1. Let a(k) = -10*f(k) + 4*u(k). Factor a(b).
2*(b + 1)**3
Let h = -56 - -56. Let k(g) be the third derivative of 0*g**7 + 0 + 0*g**3 + h*g**5 - 1/420*g**6 + 0*g**4 + 0*g + 1/1176*g**8 + 3*g**2. Factor k(m).
2*m**3*(m - 1)*(m + 1)/7
Let 0 + 0*b**2 + 1/2*b - 1/2*b**3 = 0. Calculate b.
-1, 0, 1
Let o = 26 - 21. Let l(b) be the first derivative of -1/9*b**3 + 0*b**2 - 1/6*b**4 + 2 - 1/15*b**o + 0*b. Factor l(g).
-g**2*(g + 1)**2/3
Let x(i) = -i**2 - 19*i - 31. Let h be x(-17). Factor h*t + 12/5*t**2 + 3/5*t**3 + 6/5.
3*(t + 1)**2*(t + 2)/5
Let u(v) = 10*v**2 + 7*v - 10. Let z(p) = -p + 2*p + 7 - 6*p - 7*p**2. Let f(k) = -5*u(k) - 7*z(k). Factor f(y).
-(y - 1)*(y + 1)
Let a(n) be the second derivative of n**4/12 - 7*n**3/6 + 3*n**2 - 3*n. Let c be a(6). Solve 5/3*t**4 + c + 2/3*t - 2/3*t**3 - 5/3*t**2 = 0 for t.
-1, 0, 2/5, 1
Let b = 310 + -1547/5. Factor 2/5*q**2 + 0 - b*q**3 + 1/5*q**4 + 0*q.
q**2*(q - 2)*(q - 1)/5
Let t(l) = -l**3 + 3*l**2 + 5*l - 3. Let b be t(4). Let i = b - -1. Factor -i*j**3 + 3*j**3 + 2*j**2 + 0*j**3 - j**2.
j**2*(j + 1)
Let v(n) be the second derivative of -1/4*n**4 + 1/3*n**3 + 0*n**2 + 1/30*n**6 + 0*n**5 - 4*n + 0. Determine j, given that v(j) = 0.
-2, 0, 1
Factor 4/9 - 2/9*f**2 + 2/9*f.
-2*(f - 2)*(f + 1)/9
Let z(b) be the first derivative of -27*b**4/2 + 26*b**3 - 40*b**2/3 + 8*b/3 - 5. Factor z(m).
-2*(m - 1)*(9*m - 2)**2/3
Suppose 9 = -0*u + 3*u - 5*x, -u + 3 = x. Let y(c) be the second derivative of 1/4*c**4 + 1/2*c**2 - 1/20*c**5 - 1/2*c**u + 0 + 4*c. Solve y(d) = 0.
1
Let s(m) = 2*m**3 + 2*m**2 - 2*m + 1. Let n be s(1). Find o such that 2 + 6*o + 3*o**n + 3*o**3 - 4*o**3 - 10*o**2 + 16 = 0.
-1, 3
Factor 212/13*s**2 + 50/13 - 2/13*s**5 - 116/13*s**3 - 170/13*s + 2*s**4.
-2*(s - 5)**2*(s - 1)**3/13
Let r(j) be the first derivative of -j**6/180 + j**5/60 + 2*j**3/3 + 2. Let w(b) be the third derivative of r(b). Let w(g) = 0. What is g?
0, 1
Let p(d) = -d**2 + d. Let l(y) = 3*y**2 + 3*y. Let x(r) = -l(r) - p(r). Factor x(u).
-2*u*(u + 2)
Let q(y) be the second derivative of -y**8/10080 - y**7/2520 - y**6/2160 + y**3/2 - 6*y. Let d(m) be the second derivative of q(m). Find a, given that d(a) = 0.
-1, 0
Suppose -5*o = r, -14*r = -12*r + 4*o. What is k in r + 0*k**2 - 2/7*k + 0*k**4 - 2/7*k**5 + 4/7*k**3 = 0?
-1, 0, 1
Let m(s) be the third derivative of -s**7/105 - s**6/120 + s**5/12 - s**4/12 - 12*s**2. Solve m(w) = 0.
-2, 0, 1/2, 1
Let v(u) be the second derivative of -1/4*u**2 + 2*u + 1/4*u**3 + 0 - 1/12*u**4. Factor v(k).
-(k - 1)*(2*k - 1)/2
Factor -7/8 + 1/8*i**4 + i - i**3 + 3/4*i**2.
(i - 7)*(i - 1)**2*(i + 1)/8
Let x(u) be the second derivative of 0*u**3 + 0 - 1/231*u**7 - 1/165*u**6 + 0*u**2 + 0*u**4 + 2*u + 0*u**5. Factor x(y).
-2*y**4*(y + 1)/11
Factor -122*q**2 + 161*q**2 - 3*q**3 - 2*q**3 - 35 - 84*q**2 - 75*q.
-5*(q + 1)**2*(q + 7)
Let o be -1 - 55/(-10) - 3. Suppose -3/2*t**4 + 9/4*t**5 - 1/4*t + o*t**2 - 2*t**3 + 0 = 0. Calculate t.
-1, 0, 1/3, 1
Determine a, given that 2/9*a + 2/9*a**3 - 4/9*a**2 + 0 = 0.
0, 1
Let a = 601737/56 - 10746. Let y = -1/8 - 