- 1/30*n**5 + 0 + 1/45*n**6 - 3*n. Factor y(b).
2*b*(b - 1)**2*(b + 1)/3
Let q be 1*(0 - -1)*-7. Let m be (-3)/q - 54/(-21). Factor j**m + 0*j**2 + 1/2*j**4 - j - 1/2.
(j - 1)*(j + 1)**3/2
Let x(w) be the third derivative of -1/6*w**4 + 4/15*w**6 - 10*w**2 + 0*w - 1/6*w**5 - 3/35*w**7 + 0*w**3 + 0. Let x(b) = 0. Calculate b.
-2/9, 0, 1
Let f be (-7)/(-3) + (-8)/(-12). Suppose 2*a - 3*n - 15 = 3*a, -f*a + 20 = -4*n. Factor 0*i**2 + a*i**3 + i - 2*i**2 + i**3.
i*(i - 1)**2
Factor -2 - q + 6 + 3*q - 2*q**2.
-2*(q - 2)*(q + 1)
Let k(r) be the third derivative of 8/9*r**3 + 1/15*r**5 + 0*r - 1/180*r**6 - 3*r**2 + 0 - 1/3*r**4. Factor k(n).
-2*(n - 2)**3/3
Factor -1 + l**2 - 2*l - 6*l + 8*l.
(l - 1)*(l + 1)
Let c be (-35)/28 - 146/(-104). Determine l so that 4/13 + c*l**4 + 18/13*l**2 - 10/13*l**3 - 14/13*l = 0.
1, 2
Suppose -14*o**3 + 0*o**2 - 5*o**2 + 7*o**4 - 3*o**4 + 14*o**5 + o**2 = 0. What is o?
-1, -2/7, 0, 1
Let p(l) be the first derivative of -l**7/189 + 2*l**6/135 - l**4/27 + l**3/27 + 4*l - 2. Let t(n) be the first derivative of p(n). Factor t(v).
-2*v*(v - 1)**3*(v + 1)/9
Let y(t) be the second derivative of -t**4/12 + t**3/6 - t**2/2 + 6*t. Let w(a) = a**3 + 2*a**2 - 3*a + 2. Let f(h) = -w(h) - 2*y(h). Factor f(v).
-v*(v - 1)*(v + 1)
Let g be (-95)/(-114) - (4/3 - 1). Suppose g*y**3 + 1/2*y**2 - 1/2*y - 1/2 = 0. What is y?
-1, 1
Suppose -3/2*h**3 + 3/2*h - 15/2 + 15/2*h**2 = 0. What is h?
-1, 1, 5
Let u(o) be the second derivative of -o**5/20 - o**4/4 + 2*o**2 + 2*o. Factor u(f).
-(f - 1)*(f + 2)**2
Suppose 3*s + 4*z = 0, -4*s + z - 5*z = -4. Suppose -s*a - 1 = -3*v, 2*v - 6*v + 12 = 0. Factor 4*h**2 + 8*h**2 + h - 4*h**a + 9*h + 2.
2*(h + 1)*(4*h + 1)
Let w = 1 - -5. Let t be (2 + w)/(0 - -1). Let -2*j - 8*j**2 - 2*j**3 + t*j**3 + 4*j = 0. What is j?
0, 1/3, 1
Suppose 9*o - 5*o - 124 = 0. Let v = o - 91/3. Factor 2/9*s**4 + 2/9*s**2 - v*s + 2/3*s**3 - 4/9.
2*(s - 1)*(s + 1)**2*(s + 2)/9
Let o(m) = m + 9. Let j be o(-9). Let w be j/3 - (-1 + -1). Suppose 1/2*k**3 + 1/2*k**w + 0 + 0*k = 0. Calculate k.
-1, 0
Let 0 + 0*r + 1/4*r**5 - 3/4*r**4 + 0*r**3 + r**2 = 0. What is r?
-1, 0, 2
Let a = 4 - 0. Let l(z) be the first derivative of 3 - 12/5*z**5 + 1/2*z**6 + 9/2*z**a - 4*z**3 + 0*z + 3/2*z**2. Factor l(p).
3*p*(p - 1)**4
Suppose -3*y + 2*y = -4*r - 10, 4*r = -y - 6. Solve 0 + 2/5*m**y - 2/5*m**3 + 0*m = 0 for m.
0, 1
Let p(s) be the third derivative of 9*s**8/112 + 27*s**7/35 + 111*s**6/40 + 157*s**5/30 + 35*s**4/6 + 4*s**3 + 11*s**2. Factor p(y).
(y + 1)*(y + 3)*(3*y + 2)**3
Let a(c) = 7*c**5 + 39*c**4 + 29*c**3 + 11*c**2 - 7*c. Let i(s) = -3*s**5 - 20*s**4 - 15*s**3 - 6*s**2 + 4*s. Let j(z) = 4*a(z) + 7*i(z). Factor j(d).
d**2*(d + 1)**2*(7*d + 2)
Suppose -2*m = -0*m - 6. Suppose -42 = -5*o + 3*z, -m*z = o + 7 - 1. Solve 4*h - 2*h + 10*h**2 - 5*h - o*h**3 - h = 0 for h.
0, 2/3, 1
Factor 8/11 + 2/11*t**2 + 8/11*t.
2*(t + 2)**2/11
Let m(x) be the first derivative of 10 - 2*x**3 + 0*x**2 + 0*x + 3/4*x**4 + 3/5*x**5. Factor m(g).
3*g**2*(g - 1)*(g + 2)
Let p(v) be the first derivative of -2*v**3/3 + 33. Let p(z) = 0. What is z?
0
Let j(g) = g**2 - 6*g + 4. Let l be j(5). Let y be -1 - 4*l/1. Factor -2*c**3 - 24*c**2 + 10*c**y + 8*c + 2*c**3.
2*c*(c - 2)*(5*c - 2)
Suppose 0 = -2*w - w + 9. Determine l so that -w*l**2 - 1 + 4*l**2 - 5*l**2 - 4*l = 0.
-1/2
Factor -1/2 - 5/8*m**2 - 2*m + 7/8*m**3.
(m - 2)*(m + 1)*(7*m + 2)/8
Let g(c) be the first derivative of -c**6/42 - c**5/35 + c**4/28 + c**3/21 + 43. Find a, given that g(a) = 0.
-1, 0, 1
Let v(m) = -36*m**4 - 6*m**3 + 147*m**2 + 273*m + 126. Let r(g) = -5*g**4 - g**3 + 21*g**2 + 39*g + 18. Let t(a) = -15*r(a) + 2*v(a). Factor t(d).
3*(d - 3)*(d + 1)**2*(d + 2)
Let g be (-147)/(-42)*12/14. Factor -2/3 + 1/3*q**2 + q**g + 1/3*q**4 - q.
(q - 1)*(q + 1)**2*(q + 2)/3
Let p be -1 + (-32)/63*-2. Let t(b) be the second derivative of 0 - 1/3*b**2 - 1/9*b**4 + 1/15*b**5 + 1/15*b**6 - 1/3*b**3 + b + p*b**7. Factor t(w).
2*(w - 1)*(w + 1)**4/3
Let a(g) be the second derivative of -g**5/60 + g**4/12 + 3*g**2/2 + 2*g. Let w(q) be the first derivative of a(q). Factor w(k).
-k*(k - 2)
Let s(j) = -2*j - 8. Let y be s(-6). Suppose -d - 12 = -y*d. Let -2*k**4 + 3*k**d - 5 + k**5 + 5 = 0. What is k?
-1, 0
Let t be 468/33 - (-4)/(-22). Let i be (-1 + -2)*t/(-21). Factor -l**3 + 3*l - i*l - l**2 + 0*l + 1.
-(l - 1)*(l + 1)**2
Factor 0*l**4 + 1/4*l**5 + 0 + 1/4*l + 0*l**2 - 1/2*l**3.
l*(l - 1)**2*(l + 1)**2/4
Let m(z) be the second derivative of 7*z**4/12 + 2*z**3 - 2*z**2 + z. Factor m(q).
(q + 2)*(7*q - 2)
Let x(a) be the third derivative of 1/60*a**5 + 1/70*a**7 + 0 - 4*a**2 + 0*a + 1/336*a**8 + 0*a**4 + 1/40*a**6 + 0*a**3. Factor x(n).
n**2*(n + 1)**3
Let u(o) be the second derivative of -o**4/12 - o**2/2 - 5*o. Let x(t) = -t**3 + 10*t**2 + t + 8. Let h(l) = 18*u(l) + 2*x(l). Factor h(g).
-2*(g - 1)**2*(g + 1)
Let v(g) be the second derivative of g**7/42 - g**5/5 - g**4/6 + g**3/2 + g**2 - 19*g. Determine d so that v(d) = 0.
-1, 1, 2
Let b(s) = -s**3 + s**2. Let l(x) = 2*x**4 - 2*x**3 - 2*x**2 + 4*x - 2. Suppose v - 3 = -1. Let m(i) = v*b(i) + l(i). Factor m(k).
2*(k - 1)**3*(k + 1)
Let v = -5 - -8. Factor -v*k**5 - k**5 + 2*k**4 + 6*k**5 + 0*k**5.
2*k**4*(k + 1)
Let o(y) be the second derivative of 1/24*y**3 + 1/8*y**2 - 1/48*y**4 - 5*y + 0 - 1/80*y**5. What is k in o(k) = 0?
-1, 1
Suppose -56 = 2*m - 6*m. Let l = m + -96/7. Find s such that -12/7*s**2 - l + 8/7*s + 8/7*s**3 - 2/7*s**4 = 0.
1
Let t(f) be the second derivative of 8*f**8/105 + 4*f**7/105 - f**6/5 + 11*f**5/60 - f**4/12 + f**3 + f. Let h(q) be the second derivative of t(q). Factor h(u).
2*(u + 1)*(4*u - 1)**3
Let y = 3299941/37807 + 10/5401. Let a = y + -87. Factor 0 + 4/7*z + 2/7*z**2 - a*z**3.
-2*z*(z - 2)*(z + 1)/7
Let s(p) be the second derivative of -p**4/12 + p**3/3 - p**2/2 - 14*p. Determine x, given that s(x) = 0.
1
Let p be ((-1)/3)/(8/(-432)). Let i = p + -16. Factor -2*l**i + 0 - 4/5*l.
-2*l*(5*l + 2)/5
Let k(s) be the third derivative of s**8/168 - s**7/42 + s**6/30 - s**5/60 + 4*s**2. Solve k(o) = 0.
0, 1/2, 1
Let x be ((-24)/27)/4 - 0. Let p = x + 26/9. Find g such that 2*g**2 + 2/3*g**4 - 8/3 - p*g + 8/3*g**3 = 0.
-2, -1, 1
Let p(g) = 4*g**2 + 1 + 0 + 3 - g - 1. Let z(v) be the first derivative of 5*v**3/3 - v**2/2 + 4*v + 4. Let n(b) = 4*p(b) - 3*z(b). Factor n(m).
m*(m - 1)
Suppose 2/9*n - 4/9 + 2/9*n**2 = 0. What is n?
-2, 1
Let d be 16/4 - ((-15)/(-3) + -1). Factor d + 0*s - 3/5*s**2.
-3*s**2/5
Let y(l) be the first derivative of -l**6/7 + 16*l**5/35 - 3*l**4/7 + l**2/7 + 13. Factor y(m).
-2*m*(m - 1)**3*(3*m + 1)/7
Let h(m) be the third derivative of -m**7/630 - m**6/90 - m**5/30 - m**4/18 - m**3/18 + 12*m**2. Factor h(u).
-(u + 1)**4/3
Solve -6/7*k**4 + 10/7*k**3 - 8/7*k**5 - 2/7*k + 6/7*k**2 + 0 = 0.
-1, 0, 1/4, 1
Let r be (0 - 70/(-12))*(-24)/(-90). Determine n, given that -2*n**4 + 4/9*n + 0 + 2*n**2 - r*n**5 + 10/9*n**3 = 0.
-1, -2/7, 0, 1
Let u(q) be the second derivative of q**4/48 + q**3/12 + q**2/8 - q. Suppose u(o) = 0. What is o?
-1
Factor 2/7*k + 2/7*k**3 + 0 - 4/7*k**2.
2*k*(k - 1)**2/7
Let u = 721/8 + -90. Let n(g) be the second derivative of -u*g**4 - 1/6*g**3 - 1/20*g**5 - 1/8*g**2 + 0 - g - 1/120*g**6. Factor n(i).
-(i + 1)**4/4
Suppose 5/2*m**5 + 22*m + 77/2*m**3 + 16*m**4 + 4 + 43*m**2 = 0. Calculate m.
-2, -1, -2/5
Let j = 10 + -4. Let s = j + -3. Factor 6/5*t**2 + 2/5 - 6/5*t - 2/5*t**s.
-2*(t - 1)**3/5
Factor 3*y**4 + 8*y**2 + 10*y - 12*y**3 - 11*y**2 + 2*y + 0*y**4.
3*y*(y - 4)*(y - 1)*(y + 1)
Let x = -37 - -21. Let y be x/(-7) - (-6)/(-21). Factor -4/3 - 2/3*b + 2/3*b**y.
2*(b - 2)*(b + 1)/3
Suppose 2*q - 14 = 4*b + q, 0 = 2*b + q + 4. Let p = 5 + b. Find k, given that k - 3*k - 1 + 2 + k**p = 0.
1
Let u(d) = d**2 + 4*d. Let c be u(-4). Find k, given that 0*k + 1/4*k**3 + c - 1/4*k**2 = 0.
0, 1
Let -5/6*r**5 + 5/2*r**3 + 1/3*r**4 + 2/3*r**2 - 2/3*r + 0 = 0. Calculate r.
-1, 0, 2/5, 2
Let g(s) = -s**2 + 3*s - 1. Let q be g(3). Let h = 1 - q. Factor p + 1/4*p**h + 1.
(p + 2)**2/4
Factor 24*a**3 + 6*a - 5*a**2 + 2*a**2 - 4*a**2 - 23*a**3.
a*(a - 6)*(a - 1)
Let l = 9 + -9. Let x(r) be the third derivative of -1/300*r**5 + 1/40*r**4 - 3*r**2 + 0 + l*r - 1/15*r**3. Let x(m) = 0. What is m?
1, 2
Let z 