k(n). Factor a(x).
4*(x + 1)**2*(2*x - 1)
Let l be 3/(14/4 + -2). Let -4*s**2 - l - 1 + 2*s**2 + 4*s + s**2 = 0. What is s?
1, 3
Suppose 0 = 5*g - 7*g. Suppose -13*s + 10*s = g. Determine m, given that 4/11*m**3 - 4/11*m - 14/11*m**4 + s + 14/11*m**2 = 0.
-1, 0, 2/7, 1
Let j(p) be the second derivative of -p**8/192 + p**7/70 - p**6/160 - p**5/120 + 2*p**2 - p. Let d(n) be the first derivative of j(n). Factor d(v).
-v**2*(v - 1)**2*(7*v + 2)/4
Let o(b) = -b**2 + 1. Suppose 1 = -3*f + 4. Let d(p) = 4*p**2 + p - 3. Let k(l) = f*d(l) + 5*o(l). Suppose k(a) = 0. What is a?
-1, 2
Suppose 2*b = -4*g, 3*g + 11 = 2*b + 4. Let f(n) be the second derivative of 9/2*n**3 - 3*n**b + 3*n - 5/2*n**4 + 0. Factor f(w).
-3*(2*w - 1)*(5*w - 2)
Let a be (-9132)/24*(-4)/14. Let i = 109 - a. Solve i - 2/7*o - 2/7*o**2 + 2/7*o**3 = 0.
-1, 1
Factor -3/8*y**4 - 3/4*y + 9/8*y**2 + 0*y**3 + 0.
-3*y*(y - 1)**2*(y + 2)/8
Let d be 1/(6/(-4))*(-18)/24. Determine f so that 1/2*f**2 + d*f + 0 - 1/2*f**4 - 1/2*f**3 = 0.
-1, 0, 1
Let r(u) be the second derivative of -u**5/15 + u**4/3 - 4*u**3/9 + 6*u + 4. Factor r(a).
-4*a*(a - 2)*(a - 1)/3
Let x(h) be the first derivative of -h**6/90 - h**5/60 - 3*h + 3. Let g(a) be the first derivative of x(a). Factor g(o).
-o**3*(o + 1)/3
Let w(g) be the first derivative of -2/25*g**5 - 6/5*g**3 - 4/5*g - 1/2*g**4 - 7/5*g**2 - 2. Suppose w(b) = 0. Calculate b.
-2, -1
Let k(i) be the second derivative of -i**4/24 + i**3/16 + i**2/16 - 14*i. Suppose k(b) = 0. Calculate b.
-1/4, 1
Let t(w) be the first derivative of w**4 - 2*w**2 + 8. Suppose t(q) = 0. What is q?
-1, 0, 1
Solve -10/7*v + 4/7 + 6/7*v**3 - 8/7*v**2 = 0 for v.
-1, 1/3, 2
Let t = -961 - -964. Determine i so that 0*i**4 + 6/5*i**2 + 3/5*i**5 + 0 - 9/5*i**t + 0*i = 0.
-2, 0, 1
Let 3*y + 3 + 2*y + 3*y**2 + y = 0. What is y?
-1
Let r(j) be the first derivative of 5*j**5 + 10*j**4 + 5*j**3/3 - 5*j**2 + 9. Factor r(w).
5*w*(w + 1)**2*(5*w - 2)
Let k(x) be the third derivative of 0*x**3 + 1/90*x**5 + 0*x - 9*x**2 + 1/18*x**4 + 0. Determine h, given that k(h) = 0.
-2, 0
Suppose 3*n + 0*n = 12. Suppose -b + n*b = 9. Determine p so that 0*p + 0*p**2 - 1/2*p**b + 0 = 0.
0
Let f(x) be the first derivative of 4*x**3/15 - 4*x/5 + 11. Determine c so that f(c) = 0.
-1, 1
Let b(t) be the second derivative of -1/5*t**5 + 0 + 2/3*t**3 - 3/2*t**4 - 4*t + 0*t**2 + 3/5*t**6. Factor b(w).
2*w*(w - 1)*(w + 1)*(9*w - 2)
Let y(l) be the third derivative of 0 - 1/6*l**3 - 3*l**2 - 3/40*l**5 - 11/48*l**4 + 0*l. Factor y(a).
-(a + 1)*(9*a + 2)/2
Let n(p) be the first derivative of p**4/8 + p**3/6 + 10*p - 4. Let x(h) be the first derivative of n(h). Factor x(j).
j*(3*j + 2)/2
Let a(l) be the second derivative of 3*l**5/40 + 9*l**4/8 + 6*l**3 + 12*l**2 + 4*l. Factor a(w).
3*(w + 1)*(w + 4)**2/2
Let c(l) = -l**2. Let p(q) = 7*q**2 + 8*q - 16. Let z(y) = -24*c(y) - 3*p(y). Factor z(r).
3*(r - 4)**2
Let a(q) be the third derivative of -q**6/80 + q**5/20 - q**4/16 + q**3/6 + 4*q**2. Let b(p) be the first derivative of a(p). Factor b(i).
-3*(i - 1)*(3*i - 1)/2
Suppose -3*o = -p + 4*p - 9, 3*p + o = 13. Suppose -p*f = 4*y + 5 - 35, 0 = 3*f + 2*y - 16. Factor -2/5*g**f - 2/5*g + 0.
-2*g*(g + 1)/5
Let n(i) be the second derivative of i**5/30 + i**4/9 + i. Suppose n(u) = 0. What is u?
-2, 0
Let f(u) be the third derivative of u**6/280 - 3*u**5/140 + 3*u**4/56 - u**3/14 - 8*u**2. Let f(h) = 0. What is h?
1
Let q(d) be the third derivative of -1/240*d**5 - 1/24*d**3 + 0*d - 1/160*d**6 - 4*d**2 + 1/32*d**4 + 1/420*d**7 + 0. Factor q(l).
(l - 1)**2*(l + 1)*(2*l - 1)/4
Suppose -2*c - 6*y = -y + 16, 3*c = -2*y - 2. Let a(h) be the first derivative of -2/3*h**3 + 0*h + 2 - 3/4*h**4 - 1/4*h**c - 2/5*h**5 - 1/12*h**6. Factor a(r).
-r*(r + 1)**4/2
Solve -2*t**5 + 0*t**2 + 2/3*t**4 + 0*t + 0 + 4/3*t**3 = 0 for t.
-2/3, 0, 1
Let h be 4/6*(-15)/(-2). Let w(o) be the third derivative of 0 + 7/180*o**6 - 1/63*o**7 + 0*o + 2*o**2 - 1/45*o**h + 0*o**4 + 0*o**3. Find t such that w(t) = 0.
0, 2/5, 1
Let g(u) be the first derivative of u**6/36 + u**5/30 - u**4/3 - 4*u**3/9 + 4*u**2/3 + 8*u/3 + 21. Suppose g(v) = 0. Calculate v.
-2, -1, 2
Let y(r) be the third derivative of -r**10/100800 + r**8/13440 + r**5/15 + 3*r**2. Let l(j) be the third derivative of y(j). Factor l(c).
-3*c**2*(c - 1)*(c + 1)/2
Let m(p) = -p - 3. Let x be m(-5). Let t = x - -2. Find c, given that 5*c**t - 4*c**4 + c**3 + 0*c**3 = 0.
-1, 0
Let i be (-6)/9*(-3 + -21). Let c be (-12)/i*4/(-12). Find t such that -c*t**2 + 0*t + 1/4 = 0.
-1, 1
Suppose -3*t - t = 0. Let q(k) be the third derivative of 1/60*k**5 + 0*k**3 + 0*k + t - 1/24*k**4 + 2*k**2. Factor q(s).
s*(s - 1)
Suppose -5*c - 3*f = -60, -2*c - 2*c + 40 = 4*f. Let b be 36/c + 4/(-10). Factor 2*q + 2*q**b - q**2 - 4*q**2 + q**2.
-2*q*(q - 1)
Suppose -8*l = -12*l. Let n(t) be the second derivative of 0*t**2 + 0 - 3*t + 1/36*t**4 + l*t**3. Let n(g) = 0. Calculate g.
0
Let z = 140/3 - 46. Suppose 22*m**2 - 20/3*m + 32/3*m**4 - 80/3*m**3 + z = 0. What is m?
1/4, 1
Let a(g) be the third derivative of 1/12*g**4 + 0*g + 0 - 3*g**2 - 1/30*g**5 + 0*g**3. Suppose a(c) = 0. What is c?
0, 1
Solve 24*u - 2*u**2 + 3*u**3 + 11*u**2 + 6*u**2 + 12 = 0 for u.
-2, -1
Let h(k) be the first derivative of 22/3*k**3 - 2*k**2 - 94/5*k**5 + 0*k - 2*k**4 + 14*k**6 + 2. Determine i, given that h(i) = 0.
-1/2, 0, 2/7, 1/3, 1
Let l = 23 + -37. Let a be ((-1)/(-3))/(l/(-21)). Factor a*v - 1/4 - 1/4*v**2.
-(v - 1)**2/4
Let g(l) = -3*l**2 - 6. Let p(s) = 2*s**2 + 7. Let f(v) = 5*g(v) + 6*p(v). Determine i so that f(i) = 0.
-2, 2
Let a(h) be the third derivative of h**6/360 - h**5/45 + 5*h**4/72 - h**3/9 + 8*h**2. Solve a(u) = 0.
1, 2
Factor 0*j**3 - j**4 + 0 + j**2 + 1/2*j - 1/2*j**5.
-j*(j - 1)*(j + 1)**3/2
Let m(i) be the second derivative of 3*i**5/20 - 7*i**3/2 - 9*i**2 + i - 7. Suppose m(j) = 0. Calculate j.
-2, -1, 3
Factor 4*h**3 - 8*h**2 + 4*h**2 - 2*h**3.
2*h**2*(h - 2)
Let d(o) be the first derivative of 0*o + 3 - 3/4*o**2 + 1/2*o**3. Factor d(m).
3*m*(m - 1)/2
Let h(w) be the third derivative of 0*w**4 + 1/180*w**6 - 1/126*w**8 + 0*w - 2*w**2 + 0*w**5 + 0 + 0*w**3 - 1/105*w**7. Factor h(v).
-2*v**3*(v + 1)*(4*v - 1)/3
Let u = 0 + 6. Factor 6 - 3*n**3 + 8*n - 17*n + u*n**3.
3*(n - 1)**2*(n + 2)
Let h(q) be the second derivative of q**4/6 - q**3/3 - 2*q**2 + 15*q. What is i in h(i) = 0?
-1, 2
Let w be (3/(-20))/((-63)/35). Let f(b) be the second derivative of 0 - w*b**4 - 1/3*b**3 + 0*b**2 + 2*b + 3/20*b**5. Let f(k) = 0. What is k?
-2/3, 0, 1
Let j(q) be the first derivative of q**6/12 + 7*q**5/10 + 15*q**4/8 + 3*q**3/2 - 12. Find o such that j(o) = 0.
-3, -1, 0
Let j be (-3 - -1) + 13 + -9. Let s(k) be the first derivative of -4 + 1/6*k**3 + 3/4*k**j + 0*k. Suppose s(o) = 0. Calculate o.
-3, 0
Let g(m) be the third derivative of m**6/600 - m**5/150 + m**4/120 - 3*m**2. Determine z, given that g(z) = 0.
0, 1
Let u(y) be the first derivative of -4*y**5/5 + 4*y**4 - 4*y**3 - 8*y**2 + 16*y - 6. Factor u(m).
-4*(m - 2)**2*(m - 1)*(m + 1)
Solve 9/5*w + 0 - 1/5*w**2 = 0 for w.
0, 9
Let b(k) be the third derivative of k**7/210 + k**6/15 + 3*k**5/10 + 2*k**4/3 + 5*k**3/6 + k**2. Suppose b(s) = 0. Calculate s.
-5, -1
Suppose 0 = -0*r + 3*r + 42. Let l = 9 + -5. Let c(k) = 3*k**2 + 1. Let u(q) = 10*q**2 + 4. Let j(a) = l*u(a) + r*c(a). Find n, given that j(n) = 0.
-1, 1
Let s be (138/805)/(6/10). Factor s*n**3 + 0 - 2/7*n + 0*n**2.
2*n*(n - 1)*(n + 1)/7
Let d(a) be the first derivative of a**4/12 - a**2/2 - 2*a/3 - 14. Let d(q) = 0. Calculate q.
-1, 2
Let q be ((-3)/(-2))/(7/84). Let t be q/(-10) - (-4)/2. Factor 1/5*z**2 + 2/5*z + t.
(z + 1)**2/5
Find a such that 1 + 30*a**2 + 32*a + a**4 + a**4 - 12*a**4 + 7 - 4*a**3 = 0.
-1, -2/5, 2
Solve -34*t - 2 + 0 + 6*t - 4 + 10*t**2 = 0 for t.
-1/5, 3
Let w(c) be the second derivative of -c**5/20 - c**4/3 - 2*c**3/3 - c**2/2 + 4*c. Let s(b) = b**3 + 3*b**2 + 3*b + 1. Let t(k) = -5*s(k) - 4*w(k). Factor t(u).
-(u - 1)**2*(u + 1)
Let n(j) be the second derivative of -j**6/360 - j**5/120 + j**3/2 + 3*j. Let k(f) be the second derivative of n(f). Factor k(z).
-z*(z + 1)
Let z(v) be the third derivative of -v**7/35 + 2*v**6/15 - 2*v**5/15 + 30*v**2. Factor z(o).
-2*o**2*(o - 2)*(3*o - 2)
Let d(o) be the 