- n + 1/3*n**3. Factor k(a).
(a - 1)*(a + 1)
Let w(x) = -2*x**3 + 2*x**2 + 7*x - 6. Let h be w(2). Suppose 4/9*i**3 + 0*i + 2/9*i**2 + 2/9*i**4 + h = 0. What is i?
-1, 0
Let o(k) be the first derivative of k**7/945 - k**6/135 + k**5/54 - k**4/54 + k**2/2 - 4. Let h(a) be the second derivative of o(a). Factor h(m).
2*m*(m - 2)*(m - 1)**2/9
Suppose 0 = t - 3*k, k + 14 = 3*t + 6*k. Let a(z) be the second derivative of 4/7*z**2 + 4/7*z**t - 5/14*z**4 - 3*z + 2/35*z**5 + 0. Factor a(r).
2*(r - 2)**2*(4*r + 1)/7
Suppose 0*o**2 + o**3 + 9*o**2 - o - 9*o**2 = 0. What is o?
-1, 0, 1
Let m be ((4 - 4)/(1 + -3))/(-1). Factor -1/4*l**3 + m*l - 1/4*l**2 + 0.
-l**2*(l + 1)/4
Let f(z) be the third derivative of z**6/150 - 2*z**5/25 + 2*z**4/5 - 16*z**3/15 - 4*z**2 + 2*z. Determine u so that f(u) = 0.
2
Let o(i) be the second derivative of i + 1/420*i**7 + 0*i**5 + 0 + 1/6*i**3 + 0*i**4 + 0*i**6 + 0*i**2. Let v(d) be the second derivative of o(d). Factor v(j).
2*j**3
Let c be 1 - (4/8 + 0). Suppose c*u**4 + 1/2*u**5 + 1/2*u - u**3 + 1/2 - u**2 = 0. What is u?
-1, 1
Let q = -900 - -18904/21. Let j(v) be the first derivative of 3/14*v**4 + 4/7*v - q*v**3 - 3/7*v**2 + 4. Determine l so that j(l) = 0.
-1, 2/3, 1
Let n = 4007/15 - 267. Let a(k) be the first derivative of 2/25*k**5 + 1/10*k**4 + 0*k**2 - n*k**3 - 1/15*k**6 + 0*k - 1. Determine z, given that a(z) = 0.
-1, 0, 1
Suppose 0 = j - 5*j - 32. Let g(q) = 6*q**3 - 6*q**2 + 8. Suppose -n = -3*n + 6. Let s(c) = 2*c**3 - 2*c**2 + 3. Let w(f) = j*s(f) + n*g(f). Factor w(x).
2*x**2*(x - 1)
Factor -1/5*z**2 + 0 - 1/5*z**4 + 0*z + 2/5*z**3.
-z**2*(z - 1)**2/5
Let j(b) be the third derivative of 0 + 1/90*b**6 + b**2 - 1/9*b**3 + 0*b + 0*b**4 + 1/30*b**5. Suppose j(d) = 0. What is d?
-1, 1/2
Let z(w) be the third derivative of 0*w**3 + 0*w**4 - 1/330*w**6 + 1/330*w**5 + 0*w + 9*w**2 + 0 + 1/1155*w**7. Solve z(k) = 0.
0, 1
Let o(l) = -4*l**5 - 5*l**4 - l**3 + 3*l**2 - 3*l + 3. Let u(g) = 3*g**5 + 4*g**4 + g**3 - 2*g**2 + 2*g - 2. Let k(j) = 4*o(j) + 6*u(j). Factor k(i).
2*i**3*(i + 1)**2
Suppose 2*g = -2*u + 4*u + 10, 4*g + 3*u = 6. Solve 3/2*z + 1/2 + 1/2*z**2 - 3/2*z**g - z**4 = 0 for z.
-1, -1/2, 1
Suppose 2*j + 1 = 5. Let v = -91 - -99. Factor v*n**2 + 2*n**3 + 2*n**4 + 2*n**3 - j*n**3 - 10*n**3.
2*n**2*(n - 2)**2
Let w(c) be the first derivative of 2*c**6/3 + 3*c**5/5 - 13*c**4/4 - 17*c**3/3 - 3*c**2/2 + 2*c + 46. Find x such that w(x) = 0.
-1, 1/4, 2
Let i be (-1 - 0)/(2/(-4)). Let o(k) = 2*k**3 + 0*k**3 + 7*k**4 - 3*k**4 + 2. Let t(m) = 5*m**4 + 3*m**3 + 3. Let h(s) = i*t(s) - 3*o(s). Factor h(p).
-2*p**4
Let i(w) be the third derivative of -w**8/168 + 2*w**7/105 - w**5/15 + w**4/12 - 6*w**2. Factor i(g).
-2*g*(g - 1)**3*(g + 1)
Let u(p) be the second derivative of 0*p**3 + 8*p + 0 + 2*p**2 - 1/3*p**4. Factor u(s).
-4*(s - 1)*(s + 1)
Suppose 5*j = -2*w - 1, 3*w + 9*j - 6*j = 3. Find v, given that 0*v + 0 - 1/5*v**w + 1/5*v**3 = 0.
0, 1
Let t = -126 + 128. Factor 3/2*r**3 - r**t + 5/2*r**4 + 0*r + 0.
r**2*(r + 1)*(5*r - 2)/2
Let g be (-8)/(-12) + 1194/(-9). Let s = g + 1190/9. Find m such that 0 + 2/9*m**4 - 10/9*m**2 + s*m**5 - 2/3*m**3 - 4/9*m = 0.
-1, 0, 2
Let f be 15/2*(-8)/(-6). Let i be 33/11*2/f. Factor -6/5 + i*l + 3/5*l**2.
3*(l - 1)*(l + 2)/5
Let c be ((-6)/8)/(30/(-80)). Factor 2 + c - 3*h**2 + 3 - 4.
-3*(h - 1)*(h + 1)
Let y(h) be the third derivative of -h**5/10 - 7*h**4/6 + 5*h**3/3 - 11*h**2. Let y(i) = 0. Calculate i.
-5, 1/3
Let q(x) be the third derivative of -3/2*x**3 + 0 + 1/8*x**4 + 0*x + 7*x**2 + 3/20*x**5 - 1/40*x**6. Let q(w) = 0. What is w?
-1, 1, 3
Let f(i) = 6*i**2 + 3*i + 2. Let j be f(-1). Let l(h) be the first derivative of 2 - 4/3*h**3 + 0*h + 4/5*h**j - h**2 + 0*h**4 + 1/3*h**6. Factor l(c).
2*c*(c - 1)*(c + 1)**3
Let b(x) = 4 - 2*x**2 + 0*x**2 - 2*x - 1 + x**2. Let m(n) = -n**2 - 2*n + 2. Let d(h) = -4*b(h) + 6*m(h). Suppose d(l) = 0. What is l?
-2, 0
Let t(a) be the third derivative of -a**5/360 + a**4/36 - 34*a**2. Solve t(p) = 0 for p.
0, 4
Determine h, given that 24 + 73*h - 16*h**2 - 21*h - 4*h**2 = 0.
-2/5, 3
Let u(t) be the third derivative of t**5/20 + 11*t**4/4 + 121*t**3/2 + 4*t**2 + 3. Factor u(h).
3*(h + 11)**2
Let h(w) = w**2 + 9*w + 10. Let b be h(-8). Let x(l) = 13*l**2 - 5*l + 9. Let t(k) = -3*k**2 + k - 2. Let c(r) = b*x(r) + 9*t(r). Factor c(u).
-u*(u + 1)
Let v = -7734 + 835279/108. Let u(s) be the third derivative of -s**2 - v*s**4 - 2/27*s**3 - 1/54*s**5 + 0 + 0*s. Suppose u(x) = 0. What is x?
-1, -2/5
Let w = 14 - 5. Let l = -6 + w. Suppose -y**2 + 3*y - l*y = 0. Calculate y.
0
Let v(b) be the first derivative of -b**6/6 + 3*b**5/5 + b**4/2 - 4*b**3 + 4*b**2 + 20. Factor v(h).
-h*(h - 2)**2*(h - 1)*(h + 2)
Determine m so that 24*m - 2*m**4 - 22*m**2 - 3 + 8*m**3 - 6 + 6*m**4 - 5*m**4 = 0.
1, 3
Let m(v) be the second derivative of -v**5/70 - 5*v**4/42 - v**3/3 - 3*v**2/7 - 2*v. Factor m(d).
-2*(d + 1)**2*(d + 3)/7
Let f(w) be the second derivative of w**5/110 + 2*w**4/33 + 4*w**3/33 - 14*w. Factor f(s).
2*s*(s + 2)**2/11
Suppose -2*s - 22 = 3*l, s = -3*l - 0*s - 26. Let x be (-3)/(-15) + 2/l. Solve 0 + 1/3*j**4 + x*j**3 - 1/3*j**2 + 0*j = 0 for j.
-1, 0, 1
Let h(d) be the first derivative of -2*d**6/3 + 16*d**5/5 - 3*d**4 - 16*d**3/3 + 8*d**2 - 2. Suppose h(n) = 0. What is n?
-1, 0, 1, 2
Factor s**2 - 2*s**2 + 12*s**3 - 4*s**5 + s**2 - 8*s**2.
-4*s**2*(s - 1)**2*(s + 2)
Factor -8*c**3 - c**4 + 16*c**3 - 8*c**3 + c**2.
-c**2*(c - 1)*(c + 1)
Let z(p) be the second derivative of -1/30*p**4 + 1/50*p**5 - 2/15*p**3 + 0*p**2 - 3*p + 0. Factor z(l).
2*l*(l - 2)*(l + 1)/5
Let f(x) be the first derivative of 0*x + 2 - 1/2*x**2. Let u(k) = k**3 + k**2 - k. Let c(g) = 2*f(g) - 2*u(g). Find m such that c(m) = 0.
-1, 0
Let v(g) = 5*g**2 + 3. Let u(w) = -w**3 + 3*w**2 + 5*w - 6. Let d be u(4). Let o(l) = 4*l**2 + 2. Let j(c) = d*v(c) + 3*o(c). Solve j(s) = 0.
0
Let d(j) be the second derivative of -2*j + 0 + j**2 + 1/3*j**3 - 1/10*j**5 - 1/6*j**4. Factor d(c).
-2*(c - 1)*(c + 1)**2
Suppose -4 - 11 = -3*j. Let q(l) be the first derivative of -1/6*l**6 + 0*l**j + 0*l**3 + 0*l + 1/2*l**4 + 2 - 1/2*l**2. Let q(f) = 0. What is f?
-1, 0, 1
Suppose -f - 6*f = -21. Let y(l) be the second derivative of -1/40*l**5 + 1/12*l**f + l - 1/60*l**6 + 0 + 0*l**2 + 1/24*l**4. Factor y(w).
-w*(w - 1)*(w + 1)**2/2
Solve 10/3*t - 5/6*t**2 - 10/3 = 0.
2
Let u(c) be the second derivative of 0 - 1/6*c**4 + c - 1/3*c**3 + c**2 + 1/10*c**5. Let u(b) = 0. What is b?
-1, 1
Let o be (3 - 1)/(2/3). Let d(c) be the first derivative of 3/4*c**2 + c - 1 - 5/6*c**o. Factor d(t).
-(t - 1)*(5*t + 2)/2
Let y(m) be the third derivative of m**4/24 + m**3/3 + 4*m**2. Let h be y(0). Factor 0 + 14/9*c**4 + 32/9*c**3 + 4/9*c + 22/9*c**h.
2*c*(c + 1)**2*(7*c + 2)/9
Let c(n) be the third derivative of n**9/35280 - n**8/15680 - n**4/24 + 5*n**2. Let p(w) be the second derivative of c(w). Find k such that p(k) = 0.
0, 1
Let o = -179/55 + 38/11. Factor 0 + 1/5*b + 0*b**2 - o*b**3.
-b*(b - 1)*(b + 1)/5
Let l(y) = -60*y**2 + 5*y + 5. Let c(a) = -30*a**2 + 2*a + 3. Let j(g) = -5*c(g) + 3*l(g). Factor j(w).
-5*w*(6*w - 1)
Let z(g) = g**4 - g**3 + 4*g**2 + 2*g + 2. Let h(p) = -7*p**4 + 7*p**3 - 25*p**2 - 13*p - 13. Let n(i) = -6*h(i) - 39*z(i). Factor n(v).
3*v**2*(v - 2)*(v + 1)
Let i(b) be the third derivative of b**5/150 - 7*b**4/60 - 8*b**3/15 + b**2 + 45*b. Solve i(r) = 0.
-1, 8
Suppose 0 = 5*a - 30 + 10. Find j, given that -2*j**2 + 4*j - 3*j**2 - 3*j + a*j**2 = 0.
0, 1
Let s be 7/(-21) + 2/6. Solve 1/4*q - 1/4*q**2 + s = 0 for q.
0, 1
Let w = -59 - -62. Factor -1/2 + 3/2*r**4 + r**w + 1/2*r**5 - r**2 - 3/2*r.
(r - 1)*(r + 1)**4/2
Let p(o) be the second derivative of -2/21*o**4 - 6*o + 0 + 0*o**2 + 1/21*o**3. Determine y, given that p(y) = 0.
0, 1/4
Let t(q) be the first derivative of -q**2 + q**3 - 1 + 2*q - 1 - 2*q**2. Let l(o) = 7*o**2 - 13*o + 3. Let k(a) = 2*l(a) - 5*t(a). Factor k(v).
-(v - 2)**2
Let b be (-17 - -5)/(1 - 0 - 14). Factor -18/13 - b*g - 2/13*g**2.
-2*(g + 3)**2/13
Let h = 9 - 15. Let k be ((-9)/21)/(9/h). Let k*w**4 + 0*w + 2/7 - 4/7*w**2 + 0*w**3 = 0. What is w?
-1, 1
Suppose -3*g + 2 = 2*k, -6*k + 2*k + 4 = -5*g. Factor 1/2*y**2 - 1/4*y**5 + 1/4*y + 0 - 1/2*y**4 + g*y**3.
-y*(y - 1)*(y + 1)**