 Suppose n(i) = 0. What is i?
-1, 1
Let d be (-6)/(-8) - 762/1080. Let m(r) be the third derivative of 0*r - r**2 + 0 - d*r**5 + 2/45*r**6 - 1/18*r**3 - 7/72*r**4. Factor m(x).
(x - 1)*(4*x + 1)**2/3
Let a(s) = s**3 - 2*s**2 - 3*s + 2. Let g be a(3). Factor 4*n**2 - 6*n**3 + 3*n**4 + 3*n**2 - 4*n**2 + 0*n**g.
3*n**2*(n - 1)**2
Let l be (-3)/18 - (-364)/24. Let 2*m**2 + 15 + 2*m**3 - l + m**3 = 0. What is m?
-2/3, 0
Let a(q) be the first derivative of q**3/3 - 13*q**2 + 169*q - 17. What is s in a(s) = 0?
13
Let l = 81 - 58. Suppose -4*u + 17 = -l. Factor 4 + 0 + 6*c**3 - 4*c**2 + u*c**4 - 5*c**2 - 5*c**2 - 6*c.
2*(c - 1)*(c + 1)**2*(5*c - 2)
Find c such that 34*c**5 + 9*c**3 + c**5 - 8*c**5 + 21*c**4 - 15*c**5 = 0.
-1, -3/4, 0
Let p(c) be the third derivative of -1/240*c**6 - 1/6*c**3 + 0*c**5 + 2*c**2 + 0*c + 0 + 1/16*c**4. Factor p(g).
-(g - 1)**2*(g + 2)/2
Let t(i) be the third derivative of -i**7/840 - i**6/60 - i**5/10 - i**4/3 + i**3/3 + 2*i**2. Let k(n) be the first derivative of t(n). Factor k(a).
-(a + 2)**3
Let x be (-104)/(-260) + (-48)/(-10). Let -x*r**4 - 8/5*r - 2/5*r**3 + 2*r**5 - 8/5 + 34/5*r**2 = 0. Calculate r.
-1, -2/5, 1, 2
Factor -16*b + 12*b**3 + 30*b**2 + 58*b**2 - 8*b**2 - 280*b**4 - 196*b**5.
-4*b*(b + 1)**2*(7*b - 2)**2
Let b(c) = c**2 - 7*c + 6. Let l(p) = p**2 - 4*p + 3. Let n(r) = -2*b(r) + 5*l(r). What is v in n(v) = 0?
1
Let h be 8/10*(-45)/(-18). Factor 1/3*r**3 + 1/3*r - 2/3*r**h + 0.
r*(r - 1)**2/3
Let h = 957/4 + -15091/60. Let o = 68/5 + h. Factor -2*x**2 - 4/3*x - 1/3 - 1/3*x**4 - o*x**3.
-(x + 1)**4/3
Let d(f) be the second derivative of f**4/3 + 32*f**3/3 + 128*f**2 - 4*f. Factor d(c).
4*(c + 8)**2
Let x(s) = 2*s - 8. Let k be x(5). Suppose -r**k - r - 7*r**3 + 9*r**2 - 3*r**3 + 9*r - 6*r**4 = 0. What is r?
-2, -2/3, 0, 1
Factor 15/2*o**3 + 9/2*o**4 - 3/2*o + 0 + 3/2*o**2.
3*o*(o + 1)**2*(3*o - 1)/2
Determine f so that 2*f**4 + 106*f - 106*f = 0.
0
Let n(c) be the first derivative of -c**4/4 - c**3/3 + 5*c**2/2 - 3*c + 6. Suppose n(z) = 0. Calculate z.
-3, 1
Let d(q) be the second derivative of q**6/90 - q**5/15 + q**4/9 + 9*q. Factor d(o).
o**2*(o - 2)**2/3
Let x(h) be the third derivative of h**6/1440 - h**5/240 + h**4/96 - 3*h**3/2 - 6*h**2. Let w(y) be the first derivative of x(y). Suppose w(b) = 0. Calculate b.
1
Let g(l) be the third derivative of l**6/780 - l**5/390 - 7*l**2. Factor g(r).
2*r**2*(r - 1)/13
Let c(n) be the first derivative of -2*n**3/21 + n**2/7 + 4*n/7 - 6. Factor c(g).
-2*(g - 2)*(g + 1)/7
Let g = 25321/60 - 422. Let k(h) be the third derivative of 1/24*h**4 + 0 + 0*h**3 - g*h**5 + 0*h + 4*h**2. What is o in k(o) = 0?
0, 1
Let q(j) be the first derivative of j**9/3024 - j**7/840 - 4*j**3/3 - 1. Let f(y) be the third derivative of q(y). Factor f(g).
g**3*(g - 1)*(g + 1)
Let x = 54 - 54. Let o(a) be the first derivative of 4/27*a**3 + 1/18*a**4 + 2 + 0*a**2 + x*a. Let o(d) = 0. Calculate d.
-2, 0
Factor 0 + 1/5*n + 1/5*n**2.
n*(n + 1)/5
Let c(h) be the second derivative of h**5/80 + h**4/12 - 12*h. Factor c(j).
j**2*(j + 4)/4
Let c(i) be the second derivative of -i**4/2 + 2*i**3/3 + i**2 - 4*i. Solve c(m) = 0.
-1/3, 1
Let p(j) be the second derivative of 0*j**2 - 3*j + 1/105*j**6 - 1/42*j**4 + 0*j**5 + 0*j**3 + 0. Factor p(w).
2*w**2*(w - 1)*(w + 1)/7
Suppose -10*t**4 - t + 3*t - 9*t**2 + 11*t**4 + 9*t**3 - 3*t**5 = 0. Calculate t.
-2, 0, 1/3, 1
Suppose -2 + 0 = -w. Let s(d) = -37*d**2 - 57*d + 7. Let m(a) = 9*a**2 + 14*a - 2. Let u(c) = w*s(c) + 9*m(c). Factor u(z).
(z + 2)*(7*z - 2)
Let c(b) be the first derivative of -77/2*b**4 + 98/5*b**5 - 2 - 4*b**2 + 64/3*b**3 + 0*b. Factor c(r).
2*r*(r - 1)*(7*r - 2)**2
Let s(o) be the first derivative of -o**6/30 - o**5/10 - o**4/12 - 2*o - 2. Let d(y) be the first derivative of s(y). Factor d(g).
-g**2*(g + 1)**2
Let o(r) be the third derivative of r**5/60 - r**3/6 - r**2. Solve o(d) = 0 for d.
-1, 1
Let n be 2 + -5 + (-55)/(-15). What is v in -2*v**2 + n*v**3 + 0 + 4/3*v = 0?
0, 1, 2
Let a = 2 + -3. Let g be (-8)/(-12) + a - -1. Factor 0*j + g*j**4 - 2/3*j**3 + 0 - 2/3*j**2 + 2/3*j**5.
2*j**2*(j - 1)*(j + 1)**2/3
Let b(a) = -84*a**4 - 24*a**3 + 69*a**2 + 24*a + 15. Let c(z) = 21*z**4 + 6*z**3 - 17*z**2 - 6*z - 4. Let l(q) = -4*b(q) - 15*c(q). Factor l(h).
3*h*(h - 1)*(h + 1)*(7*h + 2)
Let k(h) be the second derivative of -h**6/60 + 3*h**5/40 + h**4/12 - h**3 + 2*h**2 - 3*h. Determine y, given that k(y) = 0.
-2, 1, 2
Suppose -14 + 44 = 6*k. Let i(o) be the first derivative of 0*o**4 - 1/15*o**k + 1/9*o**3 + 0*o + 0*o**2 + 1. Let i(v) = 0. What is v?
-1, 0, 1
Suppose -2*f = 1 + 1. Let b(a) = 2*a**3 - 2*a. Let k(p) = p**2 - 1. Let o(r) = f*b(r) + 2*k(r). Find d such that o(d) = 0.
-1, 1
Let f be 2/12*-2*0. Let o(m) be the second derivative of -1/40*m**5 - 3*m + 0 + f*m**2 + 1/12*m**4 - 1/12*m**3. Determine i so that o(i) = 0.
0, 1
Let h(s) be the second derivative of s**6/40 - s**5/20 - 7*s**2/2 + 7*s. Let u(k) be the first derivative of h(k). Factor u(p).
3*p**2*(p - 1)
Let t(z) be the first derivative of -z**4/24 - z**3/18 + z**2/6 - 6. Suppose t(b) = 0. Calculate b.
-2, 0, 1
Let y(q) be the first derivative of 0*q**2 - 2 + 0*q**3 - 1/70*q**5 - 1/42*q**4 + 2*q. Let w(o) be the first derivative of y(o). Let w(k) = 0. Calculate k.
-1, 0
Let c = 72 + -143/2. Factor 3*s**2 - 2*s + c - 2*s**3 + 1/2*s**4.
(s - 1)**4/2
Let s(y) = -2*y**2 + 6*y + 5. Let c(d) = -d**2 + d + 1. Suppose 0 = -l - l - 8, -5*t = -l + 11. Let j(r) = t*c(r) + s(r). Solve j(w) = 0.
-2, -1
Factor 0 + 2/9*w**5 - 2/9*w**3 + 0*w**4 + 0*w + 0*w**2.
2*w**3*(w - 1)*(w + 1)/9
Let x(t) be the third derivative of -1/360*t**6 + 0*t + 0 + 0*t**4 - 1/252*t**7 - t**2 + 0*t**3 + 0*t**5. Let x(h) = 0. Calculate h.
-2/5, 0
Let h(f) be the first derivative of 0*f - 2 - 1/2*f**2 + 4/3*f**3 - 5/4*f**4 + 2/5*f**5. Solve h(c) = 0.
0, 1/2, 1
Suppose -k = 4*g + 14, 8*k - 3*k - 2*g - 18 = 0. Let p(u) be the first derivative of 1/2*u**4 - 2/3*u**3 + 2 + 0*u + 0*u**k. Find v, given that p(v) = 0.
0, 1
Let m be (20/12)/(10/4). Factor -m*h**3 + 0 + 2/3*h**2 + 0*h.
-2*h**2*(h - 1)/3
Suppose 0 = 4*f + 3*f. Let y(t) be the third derivative of 0*t**5 - t**2 + 0 + 0*t**7 + f*t + 1/72*t**4 + 0*t**3 - 1/180*t**6 + 1/1008*t**8. Factor y(p).
p*(p - 1)**2*(p + 1)**2/3
Let p(z) be the first derivative of -3*z**4/16 + 3*z**3/4 - 3*z**2/4 + 6. Suppose p(o) = 0. Calculate o.
0, 1, 2
Let h = 411/2 + -205. Factor -h + 7/4*f - 3/4*f**2.
-(f - 2)*(3*f - 1)/4
Let r(u) = 11*u**2 + 17*u + 11. Suppose 17*l - 12*l + 25 = 0. Let h(z) = -17*z**2 - 26*z - 17. Let q(n) = l*h(n) - 8*r(n). Find w, given that q(w) = 0.
-1
Let t(i) be the second derivative of 4/3*i**3 + 0 - 8*i**2 - 9*i - 1/12*i**4. Factor t(g).
-(g - 4)**2
Let i(t) be the third derivative of -1/60*t**4 + 0 - 3*t**2 + 1/300*t**6 + 0*t + 1/15*t**3 - 1/150*t**5. Factor i(b).
2*(b - 1)**2*(b + 1)/5
Let q be -1*(-1 - 1) - 2. Let a = -281/2 + 141. Factor r**3 + a*r**4 + q*r + 1/2*r**2 + 0.
r**2*(r + 1)**2/2
Factor 4/3*k**2 + 28/9*k + 8/9.
4*(k + 2)*(3*k + 1)/9
Let h(t) be the second derivative of -t**6/600 + t**5/50 - t**4/10 - t**3/6 - 5*t. Let m(b) be the second derivative of h(b). Factor m(a).
-3*(a - 2)**2/5
Suppose 5*c + 2*f = 30, -3*f = -3*c + 3 - 6. Let m(h) be the third derivative of 0*h + 4/21*h**3 + 0 + 3*h**2 + 2/21*h**c + 1/70*h**5. What is j in m(j) = 0?
-2, -2/3
Suppose 5*g = f + 1 - 11, 4*g = -4. Determine k so that -4*k**4 + 0*k**3 - 8*k**3 + 6*k**5 + 6*k**f = 0.
-2/3, 0, 1
Let h(u) be the first derivative of 2*u**3/15 + 6*u**2/5 + 18*u/5 + 3. Let h(s) = 0. Calculate s.
-3
Suppose -m = 4 + 1. Let g = m + 8. Factor -g*k - 17*k - 4 - 17*k**2 - 8*k**2.
-(5*k + 2)**2
Let z(n) be the third derivative of 0*n**3 - 5*n**2 - 1/180*n**5 + 0*n + 0 - 1/24*n**4. Factor z(x).
-x*(x + 3)/3
Let s = -4 - -14/3. Let q(c) be the second derivative of -s*c**2 - 5/9*c**3 + 0 - c - 1/6*c**4. Determine n so that q(n) = 0.
-1, -2/3
Determine y so that -64*y**3 - 2048/7*y - 4/7*y**5 + 1024/7 + 68/7*y**4 + 1408/7*y**2 = 0.
1, 4
Let y(d) = -d**2 - 8*d + 3. Let s be y(-8). Suppose -2*b - s*b = -20. Determine p, given that 4*p**2 - p - p + 52*p**2 - b = 0.
-1/4, 2/7
Let j(l) = l**4 + l**2 + l. Let i(k) = -9*k**4 - 6*k**3 - 9*k**2 - k + 4. Let t(a) = -2*i(a) - 14*j(a). Find d, give