hird derivative of r(g). Suppose b(n) = 0. Calculate n.
-1, 0, 1
Let b(n) be the second derivative of 0 + 1/16*n**4 + 3/80*n**5 + 4*n - 1/40*n**6 + 0*n**2 - 1/8*n**3. Determine w so that b(w) = 0.
-1, 0, 1
Let t(p) be the third derivative of 0*p**3 + 1/735*p**7 + 0*p**6 + 0*p + 2*p**2 + 0 + 0*p**5 + 0*p**4. Factor t(a).
2*a**4/7
Let s(j) be the third derivative of -j**8/14 + 64*j**7/105 - 59*j**6/60 - 77*j**5/30 + j**4/4 + 3*j**3 - 38*j**2. Find k such that s(k) = 0.
-1/2, 1/3, 3
Let f be (-77)/(-98) - 1/2. Let y = f + 3/14. Factor 0 - 1/4*i**3 + y*i**2 - 1/4*i.
-i*(i - 1)**2/4
Let f(o) be the third derivative of 0*o**3 + 0*o**6 + 0*o**4 + 2*o**2 + 0*o + 0 + 1/336*o**8 - 1/210*o**7 + 0*o**5. Solve f(j) = 0 for j.
0, 1
Let y(q) be the first derivative of q**4/8 - q**3/3 - 3*q**2/4 - 2. Factor y(j).
j*(j - 3)*(j + 1)/2
Let c(s) be the first derivative of -9/4*s**2 + 1 - 1/2*s**3 - 3*s. Find f such that c(f) = 0.
-2, -1
Let c = 121237/30 + -4049. Let v = 49/6 + c. Suppose -8/5*h + v*h**4 + 2/5 - 8/5*h**3 + 12/5*h**2 = 0. What is h?
1
Let m(h) = h**2 + 2*h + 2. Let g be m(-2). Let f(l) = -l**2 - 3*l + 4. Let j be f(-3). Factor -q**4 + 0*q**4 + 2*q**3 + g*q**5 + 2*q**2 - 4*q**3 - q**j.
2*q**2*(q - 1)**2*(q + 1)
Let d(b) = -b**3 - 7*b**2 - 3*b - 5. Let r be d(-8). Let n = 499/6 - r. Suppose 1/3 + 7/6*o + n*o**4 + 5/6*o**3 + 3/2*o**2 = 0. Calculate o.
-2, -1
Let f(t) be the second derivative of t**6/60 + t**5/40 - 14*t. Factor f(j).
j**3*(j + 1)/2
Let a(m) = -5*m**3 - 8*m**2 - 5*m + 2. Let c(z) = 66*z**3 + 105*z**2 + 66*z - 27. Let b(u) = 27*a(u) + 2*c(u). Factor b(y).
-3*y*(y + 1)**2
Let p(i) = -i**2 - 3*i + 4. Let l = -3 - -3. Suppose 3*t + 3*w + 3 - 9 = l, -4*w = 3*t - 7. Let h(o) = o - 1. Let x(m) = t*p(m) + 3*h(m). Solve x(q) = 0.
-1, 1
Let c(n) = -n**2 + n + 2. Let r be c(2). Factor 2/5*z**2 + r*z + 0.
2*z**2/5
Let y(i) be the second derivative of -25*i**7/42 + 29*i**5/20 - 2*i**3/3 + 16*i. What is d in y(d) = 0?
-1, -2/5, 0, 2/5, 1
Let w(d) be the third derivative of 0 + 1/27*d**3 + 5*d**2 - 7/108*d**4 + 0*d + 1/45*d**5. What is g in w(g) = 0?
1/6, 1
Let i = -240 - -963/4. Solve -3/4*l**2 + i*l + 0 = 0.
0, 1
Factor 4/5*v**3 + 0 + 8/5*v**2 - 12/5*v.
4*v*(v - 1)*(v + 3)/5
Let u(i) be the second derivative of i**6/10 + 9*i**5/20 + 3*i**4/4 + i**3/2 + i. Determine o, given that u(o) = 0.
-1, 0
Suppose -5*b = -0*b - 10. Suppose 4*c - x + 1 - 11 = 0, -10 = -b*c + 3*x. Factor -4*v**2 + 2*v**c - 2*v**2 + 2*v**3.
2*v**2*(v - 2)
Let g be 26/4 + 1/(-2). Suppose 3*b = -4*z + 26, -z + 7 + g = 4*b. Find d such that 2/3*d**4 - 4/3*d**3 + 2/3*d + 2/3*d**z - 4/3*d**2 + 2/3 = 0.
-1, 1
Let y(g) be the second derivative of -g**8/2240 + g**7/210 - g**6/48 + g**5/20 - g**4/2 - 6*g. Let i(n) be the third derivative of y(n). Solve i(o) = 0.
1, 2
Suppose 5*h - 5 = -0*h. Let i = 1 + h. Solve 1 + 0*m - m**4 + 2*m + i*m**3 - 4*m = 0 for m.
-1, 1
Let w be 1 + (9/(-2))/9. Let n(x) be the first derivative of 1 + 1/4*x**3 + 1/4*x + w*x**2. Factor n(q).
(q + 1)*(3*q + 1)/4
Let c(i) = i + 10. Let v be c(-7). Factor -4*k**3 + 3*k**v - 3 - 2*k**3 + 3*k + 3*k**2.
-3*(k - 1)**2*(k + 1)
Let p be (-3)/(-15) + 208/160. Factor -p*r**2 - r - 1/4 - r**3 - 1/4*r**4.
-(r + 1)**4/4
Let f(y) = y**2 + y**3 - y**2 + y. Let t(u) be the second derivative of -u**5/10 - u**4/12 - u**3/2 - 9*u. Let g(d) = -3*f(d) - t(d). Factor g(r).
-r**2*(r - 1)
Let v(c) be the second derivative of -c**8/3360 - c**7/840 + c**5/120 + c**4/48 - c**3/3 + 3*c. Let s(u) be the second derivative of v(u). Factor s(n).
-(n - 1)*(n + 1)**3/2
Let z(l) be the third derivative of -l**5/270 - l**4/108 + l**2. Factor z(y).
-2*y*(y + 1)/9
Let a(v) be the first derivative of 3/5*v**3 + 5 + 0*v + 3/20*v**4 + 0*v**2. Solve a(c) = 0 for c.
-3, 0
Let z(l) = -13*l**3 - 15*l**2 - 36*l - 9. Let r(v) = 6*v**3 + 8*v**2 + 18*v + 4. Let m(k) = 9*r(k) + 4*z(k). Find h such that m(h) = 0.
-3, 0
Factor 12*t + 1/2*t**3 + 9/2*t**2 + 8.
(t + 1)*(t + 4)**2/2
Suppose l - 8 = -3*l. Let a = l - -3. Solve -7/3*f**4 + 2/3*f**3 - 1/3 - 4/3*f**a + 2/3*f + 8/3*f**2 = 0 for f.
-1, 1/4, 1
Let x = 5 - 2. Factor -x*z**2 + 4*z + 2*z**2 - 2 - 2.
-(z - 2)**2
Let i be (-46)/(-24) - 2/(-6). Suppose -3*r = -7*r. Factor r - 1/2*j - 3*j**3 + 5/4*j**4 + i*j**2.
j*(j - 1)**2*(5*j - 2)/4
Let o(b) be the first derivative of -b**7/560 - b**6/120 + b**5/80 + b**4/8 + 3*b**3 - 5. Let z(f) be the third derivative of o(f). Find u such that z(u) = 0.
-2, -1, 1
Let q(m) be the second derivative of 2*m - 1/15*m**3 + 1/30*m**4 + 0 + 0*m**2. Factor q(b).
2*b*(b - 1)/5
Let d(g) be the first derivative of g**6/5 - g**5/5 - 7*g**4/16 - g**3/4 + 2*g**2 + 5. Let z(f) be the second derivative of d(f). Factor z(y).
3*(y - 1)*(4*y + 1)**2/2
Let v = 2/3 - 1/6. Factor 0 + 0*w**2 + 0*w - v*w**3.
-w**3/2
Let s(u) be the second derivative of 5*u + 0 + 1/12*u**3 - 1/40*u**5 + 0*u**2 + 0*u**4. Determine q, given that s(q) = 0.
-1, 0, 1
Suppose 69 = -2*z - 91. Let k be 10/25 - (-12)/z. Factor -1/4*r**2 - 1/4*r + k + 1/4*r**3.
(r - 1)**2*(r + 1)/4
Let o(v) be the third derivative of -7*v**5/300 + v**4/60 - 12*v**2. Factor o(c).
-c*(7*c - 2)/5
Let u(i) be the first derivative of -3*i**5/25 + 9*i**4/20 - 2*i**3/5 + 3. Factor u(r).
-3*r**2*(r - 2)*(r - 1)/5
Let s = 2/115 + -5/552. Let m(o) be the third derivative of 0*o**4 + 0*o + 1/20*o**5 + s*o**6 + 0 + 2*o**2 - 2/3*o**3. Factor m(x).
(x - 1)*(x + 2)**2
Let n(a) be the second derivative of -1/90*a**6 + 0*a**3 + 0*a**2 + 0 + 1/36*a**4 + 0*a**5 - a. Suppose n(c) = 0. What is c?
-1, 0, 1
Determine y so that 1/3*y + 1/6*y**2 + 1/6 = 0.
-1
Suppose -3*n + h + 0 = 1, -n + 4*h - 4 = 0. Let b be (1 - n)/((-1)/(-6)). Factor 9*k**4 - b*k**3 - 3*k**2 - 3*k**2 + 3*k**2 + 4*k**2 - 4*k**5.
-k**2*(k - 1)**2*(4*k - 1)
Let q(g) = -g**3 - 3*g**2 + g - 2. Let d be q(-2). Let o = 11 + d. Find h, given that -1/2*h**2 - 1/4 + 3/4*h - 1/4*h**5 + 3/4*h**4 - 1/2*h**o = 0.
-1, 1
Let h(t) be the third derivative of 0 - 1/96*t**4 - 1/24*t**3 + 4*t**2 + 1/240*t**5 + 0*t + 1/480*t**6. Suppose h(c) = 0. Calculate c.
-1, 1
Suppose -4*u + 3*n = -6, 3*u = 44*n - 46*n - 4. Factor 1/2*k + 1/3*k**2 + u - 1/6*k**3.
-k*(k - 3)*(k + 1)/6
Let m = -55 - -497/9. Determine y so that 0*y + m*y**4 + 0 - 4/9*y**3 + 2/9*y**2 = 0.
0, 1
Let g(w) be the second derivative of w**5/4 + 25*w**4/12 + 20*w**3/3 + 10*w**2 + 20*w. Solve g(r) = 0 for r.
-2, -1
Determine x so that -6*x**2 - 7*x - 5/2 - x**3 + 1/2*x**4 = 0.
-1, 5
Suppose 5*u = -4*z + 184, 3 = z + 2*z. Factor -8*r - r**3 - 5*r**3 + 0*r**3 + 40*r**2 - u*r**3.
-2*r*(3*r - 2)*(7*r - 2)
Let p = 382/297 + -20/27. Factor -6/11*c**3 - p*c**2 + 0 - 2/11*c - 2/11*c**4.
-2*c*(c + 1)**3/11
Let a = -2 + 6. Suppose 2*v**2 - 4 + a*v - 9*v + 3*v = 0. What is v?
-1, 2
Let u be ((-44)/(-6))/(3/(-54)). Let d be -3*(u/(-9))/4. Let q(v) = 5*v**2 - 18*v - 12. Let z(c) = -2*c**2 + 6*c + 4. Let x(r) = d*z(r) - 4*q(r). Factor x(s).
2*(s + 1)*(s + 2)
Let s(n) be the second derivative of -3/35*n**5 + 0 - 4/105*n**6 - 1/21*n**3 + 3*n + 0*n**2 - 2/21*n**4 - 1/147*n**7. Factor s(t).
-2*t*(t + 1)**4/7
Let d(x) = x**4 + x**3 + x**2 - x - 1. Let b(k) = 3*k**4 - 2*k**2 + 1. Let n(j) = -b(j) + 2*d(j). What is a in n(a) = 0?
-1, 1, 3
Let p be (-82)/(-110) - (-1)/(-5). Let a = -13/44 + p. Find r such that 0 + 0*r**2 + a*r - 1/4*r**3 = 0.
-1, 0, 1
Factor -3/4 + 3/2*n - 3/4*n**2.
-3*(n - 1)**2/4
Suppose 3 = 3*c - 15. Suppose 2*f - 2*s + 4 = 0, 8 = -3*f + 5*s - c. Factor -2*z**2 + 0*z**3 - 2*z**5 + 2*z**3 + 4*z**4 - f*z**4.
-2*z**2*(z - 1)**2*(z + 1)
Let i(l) = -2*l**2. Let y be i(0). Let w = -23 + 93/4. Find h such that -1/4 + y*h + w*h**2 = 0.
-1, 1
Let v = 40 + 20. Let g be (-10)/v + 2/4. Determine z, given that 1/3 + 0*z - g*z**2 = 0.
-1, 1
Find a such that 4/7*a**2 - 10/7*a + 4/7 = 0.
1/2, 2
Suppose -3 = 3*l - 5*c, -l + 5 = -2*c + 7. Suppose -2/3*h**3 + 1/3*h + 1/3*h**5 + 0 + 0*h**2 + 0*h**l = 0. What is h?
-1, 0, 1
Suppose -22/13*c**4 - 6/13*c**5 + 4/13*c + 0 - 2/13*c**2 - 22/13*c**3 = 0. Calculate c.
-2, -1, 0, 1/3
Let d(c) be the first derivative of 9*c**6/2 + 99*c**5/5 + 69*c**4/2 + 30*c**3 + 27*c**2/2 + 3*c - 1. Factor d(x).
3*(x + 1)**3*(3*x + 1)**2
Let g be 3*(3 + -1) + 3. Factor -5*t**2 - 3*t + 5 + 13*t**2 - g + 7*t.
4*(t + 1)*(2*t - 1)
Let s(d) be the first deri