be the second derivative of -1/10*z**5 + 1/3*z**3 + 0*z**4 + 0*z**2 + z + 0. Determine b so that i(b) = 0.
-1, 0, 1
Let r(g) be the second derivative of 1/98*g**7 - 3*g + 0 + 1/14*g**3 + 0*g**2 + 0*g**6 - 3/70*g**5 + 0*g**4. Determine k so that r(k) = 0.
-1, 0, 1
Suppose 1/2*l**3 - 1/2*l**2 + 1/4*l**4 - 1/4*l**5 - 1/4*l + 1/4 = 0. Calculate l.
-1, 1
Solve -6/7*i**2 + 2/7*i**3 - 2/7 + 6/7*i = 0.
1
Let l = -9 + 11. Factor 4*d**3 + 0*d**4 + 3*d**4 + 0*d**4 + 4*d**l - 2*d**4.
d**2*(d + 2)**2
Let t = 21 + -15. Find h such that -2*h**2 + 0*h**2 + 6*h - 10 + t = 0.
1, 2
Let j(b) be the third derivative of -27*b**5/80 + 3*b**4/16 - b**3/24 + 30*b**2. Factor j(y).
-(9*y - 1)**2/4
Let 4*l**2 - 5*l**3 - 2*l**5 - 34*l + 19*l**3 + 10*l - 16 = 0. Calculate l.
-2, -1, 2
Suppose 0 = 4*b - 8, 3*b - 15 = i - 4*i. Suppose 7*n = 2*n + 3*f - 5, 0 = -4*n + i*f - 7. Solve 0*p + 0 + 4/7*p**n + 6/7*p**3 = 0 for p.
-2/3, 0
Let h(j) be the third derivative of -j**8/1680 - j**7/280 - j**6/120 - j**5/120 - j**3/2 + 4*j**2. Let v(t) be the first derivative of h(t). Factor v(m).
-m*(m + 1)**3
Let o(i) be the third derivative of 0 - 1/120*i**4 - 1/100*i**5 - 1/200*i**6 - 1/1050*i**7 + 0*i**3 + 0*i + 5*i**2. Factor o(c).
-c*(c + 1)**3/5
Suppose 0 = -5*u - 5, -u - 1 - 4 = -i. Suppose -r + i + 0 = 0. Find y such that -5/2*y - 3/2*y**2 + 1/2*y**r - 1 + 1/2*y**3 = 0.
-1, 2
Suppose 10 = -w + 6*w. Determine t so that -1 - 2*t**2 + w - t**4 + t**4 + t**4 = 0.
-1, 1
Let h(c) be the first derivative of 13/4*c**4 + 3 - 5*c**3 - c + 7/2*c**2 - 4/5*c**5. Solve h(r) = 0 for r.
1/4, 1
Let i(t) = -20*t**2 - 25*t + 20. Let x(o) = 21*o**2 + 26*o - 20. Let g(q) = -6*i(q) - 5*x(q). Solve g(h) = 0 for h.
-2, 2/3
Let x be (24/(-14))/(1/(-7)). Let h be ((-24)/20)/(x/(-15)). Determine b, given that -3/4*b**2 + h*b - 3/4 = 0.
1
Let j(c) be the second derivative of -c**6/30 - 7*c**5/20 - 11*c**4/12 - 5*c**3/6 + 46*c. Factor j(f).
-f*(f + 1)**2*(f + 5)
Let r = -17 + 12. Let d = -2 - r. Factor 0*x**d - x**3 - 4*x + 5*x.
-x*(x - 1)*(x + 1)
Suppose -12 = -a - 2. Suppose 3*m - a = -4. Let 2*g + 4*g**m - 2*g**2 - 4*g**2 = 0. What is g?
0, 1
Let d(l) be the first derivative of l**8/560 - l**7/210 - l**6/360 + l**5/60 + l**3 + 1. Let f(g) be the third derivative of d(g). Factor f(b).
b*(b - 1)**2*(3*b + 2)
Let v(a) = -a**3 + 7*a**2 - 6*a + 2. Let o be v(6). Factor 0*f**2 + 2*f + f**2 + 0*f + 0*f**o.
f*(f + 2)
Factor 1/3*i**4 + 5/3*i**2 + 0 + 4/3*i**3 + 2/3*i.
i*(i + 1)**2*(i + 2)/3
Factor -2/5*y**3 - 96/5*y + 24/5*y**2 + 128/5.
-2*(y - 4)**3/5
Let y be (0 - (-1 - 1)) + 3. Let d(q) be the third derivative of 0*q - 1/6*q**3 + 0 - 1/16*q**4 - 3*q**2 - 1/120*q**y. Factor d(i).
-(i + 1)*(i + 2)/2
Let i be (1/(-2))/(-1 + -4). Let p(h) be the first derivative of 0*h**2 + 1 + 0*h**3 + 0*h + i*h**4. Determine g, given that p(g) = 0.
0
Let l(t) be the first derivative of -5 - 1/2*t**4 + 1/3*t**6 + 0*t**2 - 4/5*t**5 + 0*t + 4/3*t**3. Factor l(z).
2*z**2*(z - 2)*(z - 1)*(z + 1)
Let j = 3 + 0. Suppose 0 = 3*d - 2*d - 2. Factor -2*s**d + s**4 + s**j - s**2 - s + 2*s**2.
s*(s - 1)*(s + 1)**2
Let g = 3 + 2. Find c such that -c - g*c + 1 + 3*c**2 - 1 = 0.
0, 2
Let o = -80/3 + 27. Factor -o*v**4 + 1/3*v - v**2 + v**3 + 0.
-v*(v - 1)**3/3
Let z(u) be the third derivative of -u**5/30 - u**4/2 - 3*u**3 + 25*u**2. Let z(t) = 0. What is t?
-3
Let a = -9 + 4. Let n be (-3 + 1)/(-8 - a). Factor -2/3*k**2 - n - 4/3*k.
-2*(k + 1)**2/3
Let k(c) = c**4 + c**2 - c - 1. Let s(x) = 4*x**5 - 10*x**4 + 20*x**3 - 2*x**2 - 6*x - 6. Let v(w) = -6*k(w) + s(w). Factor v(n).
4*n**2*(n - 2)*(n - 1)**2
Let g(u) = -u**3 + u**2 + u + 1. Let k(y) be the first derivative of 7*y**4/4 - 7*y**3/3 - 3*y**2 - 6*y + 1. Let a(m) = 6*g(m) + k(m). Factor a(r).
r**2*(r - 1)
Factor 2/5*f**2 - 6/5*f + 4/5.
2*(f - 2)*(f - 1)/5
Let o(l) = 5*l**4 + 44*l**3 + 78*l**2 + 2*l + 2. Let v(h) = -35*h**4 - 310*h**3 - 545*h**2 - 15*h - 15. Let j(t) = -15*o(t) - 2*v(t). Find b such that j(b) = 0.
-4, 0
Let n(q) = 735*q**3 + 384*q**2 + 48*q + 33. Let i(z) = -46*z**3 - 24*z**2 - 3*z - 2. Let f(w) = -33*i(w) - 2*n(w). Factor f(l).
3*l*(4*l + 1)**2
Let l(q) be the first derivative of -q**6/180 - q**5/20 - q**4/6 + q**3/3 - 1. Let d(z) be the third derivative of l(z). Factor d(s).
-2*(s + 1)*(s + 2)
Suppose 16 = 4*p - 4*d, -3*p - 4*d = -2*p + 1. Factor 4/7*u**2 + 0 + 2/7*u + 2/7*u**p.
2*u*(u + 1)**2/7
Let v be (9/(-2))/((-24)/32). Let k(i) be the first derivative of 5*i**4 - 4*i - 4/5*i**5 - 5*i**2 - 5/3*i**v + 8/3*i**3 + 1. Find r such that k(r) = 0.
-1, -2/5, 1
Let w(r) be the second derivative of 0*r**2 - 1/14*r**7 + 0*r**3 + 3/20*r**5 - 6*r + 0 + 0*r**4 + 0*r**6. Factor w(a).
-3*a**3*(a - 1)*(a + 1)
Suppose -4*i + 12 = 4*m, 2*i - 4*m - 16 = 8. Factor -9*d**2 + 12*d - i*d**3 + 5 + 2 + 5 + 3*d**4.
3*(d - 2)**2*(d + 1)**2
Let o be 1*(3 - (1 - 0)). Factor -u - u**o + 2*u**2 - 2 + 4 + 4*u.
(u + 1)*(u + 2)
Let c be 111/6*(-3)/18. Let y = c - -15/4. Factor -8/3 - 1/3*u**3 + y*u**2 + 4/3*u.
-(u - 2)**2*(u + 2)/3
Let b be (((-12)/7)/6)/(1/(-6)). Solve -2/7*a**4 - b*a**2 - 8/7*a - 8/7*a**3 - 2/7 = 0 for a.
-1
Solve -8/21*k**2 + 46/21*k**3 + 0 - 8/7*k + 10/7*k**4 = 0.
-6/5, -1, 0, 2/3
Let r(f) be the second derivative of -5/54*f**4 + 2*f + 0 + 1/9*f**3 + 2/9*f**2. What is m in r(m) = 0?
-2/5, 1
Let g = 3 - -1. Let m(c) be the first derivative of 0*c - 1/3*c**3 - 4 - 1/2*c**g - 1/5*c**5 + 0*c**2. Factor m(u).
-u**2*(u + 1)**2
Factor 4/7*r**4 + 0*r - 2/7*r**5 - 2/7*r**3 + 0*r**2 + 0.
-2*r**3*(r - 1)**2/7
Suppose 3*w + 4*q = 324, -3*q = -w + 116 - 8. Let o = w - 77. Factor o*b**2 + 2 + 6*b - 2 - 10*b**2 + 9*b**3.
3*b*(b + 2)*(3*b + 1)
Let x(v) be the second derivative of -3/20*v**5 + 0*v**3 + 0*v**2 + 1/4*v**4 + 0 + 3*v. Solve x(g) = 0 for g.
0, 1
Let k(i) be the third derivative of 2/3*i**4 + 1/60*i**6 + 0*i + 4/3*i**3 + 1/6*i**5 - i**2 + 0. Let k(w) = 0. What is w?
-2, -1
Factor -4*x + 5*x**3 + 100*x**4 - 101*x**4 - 5 - x**3 + 6*x**2 + 0.
-(x - 5)*(x - 1)*(x + 1)**2
Let r(v) be the third derivative of 0*v**5 - 1/336*v**8 + 0*v**4 + 0*v - 2*v**2 + 0*v**3 + 0 + 1/210*v**7 + 1/60*v**6. Factor r(z).
-z**3*(z - 2)*(z + 1)
Let f = -17/53 + 577/477. Let -8/9*q**2 + 50/3*q**5 + f*q + 0 + 80/9*q**4 - 86/9*q**3 = 0. What is q?
-1, -1/3, 0, 2/5
Let y = 8384/7645 - 4/695. Let l = 82/55 - y. Factor -6/5*h**2 - 2/5*h**4 + 6/5*h**3 + l*h + 0.
-2*h*(h - 1)**3/5
Suppose -y = 3*y - 12. Factor -r**y - r**2 - r - r**4 + 2*r**3 + 2*r**2.
-r*(r - 1)**2*(r + 1)
Let v(s) = -5*s**2 + 4*s - 6. Let w(a) = -a**2 - a + 2. Let j(g) = v(g) + 3*w(g). Solve j(p) = 0.
0, 1/8
Let x(r) be the second derivative of 2*r + 1/12*r**4 + 0*r**3 - 1/2*r**2 + 0. Find c, given that x(c) = 0.
-1, 1
Let -2/11*a**2 - 4/11*a + 6/11 = 0. Calculate a.
-3, 1
Solve -8*u - 32*u**4 + 10*u**5 + 68/5*u**2 - 16/5 + 98/5*u**3 = 0.
-2/5, 1, 2
Let a(v) be the second derivative of v**7/126 + v**6/90 + 2*v. Find f, given that a(f) = 0.
-1, 0
Let y(a) be the third derivative of a**8/84 + 2*a**7/21 + a**6/3 + 2*a**5/3 + 5*a**4/6 + 2*a**3/3 - 7*a**2. Suppose y(d) = 0. Calculate d.
-1
Let v be 5/20*(-1)/(-75). Let t(g) be the third derivative of -v*g**5 + 0*g + 1/120*g**4 + 2*g**2 + 0*g**3 + 0. Factor t(h).
-h*(h - 1)/5
Suppose -22/3*g - 38/3*g**3 + 4*g**4 + 44/3*g**2 + 4/3 = 0. Calculate g.
1/2, 2/3, 1
Let q be (1 - 3) + (2 - -3). Suppose 0*l - q*l + 9 = 0. Factor -2*x**4 - 4*x**4 - 6*x**l + x**5 - 2*x**2 - 3*x**5.
-2*x**2*(x + 1)**3
Let c(y) be the second derivative of -y**4/4 + 5*y**3/2 - 9*y**2 - 2*y - 45. Factor c(f).
-3*(f - 3)*(f - 2)
Let m = -12 - -12. Let k(i) be the second derivative of -7/6*i**4 + i**2 + m - i - 1/2*i**3. Factor k(p).
-(2*p + 1)*(7*p - 2)
Let y be (-4)/6 + (-27)/(-40). Let a(x) be the third derivative of y*x**6 + 0*x**4 + 0*x**3 - 2*x**2 + 0*x - 1/60*x**5 + 0. Factor a(k).
k**2*(k - 1)
Let f = -1421 - -1423. Let -2/3 - 2/3*g**3 + 2/3*g**f + 2/3*g = 0. What is g?
-1, 1
Let w(y) be the third derivative of y**8/3024 + y**7/630 + y**6/540 - 2*y**2. Factor w(x).
x**3*(x + 1)*(x + 2)/9
Suppose 52 = -4*k - 5*n, 5*k + 40 = 2*n - 58. Let l = k + 39/2. Factor -3/2*s**2 - 1/2 + 1/2*s**3 + l*s.
(s - 1)**3/2
Let r(n) be the third derivative of 0 + 0*n**3 - 1/60*n**6 - 1/54*n**4 - 2*n**2 + 7/270*n**5 + 1/189*n**7 + 0*n - 1/1512*n**8. What