i. Determine q, given that y(q) = 0.
-1, 0, 2
Let v(r) be the first derivative of -r**3/15 + r**2/10 + 2*r/5 - 17. Find y, given that v(y) = 0.
-1, 2
Let g(r) = -r**4 - r**2 + 1. Let y(z) = -40*z**4 - 150*z**3 - 150*z**2 - 30*z + 5. Let t(i) = -5*g(i) + y(i). Suppose t(d) = 0. What is d?
-3, -1, -2/7, 0
Suppose 0*p + 10 = 2*p. Let w = 10 - p. Factor 9*m**2 - 10*m**2 - 2*m**3 - 4 - m + w + 3*m**3.
(m - 1)**2*(m + 1)
Let t(f) = -5*f**5 - 12*f**4 - 13*f**3 - 3*f**2 + 3*f + 3. Let k(c) = c**4 - c**3 - c**2 + c + 1. Let b(y) = -3*k(y) + t(y). Determine o, given that b(o) = 0.
-2, -1, 0
Let 464 + 4*n**2 - 47*n - 17*n - 208 = 0. Calculate n.
8
Factor 3/2*y**2 + 1/4*y**3 + 0*y + 0.
y**2*(y + 6)/4
Let k be (27/12)/((-3)/(-8)). Suppose -v + k*x - 2 = 2*x, 4*v + 2*x = 10. Factor y**2 + 3*y**4 + 2*y - y**4 - 3*y**2 - v*y**3.
2*y*(y - 1)**2*(y + 1)
Let o(t) = 2*t**2 - 29*t - 16. Let l(i) = 3*i**2 - 30*i - 15. Let m(s) = 5*l(s) - 6*o(s). Factor m(x).
3*(x + 1)*(x + 7)
Let x(u) be the second derivative of u**9/3024 + u**8/840 + u**7/840 - u**3/6 + u. Let f(g) be the second derivative of x(g). Suppose f(i) = 0. Calculate i.
-1, 0
Let s(j) be the second derivative of 0*j**2 + 4*j - 1/10*j**5 + 0 + 0*j**3 + 0*j**4. Factor s(r).
-2*r**3
Let m(t) be the first derivative of 0*t + 1/9*t**3 + 1 + 1/6*t**2. Factor m(h).
h*(h + 1)/3
Let x(f) be the second derivative of 0*f**4 + 1/84*f**7 - 5/36*f**3 + 1/6*f**2 - 2*f + 0 - 1/18*f**6 + 1/12*f**5. Suppose x(m) = 0. What is m?
-2/3, 1
Let k be 6*1 - (-2 - -2). Suppose -3*q + 48 + 39 = 2*s, -5*q + 3*s + 164 = 0. Factor -56*r**3 - 38 - r**4 - r + 11*r**4 - q*r + 96*r**2 + k.
2*(r - 2)**3*(5*r + 2)
Let u(w) = w**2 + 1. Let k(m) = -m**2 + 2*m - 5. Let x(a) = -k(a) - 5*u(a). Let h = 1 - 0. Let c(q) = q**2 - q. Let s(z) = h*x(z) + c(z). Factor s(f).
-3*f*(f + 1)
Factor 0 + 2*q + 1/2*q**2.
q*(q + 4)/2
Let d be (-12 + 434/35)*(-1 + 6). Factor 4/7 + 2/7*o**4 + 10/7*o**3 + 2*o + 18/7*o**d.
2*(o + 1)**3*(o + 2)/7
Let g(k) be the third derivative of k**7/1785 - k**6/1020 - k**5/510 + k**4/204 - 11*k**2. Factor g(m).
2*m*(m - 1)**2*(m + 1)/17
Let b(k) = k**2 - 4*k**3 - k + 7*k**2 - 3*k**2. Let n(q) = 7*q**3 - 9*q**2 + 2*q. Let z(u) = -10*b(u) - 6*n(u). Factor z(i).
-2*i*(i - 1)**2
Factor 1/4*v**3 + v**2 + 3/4*v + 0.
v*(v + 1)*(v + 3)/4
Let r(b) = -5*b**2 + 3*b - 1. Let c be (-2*9/(-6))/1. Let n(z) = z - 2 + z**2 - 7*z**2 + 3*z. Let a(j) = c*n(j) - 4*r(j). Factor a(s).
2*(s - 1)*(s + 1)
Let j be ((-4348)/44 - 0)/1. Let z = 99 + j. Determine o so that -8/11*o**3 + 0 + 10/11*o**2 - z*o = 0.
0, 1/4, 1
What is w in 0 - 27/4*w**2 + 9/4*w**3 + 15/4*w + 3/4*w**4 = 0?
-5, 0, 1
Let i(k) = k**2 + 3 - 2*k + 0*k**2 + 2*k - 4*k. Let h be i(3). Let h + 1/4*y - 1/4*y**2 = 0. Calculate y.
0, 1
Let n be (-6)/((-21)/6 + 2). Factor 8*g**3 - 8*g**2 - 15*g - n*g**2 + 12*g**4 + 7*g.
4*g*(g - 1)*(g + 1)*(3*g + 2)
Let i(x) = x**3 - 8*x**2 + 2*x - 11. Let d be i(8). Suppose -3 - d = -2*a. Let r**3 - 7*r - 6*r**5 + r - 2 - 2*r**4 + 11*r**3 + a*r**2 = 0. Calculate r.
-1, -1/3, 1
Let j(v) be the third derivative of -3*v**8/112 - 5*v**7/14 - 2*v**6 - 6*v**5 - 10*v**4 - 8*v**3 - 12*v**2. Solve j(f) = 0.
-2, -1/3
Let t = 137/1170 + -2/117. Let b(j) be the first derivative of 0*j**2 - 2/15*j**3 - 2 + t*j**4 + 0*j. Solve b(y) = 0 for y.
0, 1
Let t be (858/24)/(-13) - (-2 + -1). Factor -1/4*x + t - 1/4*x**2 + 1/4*x**3.
(x - 1)**2*(x + 1)/4
Let q(u) = 5*u**4 + 13*u**3 + u**2 - 5*u + 7. Let j(b) = 2*b**4 + 6*b**3 - 2*b + 3. Let c(h) = -7*j(h) + 3*q(h). What is v in c(v) = 0?
0, 1
Let z(v) be the second derivative of v**8/4200 + v**7/2100 - v**3/3 - v. Let i(s) be the second derivative of z(s). Find n such that i(n) = 0.
-1, 0
Let j(i) = -7*i - i**3 + 3*i**4 - 6*i**4 + 2 + 3 + 11*i**2. Let m(t) = t**4 + t**3 - 5*t**2 + 3*t - 2. Let r(q) = -2*j(q) - 5*m(q). Solve r(x) = 0.
0, 1
Let z(j) = 3*j**2 + 8*j + 9. Let m be z(-6). Let q be 6/(-2) - m/(-21). Let q*p + 2/7 - 2/7*p**3 - 2/7*p**2 = 0. Calculate p.
-1, 1
Let 0 + 0*t - 1/11*t**2 + 1/11*t**4 + 0*t**3 = 0. Calculate t.
-1, 0, 1
Suppose v - 13 = -4*v + 3*w, 5*v + 4*w = 6. Factor -v*a**2 + 3*a**2 + 0*a**2 - 1.
(a - 1)*(a + 1)
Suppose 14*a - 17*a + 9 = 0. Let x(d) be the second derivative of 2*d + 0*d**2 + 1/16*d**4 - 3/40*d**6 - 3/20*d**5 + 0 + 1/4*d**a. Factor x(w).
-3*w*(w + 1)**2*(3*w - 2)/4
Suppose 0 = -l + 7 + 1. Factor -l*k + k**5 + 8*k - 4*k**4 + 3*k**3 + k**4 - k**2.
k**2*(k - 1)**3
Let 1/3*h + 1/3*h**5 - 1/3 + 2/3*h**2 - 2/3*h**3 - 1/3*h**4 = 0. What is h?
-1, 1
Let r(f) = -f + 21. Let w be r(5). Suppose -3 = g - 4*c - 0, -4*g + 2*c + w = 0. Find i such that 0 + 2/7*i**2 - 6/7*i**3 + 4/7*i - 2/7*i**4 + 2/7*i**g = 0.
-1, 0, 1, 2
Let v(u) be the second derivative of -u**8/6720 - u**7/2520 + 5*u**4/12 - u. Let j(l) be the third derivative of v(l). Suppose j(t) = 0. What is t?
-1, 0
Let p(n) be the first derivative of n**6/1080 + n**5/360 + 2*n**3/3 + 1. Let d(w) be the third derivative of p(w). Factor d(q).
q*(q + 1)/3
Let w be -1*2/1 + (-10)/(-5). Suppose -2*m**3 + 8/3*m**4 + 4/9*m**2 + w*m - 10/9*m**5 + 0 = 0. Calculate m.
0, 2/5, 1
Let u(m) be the first derivative of m**3/7 - 12*m**2/7 + 48*m/7 - 5. Factor u(b).
3*(b - 4)**2/7
Let a(q) be the third derivative of q**8/1008 + q**7/630 - q**6/120 - q**5/36 - q**4/36 + 9*q**2. Factor a(x).
x*(x - 2)*(x + 1)**3/3
Let a(i) = 3*i**4 - 5*i**3 - 10*i**2 + 12. Let j(w) = -w**4 + w**2 + w - 1. Let o(d) = -a(d) - 4*j(d). Factor o(v).
(v - 1)*(v + 2)**3
Let h = -1 + 4. Let a(l) be the first derivative of 0*l - 3 - 1/3*l**h + 0*l**2. Factor a(j).
-j**2
Suppose -4*s - b = -7, 4*b - 6 + 14 = 2*s. Let x = 7 - 7. Let -n**s + 1/2*n**4 + 1/2 + 0*n + x*n**3 = 0. What is n?
-1, 1
Let t be ((-8)/(-12))/(28/48). Factor 4/7*n**2 - 12/7*n + 4/7*n**4 + 12/7*n**3 - t.
4*(n - 1)*(n + 1)**2*(n + 2)/7
Let y(z) be the third derivative of -z**8/10080 + z**7/840 - z**6/180 + z**5/30 - 3*z**2. Let g(h) be the third derivative of y(h). Find l such that g(l) = 0.
1, 2
Let v = 4 + -2. Let a(t) be the second derivative of 0*t**3 + 2*t + 0 + 0*t**v - 1/12*t**4. Solve a(b) = 0 for b.
0
Factor -1/2*o**2 - 2 + 5/2*o.
-(o - 4)*(o - 1)/2
Let s(a) = a**5 - a**4 + a**3. Let m(v) = -4*v**5 + 4*v**4 - 24*v**3 - 22*v**2 - 8*v. Let k(i) = m(i) + 6*s(i). Determine t, given that k(t) = 0.
-1, 0, 4
Let y = -13 + 16. Factor -n**3 - 1 - 2*n - 2*n**2 + 3 + 3*n**y.
2*(n - 1)**2*(n + 1)
Factor -74 + 2*w**4 + 103*w**2 - 22*w**3 - 32*w - 31*w**2 - 54.
2*(w - 4)**3*(w + 1)
Let r be (-6 - -7)*(-2 - -2). Let s(x) be the third derivative of 1/20*x**5 + r*x + 0 + 5/24*x**4 + x**2 + 1/3*x**3. Determine d so that s(d) = 0.
-1, -2/3
Let b(q) be the third derivative of 1/36*q**4 + 1/18*q**3 - q**2 + 1/180*q**5 + 0*q + 0. Find v, given that b(v) = 0.
-1
Suppose 4*h + 22 - 74 = 0. Suppose -4 + h = p. Solve -2 + 6*j**5 + p*j**5 - 12*j**5 + 13*j + 32*j**3 - 16*j**4 - 30*j**2 = 0 for j.
1/3, 1, 2
Let c = 31 + -277/9. What is i in 4/9*i**3 - c*i + 0*i**2 + 0*i**4 - 2/9*i**5 + 0 = 0?
-1, 0, 1
Let k be 0/((8 + -2)*1). Determine i, given that k + 0*i - 2/9*i**2 + 2/9*i**5 - 2/3*i**4 + 2/3*i**3 = 0.
0, 1
Let u(p) be the first derivative of -2/7*p - 5 + 2/7*p**2 - 2/21*p**3. Factor u(y).
-2*(y - 1)**2/7
Let d(l) = l - 3. Let b be d(4). Factor 0*g + 5*g + g**2 + g - 4*g + b.
(g + 1)**2
Let o(x) be the second derivative of x**4/14 - x**3/21 - 2*x**2/7 - 35*x. Factor o(l).
2*(l - 1)*(3*l + 2)/7
Let i(h) = 3*h**4 + 37*h**3 + 24*h**2 - 32*h - 27. Let b(z) = -2*z**4 - 18*z**3 - 12*z**2 + 16*z + 14. Let l(r) = 5*b(r) + 2*i(r). Factor l(w).
-4*(w - 1)*(w + 1)*(w + 2)**2
Let b(n) be the first derivative of -4*n**5/5 + 37*n**4 - 624*n**3 + 4320*n**2 - 6912*n + 7. Let b(v) = 0. What is v?
1, 12
Let a be 1 - (231/39)/7. Factor 2/13*d - a*d**3 - 2/13*d**2 + 2/13.
-2*(d - 1)*(d + 1)**2/13
Let p(t) = -t**3 - t**2 + t - 1. Let b(w) = -3*w**3 - 8*w**2 - 7*w - 4. Let v(g) = 5*b(g) - 5*p(g). What is c in v(c) = 0?
-3/2, -1
Factor 1/11*o**2 - 1/11*o + 1/11*o**3 - 1/11.
(o - 1)*(o + 1)**2/11
Let o(y) be the third derivative of 0*y**3 + 0 - 1/60*y**5 + 1/120*y**6 + 1/210*y**7 + 0*y - 3*y**2 - 1/336*y**8 + 0*y**4. Suppose o(a) = 0. What is a?
-1, 0, 1
Let u(l) be the first derivative of l**5/30 + l**4/8 + l**3/18 - l**2/4 - l/3 - 13. Factor u(m).
(m - 1)*(m + 1)*