so that 1/2*o**2 + 1/4*o**3 - y*o - 1/2 = 0.
-2, -1, 1
Let j(r) be the second derivative of -r**4/4 + 4*r**3 - 21*r**2/2 - 10*r. Suppose j(i) = 0. What is i?
1, 7
Let d = -1061/2 + 532. Let v = 7 + -11/2. Factor 0 + v*j - d*j**2.
-3*j*(j - 1)/2
Let a = -726/5 + 529/5. Let b = -39 - a. Determine i so that -6/5*i**2 + 4/5*i**4 + 2/5 - b*i + 2/5*i**3 = 0.
-1, 1/2, 1
Let g = -226/3 - -76. Let k = -18 + 21. Factor 0*o**2 + 0 + g*o**k - 2/3*o.
2*o*(o - 1)*(o + 1)/3
Let s(o) be the first derivative of -o**5/35 - o**4/7 - 2*o**3/21 + 2*o**2/7 + 3*o/7 + 55. Determine k so that s(k) = 0.
-3, -1, 1
Let a(b) = -5*b**4 + 0*b**2 + 4*b**4 - 2*b**2 - b**3 + 3*b**2. Let k(y) = 16*y**4 + 18*y**3 - 12*y**2. Let h(g) = 28*a(g) + 2*k(g). Factor h(n).
4*n**2*(n + 1)**2
Determine f so that 9*f**2 + 3 - 2 - 2 + 6*f - 2 = 0.
-1, 1/3
Let b(p) = -18*p**2 + 12*p + 5. Let j(w) = -w**2 - w + 1. Let v(q) = -4*b(q) + 44*j(q). Factor v(y).
4*(y - 3)*(7*y - 2)
Let z be (8/(64/(-3)))/(-15). Let a(d) be the second derivative of 0 - 1/12*d**3 + 1/4*d**2 + z*d**5 - 1/24*d**4 - d. Factor a(p).
(p - 1)**2*(p + 1)/2
Let c(i) be the first derivative of -2*i**5/25 + 2*i**3/15 + 15. Factor c(b).
-2*b**2*(b - 1)*(b + 1)/5
Solve 0 + 4/5*d - 56/5*d**4 - 34/5*d**2 + 86/5*d**3 = 0 for d.
0, 1/4, 2/7, 1
Let d(t) be the second derivative of -t**6/10 + 9*t**5/20 - t**4/2 + 9*t. Factor d(z).
-3*z**2*(z - 2)*(z - 1)
Let a(i) be the third derivative of i**5/150 + i**4/20 + 2*i**3/15 + 2*i**2. What is w in a(w) = 0?
-2, -1
Let d = -9 + 16. Let s(a) be the third derivative of 0 + 0*a + 0*a**4 + 1/84*a**6 + 0*a**3 + a**2 - 1/105*a**5 + 1/105*a**d. Factor s(z).
2*z**2*(z + 1)*(7*z - 2)/7
Let x(i) be the first derivative of 2*i**3/21 + 2*i**2/7 - 6*i/7 - 4. Factor x(h).
2*(h - 1)*(h + 3)/7
Let f = -7 - -16. Factor 9*m**5 - 5*m + f*m**3 + 2*m - 27*m**4 + 9*m**3 + 3*m**4.
3*m*(m - 1)**3*(3*m + 1)
Let d be (-130)/(-84) - (-1 + 2). Let g = d - 1/21. Solve 0 - g*t**2 - 1/2*t = 0 for t.
-1, 0
Let m be (-4 - -4)/(-1 - -2). Suppose -5*g + 4 = h - m, 5*g - h = -4. Factor 0 + g*f - 2/3*f**5 + 2/3*f**3 + 2/3*f**4 - 2/3*f**2.
-2*f**2*(f - 1)**2*(f + 1)/3
Let l(m) = -2*m - 6. Let a be (20/(-6)*3)/2. Let i be l(a). Factor 19*w**3 + 0*w + 2*w - 40*w**i + 13*w**2 + 16*w**5 - 10*w**3.
w*(w - 2)*(w - 1)*(4*w + 1)**2
Suppose -4*w + 1 = -3. Let m(k) be the first derivative of 3/2*k**4 + 1/3*k**6 + 6/5*k**5 + 0*k + 0*k**2 + 2/3*k**3 + w. Factor m(b).
2*b**2*(b + 1)**3
Let c be -3*(-3)/360*(-2)/(-1). Let d(g) be the second derivative of 0*g**2 + c*g**5 - 1/12*g**4 + 0 + 0*g**3 - 4*g. Factor d(l).
l**2*(l - 1)
Let y(p) be the third derivative of 8*p**2 - 1/9*p**3 + 0 + 1/90*p**5 + 0*p**4 + 0*p. Let y(a) = 0. What is a?
-1, 1
Suppose -6*s + 7 = s. Let i(z) be the first derivative of -s + 0*z**2 - 1/12*z**3 + 1/4*z. Let i(d) = 0. Calculate d.
-1, 1
Let a(w) be the second derivative of -w**6/180 - w**5/20 - w**4/6 - w**3/3 + 2*w. Let x(b) be the second derivative of a(b). Factor x(r).
-2*(r + 1)*(r + 2)
Let f(g) be the first derivative of -g**5/10 - g**4/2 - 2*g**3/3 + 2*g - 4. Let j(i) be the first derivative of f(i). Factor j(u).
-2*u*(u + 1)*(u + 2)
Let m = -14 - -21. Let h = m - 4. Factor 1/2*j**4 + 1/2*j**2 - j**h + 0*j + 0.
j**2*(j - 1)**2/2
Factor -4*g**2 - 2*g + 16 + 22*g + 8*g**2.
4*(g + 1)*(g + 4)
Let j(g) = -g + 7. Let p be j(-8). Suppose -2*z + p*z**2 + 10*z + 9*z**2 + 18*z**3 + 4*z**4 = 0. What is z?
-2, -1/2, 0
Let h(r) be the first derivative of -6*r**6/7 - 12*r**5/7 - r**4 - 4*r**3/21 + 21. Determine s so that h(s) = 0.
-1, -1/3, 0
Suppose 0 = -4*n + 5*i + 12 - 46, 4*i - 26 = 3*n. Let q be (3/(-27))/(2/n). Determine h so that -1/3*h - q*h**2 + 0 = 0.
-1, 0
Let g(q) = -q**2 + 9*q. Let a be g(7). Let n be a/24 - (-2)/(-8). Factor n*c - 1/3*c**3 + 0 - 1/3*c**2 + 1/3*c**4.
c*(c - 1)**2*(c + 1)/3
Let l(m) be the first derivative of m + 0*m**2 + 1 + 0*m**4 + 1/40*m**5 + 1/60*m**6 + 0*m**3. Let s(y) be the first derivative of l(y). Solve s(n) = 0 for n.
-1, 0
Suppose 0 = -d + 3*v + 18, 13*d = 9*d - 5*v - 13. Factor 2/9*t**d + 2/9*t**4 + 0 + 0*t - 4/9*t**2.
2*t**2*(t - 1)*(t + 2)/9
Let u(o) = -o**3 + 4*o**2 + o + 20. Let b be u(5). Factor 0*g + 0*g**2 + b + 12/5*g**4 + 4/5*g**3.
4*g**3*(3*g + 1)/5
Let y be (-66)/(-2)*(3 - 2). Let a be 6/14*286/y. Solve -4/7*s + a*s**2 - 6*s**3 + 0 = 0 for s.
0, 2/7, 1/3
Let r(v) be the second derivative of 0*v**4 + 0 + 7*v - 1/5*v**5 - v**2 + 1/15*v**6 + 2/3*v**3. Determine g, given that r(g) = 0.
-1, 1
Factor 2/5*v**2 - 2/5*v + 2/5*v**3 - 2/5.
2*(v - 1)*(v + 1)**2/5
Let b be (-3)/(-1) - 31/2. Let j = -12 - b. Solve -j*k**4 - 1/2*k**2 - k**3 + 0*k + 0 = 0.
-1, 0
Let j(w) be the third derivative of -w**5/450 + w**4/30 + 7*w**3/45 + 17*w**2. Factor j(l).
-2*(l - 7)*(l + 1)/15
Factor 11/2*w**2 - 1 + 2*w**3 + 5/2*w.
(w + 1)*(w + 2)*(4*w - 1)/2
Let c = 16 + -13. Factor -5*u**c + 11*u**3 - 4*u**2 - 12 - 10*u**3 + 20*u.
-4*(u - 1)**2*(u + 3)
Let o(z) be the first derivative of 35*z**5 + 185*z**4/2 + 20*z**3/3 - 20*z**2 + 10. Solve o(x) = 0.
-2, -2/5, 0, 2/7
Let s(x) be the third derivative of -x**4/24 + 7*x**3/6 - 12*x**2. Let w be s(5). Factor 1/4*o**w - 1/4*o + 0.
o*(o - 1)/4
Let o(u) be the second derivative of u**6/120 + u**5/30 + u**4/24 + 3*u**2 + 8*u. Let d(b) be the first derivative of o(b). Factor d(i).
i*(i + 1)**2
Let g be ((-12)/(-10))/(1/((-20)/(-12))). Suppose -i - 4*l - 7 = 0, -7*l + 2*l = -4*i + 35. Solve -1/4*s**i - 1/4*s**4 + 0*s + 0*s**3 + 0*s**g + 0 = 0.
-1, 0
Let f = -2999/5 + 601. Factor -2/5*h**2 - 4/5 - f*h.
-2*(h + 1)*(h + 2)/5
Let m(z) = z**4 + z**2 + z. Let t(j) = -6*j**4 + 21*j**3 + 0*j - 18*j**4 - 12*j - 30*j**2. Let l(q) = -15*m(q) - t(q). Factor l(a).
3*a*(a - 1)**2*(3*a - 1)
Let a(j) be the first derivative of -7*j**6/6 + 12*j**5/5 + j**4 - 14*j**3/3 + 3*j**2/2 + 2*j - 7. Find z such that a(z) = 0.
-1, -2/7, 1
Factor 0 + 1/8*m + 1/8*m**2.
m*(m + 1)/8
Let s(p) = -4*p**3 - 3*p**2 - p - 2. Let f(n) = -5*n**3 - 4*n**2 - n - 2. Let y(g) = 5*f(g) - 6*s(g). Let y(u) = 0. Calculate u.
-2, -1, 1
Suppose 6*z + 2*i = z - 4, -2*z = 3*i + 6. Let k(l) be the second derivative of -1/21*l**3 + 0 + z*l**2 + 1/42*l**4 - 2*l. Factor k(b).
2*b*(b - 1)/7
Let r(s) be the first derivative of 0*s**2 + 2 + 1/12*s**3 + 0*s. Let r(p) = 0. What is p?
0
Let n(q) = -3*q**2 + 16*q + 23. Let o be (-3)/(-3)*-1 - 3. Let p(z) = -2*z**2 + 8*z + 12. Let x(b) = o*n(b) + 7*p(b). Suppose x(l) = 0. What is l?
-2
Let z = 97 - 94. Let c(r) be the third derivative of 0 - 1/90*r**5 - r**2 + 0*r + 1/180*r**6 - 1/36*r**4 + 1/9*r**z. Factor c(p).
2*(p - 1)**2*(p + 1)/3
Suppose 0 = -4*z + 3*z. Suppose -5*j + w - 8 + 33 = z, j + 2*w + 6 = 0. Suppose -2/3*a**2 - 1/3*a**5 + 1/3 - 1/3*a + 2/3*a**3 + 1/3*a**j = 0. Calculate a.
-1, 1
Let q(y) = -y**2 + 12*y + 8. Let z be q(9). Let u = -139/4 + z. Determine x, given that 0 + 0*x + x**3 - u*x**2 = 0.
0, 1/4
Suppose -4*t**2 - 4*t**2 - 21*t + 31*t + 3*t**2 = 0. Calculate t.
0, 2
Let u be (36/8)/(-9)*-1. Find b, given that u - b**2 + 1/2*b**5 - b**3 + 1/2*b + 1/2*b**4 = 0.
-1, 1
Suppose 0 = 2*u - 10 - 0. Suppose -2*v - 12 = -u*v. Factor -2/9*k**2 + 2/9*k**3 + 0 + 0*k + 2/9*k**v - 2/9*k**5.
-2*k**2*(k - 1)**2*(k + 1)/9
Suppose -10 = -0*s - s. Suppose 2*q - 31 = -5*i, 3*q + 4*i - 39 + s = 0. Let 2/9*t**q + 0 + 0*t + 0*t**2 = 0. What is t?
0
Let a = 0 + -5. Let o be (3/(-30))/(2/a). Factor 1/4*d**3 - 1/2*d**2 + o*d + 0.
d*(d - 1)**2/4
Let h be (-24)/(-9) + 1/3. What is v in 2 + v**h + 12*v - 5*v - 2*v + 4*v**2 = 0?
-2, -1
Let q(y) be the second derivative of -1/24*y**4 + 2*y + 0*y**3 + 0 + 1/4*y**2. Suppose q(s) = 0. Calculate s.
-1, 1
Let s(i) = i**2 + i - 1. Let w(m) = 3*m**3 + 6*m**2 + m - 6. Let l(b) = -20*s(b) + 5*w(b). Suppose l(f) = 0. Calculate f.
-1, -2/3, 1
Let a(g) be the first derivative of -1/21*g**3 - 6 + 1/14*g**2 + 0*g. Find k such that a(k) = 0.
0, 1
Let b be ((-260)/(-48) + -5)/((-25)/(-10)). Determine q, given that 0*q + 0 + b*q**4 - 2/3*q**3 + 2/3*q**2 = 0.
0, 2
Let b be 4/6 + (-22)/(-12). Factor 0 + 0*z + z**2 + b*z**3 - 7/2*z**4.
-z**2*(z - 1)*(7*z + 2)/2
Determine p so that 2/5*p**2 - 8/5 - 8/5*p + 2/5*p**3 = 0.
-2, -1, 2
Let x(i) be the second derivative of -i**5/90 + i**4/27 + i**3/27 - 2*i**2/9 - 17*i. Factor x(n).
-2*(n - 2)*(n - 1)*(n + 1)/9