e 5*y - 6 = 6*y. Let d be (y/54)/((-1)/3). Solve -1/3*p**3 - d*p + 0 + 2/3*p**2 = 0 for p.
0, 1
Suppose -3*a = a - 11*a. Solve a*q - 2/7*q**2 - 6/7*q**4 + 0 - 6/7*q**3 - 2/7*q**5 = 0 for q.
-1, 0
Factor 2/7*c**5 + 4/7*c**2 - 2*c - 10/7*c**4 + 12/7*c**3 + 6/7.
2*(c - 3)*(c - 1)**3*(c + 1)/7
Let f(b) be the second derivative of b**4/3 - b**3 - 2*b**2 - 43*b. Suppose f(v) = 0. Calculate v.
-1/2, 2
Let o = 32 - 30. Factor -1/2*a**o + 0 + 0*a - 1/4*a**3.
-a**2*(a + 2)/4
Let w = -1/32 + 49/32. Factor -1/2*h + 0 - w*h**2 - 1/2*h**4 - 3/2*h**3.
-h*(h + 1)**3/2
Suppose 0 = 3*y - 128 - 7. Suppose 0*u - 5 = -2*c + 3*u, 5*c = u + y. Factor -4*r**3 - 4*r**4 + 12*r**4 - r + 5*r**5 + 2 + 0*r - c*r**2.
(r - 1)*(r + 1)**3*(5*r - 2)
Let x(z) = -z**2 + 7*z + 4. Suppose -8 = c - 5*c. Let l(b) = -2 + 9*b**c + 7 + 8*b - 11*b**2. Let v(s) = 4*l(s) - 5*x(s). Factor v(i).
-3*i*(i + 1)
Determine k, given that -3*k**3 - 3*k**2 - 3*k**2 - 3*k - k + k**3 = 0.
-2, -1, 0
Let x(o) = o**2 - 20*o + 103. Let z be x(10). Factor -3/2*g**2 - 2 - 1/4*g**z - 3*g.
-(g + 2)**3/4
Let i(j) be the third derivative of 2*j**7/105 - j**5/15 + j**2. Factor i(o).
4*o**2*(o - 1)*(o + 1)
Let o(s) be the first derivative of -1 + 1/2*s**2 + 2/3*s**3 + 1/6*s**4 + 0*s + 1/60*s**5. Let z(i) be the second derivative of o(i). Solve z(d) = 0 for d.
-2
Let d(p) = -10*p**2 + 13*p - 10. Let g(i) = 2 + 5*i**2 - 4*i + 1 - 2*i**2. Let o(v) = -4*d(v) - 14*g(v). Factor o(w).
-2*(w - 1)**2
Suppose 0 = 2*w - j - 10, -w - j + 6 = w. Suppose 3*o**2 + 3*o - w*o + o**3 + 3*o = 0. Calculate o.
-2, -1, 0
Let l be -2 + 3 + (-6)/24. Solve 3/4*b**4 + 0 - l*b**2 - 1/4*b**3 + 1/4*b = 0.
-1, 0, 1/3, 1
Let x(v) be the second derivative of v**6/165 + v**5/110 - 2*v**4/33 - 4*v**3/33 - 16*v. Solve x(z) = 0 for z.
-2, -1, 0, 2
Let n = 263 + -4733/18. Let u(b) be the second derivative of -1/9*b**3 - n*b**4 + 0*b**2 + b + 0. Let u(a) = 0. Calculate a.
-1, 0
Suppose -3*o + 2*u + 10 = 0, o - 9 = 5*u + 3. Factor -4/7*l + 2/7 + 2/7*l**o.
2*(l - 1)**2/7
Let r(l) be the first derivative of -l**6/60 + l**5/20 + l**4/6 - l**3/6 - 3*l**2/4 - 3*l - 5. Let s(j) be the first derivative of r(j). Factor s(x).
-(x - 3)*(x - 1)*(x + 1)**2/2
Let b(p) be the first derivative of -p**6/6 + 2*p**5/5 - 2*p**3/3 + p**2/2 - 1. Factor b(c).
-c*(c - 1)**3*(c + 1)
Let v(j) be the first derivative of j**6/6 - j**5/5 - 3*j**4/16 + j**3/3 - j**2/8 + 49. Solve v(g) = 0 for g.
-1, 0, 1/2, 1
Let 2/9*d**3 + 4/9*d**2 + 2/9*d + 0 = 0. Calculate d.
-1, 0
Let t(q) be the third derivative of -q**8/10080 + q**6/360 - q**5/30 - 4*q**2. Let x(g) be the third derivative of t(g). Factor x(b).
-2*(b - 1)*(b + 1)
Let c be (15 + -5)*12/30. Let -1/6*x**c + 1/6*x**3 + 0 + 1/6*x**2 - 1/6*x = 0. Calculate x.
-1, 0, 1
Let n(o) = 3*o**3 - 2*o**2 + 2*o - 1. Let z be n(1). Let w(x) be the first derivative of 3/2*x**2 + 1/4*x**4 - z + x + x**3. Solve w(b) = 0.
-1
Find f, given that -16*f - 28*f**4 - 4*f**3 + 16*f**4 + 23*f**2 + 9*f**2 = 0.
-2, 0, 2/3, 1
Let w(c) be the first derivative of c**6/1440 - c**4/96 - 4*c**3/3 + 8. Let m(s) be the third derivative of w(s). Suppose m(o) = 0. What is o?
-1, 1
Determine a so that -5*a**2 + 2*a**3 + 7*a**2 - 1 + 1 = 0.
-1, 0
Let y(t) be the second derivative of -t**4/3 - 4*t**3/3 - 2*t**2 + 12*t. Determine v, given that y(v) = 0.
-1
Let i = 7 - 6. Let z be i/(-3 + (-20)/(-6)). Suppose 2*f**4 + 0*f**4 + 2*f**5 - z*f**5 - f**3 = 0. What is f?
0, 1
Suppose -2*t + 19 = 15. Factor 2/3*m**3 + 0*m - 2/9*m**t + 0.
2*m**2*(3*m - 1)/9
Find v such that 14*v**4 + 6*v**5 + 0 - 16/3*v - 4/3*v**3 - 40/3*v**2 = 0.
-2, -2/3, 0, 1
Let q(k) be the second derivative of -2*k + 1/3*k**2 + 1/3*k**4 + 1/45*k**6 + 0 + 4/9*k**3 + 2/15*k**5. Factor q(t).
2*(t + 1)**4/3
Let o(g) = 2*g + 1. Let p(r) = 2*r + 1. Let z(k) = -5*o(k) + 4*p(k). Let d be z(-2). Factor 2*m**2 - 2*m**3 - 3*m**2 + m**d.
-m**2*(m + 1)
Determine r so that -16/5*r + 40*r**5 + 0 - 24/5*r**2 + 212/5*r**3 + 102*r**4 = 0.
-2, -2/5, 0, 1/4
Suppose -2*k = 5 + 3, -5*c = 2*k - 2. Factor -2/9*r + 2/9*r**c + 0.
2*r*(r - 1)/9
Factor -p + 2/3 + 1/3*p**2.
(p - 2)*(p - 1)/3
Suppose -2*s - 3*n + 1 = -0*s, -2*n - 21 = -3*s. Let l = 7 - s. Factor 2/9*r**l - 4/9*r + 2/9.
2*(r - 1)**2/9
Solve -1/2*x**4 - 1/2*x + 1/2*x**2 + 1/2*x**3 + 0 = 0 for x.
-1, 0, 1
Suppose -25/2*a**2 + 15/2*a + 5/2*a**3 + 0 + 5/2*a**4 = 0. Calculate a.
-3, 0, 1
Let p be (2/2)/(1/2). Suppose -2*i + 8 = p*i. Find m such that 6/7*m**3 - 2/7*m + 4/7*m**i + 0 = 0.
-1, 0, 1/3
Let f be -1 + 9 - (-10)/(-5). Suppose 5*m + f = 6*m. Find y, given that -m*y + 3*y**2 + 4*y - y**2 = 0.
0, 1
Suppose 240*f + 30*f**2 - 20*f + 45*f**4 - 40 - 175*f**3 + 10*f**4 = 0. Calculate f.
-1, 2/11, 2
Let z be (-4)/(-3)*-2 - -3. Let r(f) be the first derivative of -1/2*f + z*f**3 + 1/4*f**2 + 2. Factor r(m).
(m + 1)*(2*m - 1)/2
Let o = 18 + -16. Let i be o/11 + 6/88. Factor 1/4*r**2 + 0*r + 0 - i*r**3.
-r**2*(r - 1)/4
Let c(h) be the third derivative of -h**6/120 + h**5/30 + 3*h**2. Find b such that c(b) = 0.
0, 2
Factor 19*r - 48*r**2 - 32*r**4 - 7*r + 5*r**4 + 63*r**3 + 0*r**4.
-3*r*(r - 1)*(3*r - 2)**2
Let t(g) be the second derivative of 2*g**6/15 - 6*g**5/5 + 13*g**4/3 - 8*g**3 + 8*g**2 - 4*g. Suppose t(q) = 0. What is q?
1, 2
Let t(q) be the second derivative of -q**4/18 + 2*q**3/9 - q**2/3 - 6*q. Solve t(u) = 0.
1
Let s(t) = t**3 + 3*t**2 - 3*t - 4. Let r be s(-3). Suppose -r*i - 13 = -33. Determine w, given that w**3 + 2*w + 3*w**3 + 2*w**3 + 2*w**i + 6*w**2 = 0.
-1, 0
Let q(k) = -2*k**2 - 25*k - 3. Let u(y) = 5*y**2 + 50*y + 5. Let d(v) = -5*q(v) - 3*u(v). Solve d(l) = 0.
-5, 0
Let d(v) = -2*v**2 - 5*v + 3. Let j(t) = -t**2 + 10*t. Let r(l) = -9*l + 1. Let o(u) = -3*j(u) - 4*r(u). Let f(m) = 4*d(m) + 3*o(m). Let f(g) = 0. Calculate g.
0, 2
Suppose 20 = 12*f - 40. Let k(z) be the third derivative of 4*z**2 + 1/270*z**f + 1/27*z**3 + 1/54*z**4 + 0 + 0*z. Let k(v) = 0. What is v?
-1
Let m(x) = -3*x + 2 + 10 + 2*x**2 - 11. Let y(q) = q**2 + 1. Let g(w) = m(w) - 3*y(w). Factor g(c).
-(c + 1)*(c + 2)
Let i(m) = m + 15. Let l be i(-13). What is n in n**3 - 4*n**2 + 16*n - l*n**3 - 14*n + 3*n**3 = 0?
0, 1
Let k(j) = -j**3 + j + 1. Let o(v) = -88*v**3 - 36*v**2 + 7*v + 11. Let s(u) = 44*k(u) - 4*o(u). Factor s(a).
4*a*(7*a + 2)*(11*a + 2)
Let z(g) be the second derivative of 5*g**6/6 + g**5 - 3*g**4/2 - 18*g**3/5 - 27*g**2/10 - 12*g. Factor z(u).
(u - 1)*(5*u + 3)**3/5
Let q be (-6)/(-4)*4/(-3). Let v = q - -4. Factor 2/7*o**v + 2/7 + 4/7*o.
2*(o + 1)**2/7
Factor 2/9*v**2 + 8/9*v + 8/9.
2*(v + 2)**2/9
Let g(a) = 2*a**3 - 3*a**2 + a - 1. Let z be g(2). Suppose -5*k - 4*h = -h - 30, -2*k - 5*h = -31. Factor -t**4 + t**z + k*t**3 + t**4 + t**2 + 3*t**4.
t**2*(t + 1)**3
Let z(m) be the second derivative of -m**6/30 + 3*m**5/20 - m**4/12 - m**3/2 + m**2 - 7*m. Determine k, given that z(k) = 0.
-1, 1, 2
Let j(m) be the second derivative of 1/10*m**6 + 5*m + 0 + 0*m**3 + 0*m**5 + 0*m**2 - 1/4*m**4. Determine f so that j(f) = 0.
-1, 0, 1
Let s(q) be the second derivative of -q**6/75 - 3*q**5/50 + 4*q**3/15 - 14*q + 1. Factor s(i).
-2*i*(i - 1)*(i + 2)**2/5
Let d = -40 + 42. Solve 0 - 1/5*s - 1/5*s**d = 0.
-1, 0
Factor 5*f + 9*f - 2*f - 2*f + 55*f**2.
5*f*(11*f + 2)
Let q be (-1 + 10)/(-2 + (6 - 1)). Factor 1/3*m**4 - 1/3 - 2/3*m**q + 0*m**2 + 2/3*m.
(m - 1)**3*(m + 1)/3
Let h be -28 + 28 - (2 - (0 - -2)). Suppose l - 2 = -0*l. Determine g so that h + 4/5*g**l - 2/5*g - 2/5*g**3 = 0.
0, 1
Let u(h) be the first derivative of 1/7*h**2 - 43/14*h**4 - 16/7*h**3 + 4/7*h - 8/7*h**5 + 1. Solve u(f) = 0.
-1, -2/5, 1/4
Let w(s) be the second derivative of s**6/75 + 12*s**5/25 + 32*s**4/5 + 512*s**3/15 - 2*s + 15. Find v such that w(v) = 0.
-8, 0
Let y(c) be the third derivative of -1/7*c**3 - 1/56*c**4 + 0*c + 6*c**2 + 1/140*c**5 + 0. Factor y(d).
3*(d - 2)*(d + 1)/7
Let t(n) = -n**3 + 4*n**2 - 3. Let y be (4/12)/((-1)/(-9)). Let k be t(y). Solve -3 + 1 - 2*f**3 + 3*f - f**2 + k + 5*f = 0 for f.
-2, -1/2, 2
Let x(k) be the third derivative of -k**5/80 + k**4/16 + 6*k**2. Factor x(l).
-3*l*(l - 2)/4
Let j(f) be the first derivative of 6/5*f**5 - 3 + 0*f + 0*f**2 + 0*f**3 - 1/2*f**6 + 0*f**4. Factor j(n).
-3*n**4*(n - 2)
Find j such that 9*j**2 - 9*j**2 + 16*j - 6*j**2 - 4 - 10*j**2 = 0.
1/2
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