2
Let x(v) = -v**2 + 8*v. Let c(p) = p**3 + 4*p**2 - 2. Let g be c(-4). Let l(i) = 2*i. Let d(z) = g*x(z) + 9*l(z). Factor d(u).
2*u*(u + 1)
Suppose 4*a = -0*a + 20. Suppose 5*n + 2*l - 1 = 7, -a*n + 4*l - 16 = 0. Factor -2/3*h**2 + n*h + 0.
-2*h**2/3
Let o(l) be the second derivative of -l**6/40 + 3*l**4/8 + l**3 + 3*l**2/2 - 6*l. Let h(y) be the first derivative of o(y). Factor h(d).
-3*(d - 2)*(d + 1)**2
Let g(v) = v**3 + v**2 - v + 2. Let c be g(0). Let 2/5*o**c + 2/5 - 4/5*o = 0. Calculate o.
1
Let u(d) be the second derivative of -d**5/30 + 4*d**4/3 - 64*d**3/3 + 512*d**2/3 - 17*d. Find j such that u(j) = 0.
8
Let s(v) = -5*v**3 + v**2 + v - 1. Let t(x) = x. Let o(i) = s(i) - 2*t(i). Let g(a) = 6*a**3 - a**2 + a + 1. Let u(y) = -6*g(y) - 7*o(y). Solve u(w) = 0 for w.
-1, 1
Let i(u) be the second derivative of -1/30*u**5 + 1/9*u**4 + 0*u**3 + 0*u**2 + 0 + 2*u. Factor i(s).
-2*s**2*(s - 2)/3
Let z(i) be the second derivative of i**7/126 - i**5/15 - i**4/18 + i**3/6 + i**2/3 - i. Suppose z(x) = 0. Calculate x.
-1, 1, 2
Let -12*k**3 - 5*k**4 + 5*k**3 + 5*k**2 - k**5 - 4*k**2 - 4*k**2 = 0. Calculate k.
-3, -1, 0
Let g(s) = s**2 + 4*s - 8. Suppose 13 = -z - z - n, -5*z = -3*n + 27. Let c be g(z). Find h such that 12*h**c - 13*h**4 - 3*h**2 + h - 2*h - 3*h**3 = 0.
-1, 0
Suppose 21*l = 19*l - 10. Let r be 3/1 - l/3. Find k, given that -68/3*k**3 + 32/3*k**2 + 52/3*k**4 - 4/3 + 2/3*k - r*k**5 = 0.
-2/7, 1
Let s be 2 - (60/(-21))/(-4). Factor 6/7*a + 1/7*a**2 + s.
(a + 3)**2/7
Let v(k) = k**2 - k - 1. Suppose -2*j - 10 = 2. Let m = j + 7. Let x(y) = -4*y**2 + 2*y + 8. Let p(b) = m*x(b) + 6*v(b). Solve p(r) = 0.
1
Let n(o) be the first derivative of -169*o**3 - 78*o**2 - 12*o - 5. Solve n(f) = 0 for f.
-2/13
Let k(w) be the second derivative of w**6/15 + 3*w**5/10 + w**4/3 - 9*w. Factor k(l).
2*l**2*(l + 1)*(l + 2)
Suppose 3*n**4 - 80*n**2 - n**5 + 80*n**2 = 0. What is n?
0, 3
Let g(p) be the first derivative of p**3/15 - p**2/10 - 2*p/5 + 17. Factor g(q).
(q - 2)*(q + 1)/5
Find d such that 5/6*d**3 - 3/2*d + 0 + 1/2*d**2 + 1/6*d**4 = 0.
-3, 0, 1
Let i be (20/(-30))/(1/(-3)). Suppose 4*b + 5*s - 6 = -22, -b + s = -5. Factor b + 1/4*c**i + c.
(c + 2)**2/4
Let f(o) be the second derivative of -o**4/12 + 4*o. Suppose f(l) = 0. What is l?
0
Let i = -540 - -542. Factor 1/2*z**4 + 0*z + 1/2 - z**i + 0*z**3.
(z - 1)**2*(z + 1)**2/2
Let v = 31 - 52. Let g be v/(-45) + (-5)/(-25). Determine u so that 0*u**2 + 2/3*u + 0 - g*u**3 = 0.
-1, 0, 1
Let v(a) be the first derivative of 2*a**3/3 - 3*a**2 + 4*a - 21. Find j, given that v(j) = 0.
1, 2
Suppose -4*z = -2*n + 5*n - 5, -2*z - 2*n = 0. Let j(d) be the second derivative of 0*d**2 + 2*d + 0*d**3 + 1/12*d**4 + 3/10*d**z + 3/10*d**6 + 0. Factor j(f).
f**2*(3*f + 1)**2
Let j(s) be the first derivative of -s**5/25 - 7*s**4/20 - s**3 - 9*s**2/10 - 2. Factor j(m).
-m*(m + 1)*(m + 3)**2/5
Determine u, given that 9/4*u**2 + 9/4*u + 3/4 + 3/4*u**3 = 0.
-1
Let t(a) = 8*a**2 + 2*a + 1. Let l be t(-1). Factor 3*g - 3*g**3 - 3*g - 4*g**5 + l*g**5.
3*g**3*(g - 1)*(g + 1)
Let l(i) be the third derivative of 1/105*i**7 + 0 - 1/3*i**4 + 0*i**5 + 0*i + 0*i**3 + 1/20*i**6 - 5*i**2. Factor l(f).
2*f*(f - 1)*(f + 2)**2
Let l be 2*(100/1155)/(-1). Let n = 32/33 - l. Find i such that n*i + 12/7*i**2 + 8/7*i**3 + 2/7*i**4 + 2/7 = 0.
-1
Let d(h) be the third derivative of -5*h**2 + 1/105*h**7 - 1/12*h**4 + 0 + 1/60*h**6 + 0*h - 1/10*h**5 + 2/3*h**3. Factor d(b).
2*(b - 1)**2*(b + 1)*(b + 2)
Suppose -14 = -0*h - h. Let b be h/4 + (-3)/(-6). Factor 2*c**2 + c - 1 + b + 0*c - c**3 - 5.
-(c - 2)*(c - 1)*(c + 1)
Let -84*g - 18 - 4*g + 10 - 242*g**2 = 0. What is g?
-2/11
Let h be (3 + (-140)/12)*(-1 - 0). Suppose 22 = 3*f - 2*f - 4*k, -f + 27 = -5*k. Solve 2/3 + h*n**3 + 14/3*n + 8/3*n**4 + 10*n**f = 0 for n.
-1, -1/4
Let d(q) = -q**2 - 2*q. Let b(c) = c**3 + c + 1. Let v(f) = 3*b(f) + 3*d(f). Factor v(w).
3*(w - 1)**2*(w + 1)
Let m = 3 - 1. What is x in 10*x - x**3 - 6*x**m - 4 - x**3 + 3*x**4 - x**4 = 0?
-2, 1
Let n(g) be the first derivative of g**5 + 5*g**4/2 - 35*g**3/3 + 10*g**2 - 59. Suppose n(d) = 0. Calculate d.
-4, 0, 1
Determine i so that 1/2*i**5 - 5/2*i**3 + 2*i + 0*i**4 + 0 + 0*i**2 = 0.
-2, -1, 0, 1, 2
Let d(l) = -l**3 - l**2 + l. Let f(i) = -95*i**3 + 88*i**2 - 16*i. Let y(r) = 4*d(r) + f(r). Find s such that y(s) = 0.
0, 2/11, 2/3
Let o(x) be the third derivative of -x**6/300 + x**4/15 + 8*x**2. Let o(h) = 0. Calculate h.
-2, 0, 2
Let l(o) be the first derivative of -1/5*o**2 + 8 + 7/10*o**4 + 0*o**3 + 0*o + 12/25*o**5. Suppose l(d) = 0. What is d?
-1, -1/2, 0, 1/3
Let j be -5 + 102*(-24)/(-486). Let h(m) be the first derivative of -4 - 1/9*m**4 - j*m**6 - 2/15*m**5 + 4/27*m**3 + 2/9*m + 1/3*m**2. Factor h(n).
-2*(n - 1)*(n + 1)**4/9
Let l(q) = q**2 + 2*q - 2. Let p be l(-4). Let z be (-4)/(-6)*p/10. Find r such that -z*r**2 - 4/5 - 6/5*r = 0.
-2, -1
Factor -6*a**3 + 0*a**2 + 3*a**4 + 6*a**2 - 3*a**2.
3*a**2*(a - 1)**2
Let i(u) be the third derivative of -u**6/40 - u**5/5 - 3*u**4/8 - 60*u**2. Determine l, given that i(l) = 0.
-3, -1, 0
Let z(g) = -g**2 + 3*g + 3. Let i be z(3). Suppose -i*b = b. Solve 0*v**2 + 0*v + 0 - 2/3*v**4 + b*v**3 = 0.
0
Let u(d) be the third derivative of -d**7/1575 - d**6/900 + d**5/150 + d**4/180 - 2*d**3/45 + 13*d**2. Solve u(v) = 0 for v.
-2, -1, 1
Let p be 7/(-560)*-124 + 8/(-10). Factor 0 + 3/4*b**3 - 3/4*b**2 + 3/4*b**4 - p*b.
3*b*(b - 1)*(b + 1)**2/4
Let k be 36/15 + (0/(-2))/(-3). Factor -k*i + 2/5*i**2 + 18/5.
2*(i - 3)**2/5
Suppose -8*n + 4*n = -60. Let u be (3/10)/(n/140). Solve 0 - 4/5*l**3 + u*l**4 - 2/5*l**2 - 8/5*l**5 + 0*l = 0 for l.
-1/4, 0, 1
Let n(x) be the first derivative of -x**6/60 + x**4/24 + 4*x - 2. Let f(l) be the first derivative of n(l). Factor f(d).
-d**2*(d - 1)*(d + 1)/2
Let x(n) be the second derivative of n**5/20 - n**4/3 + 2*n**3/3 - 29*n. Factor x(p).
p*(p - 2)**2
Let d(a) be the first derivative of a**6/6 - 4*a**5/5 + 3*a**4/2 - 4*a**3/3 + a**2/2 - 21. Factor d(v).
v*(v - 1)**4
Let a(c) be the first derivative of 2*c**6/21 - 12*c**5/35 + 3*c**4/7 - 4*c**3/21 - 7. Factor a(z).
4*z**2*(z - 1)**3/7
Let x = -73 - -77. Let f(z) be the third derivative of 3/70*z**7 - 1/24*z**4 + 0 + 0*z**3 - 1/8*z**6 + 7/60*z**5 + 0*z + x*z**2. Find g such that f(g) = 0.
0, 1/3, 1
Factor 0*i**2 + 4/3*i + 2/3*i**4 - 4/3*i**3 - 2/3.
2*(i - 1)**3*(i + 1)/3
Let y(i) = 492*i**4 + 945*i**3 + 591*i**2 + 144*i + 6. Let a(x) = -491*x**4 - 945*x**3 - 591*x**2 - 144*x - 7. Let r(d) = -6*a(d) - 5*y(d). Solve r(l) = 0.
-1, -1/2, -2/9
Let r(g) = -6 - 2*g + 3 - 2*g + 0*g. Let b be r(-2). Find f, given that -f**b + 5*f**2 - f**5 - 10*f**4 - 13*f**2 - 16*f**3 + 0*f**5 = 0.
-2, -1, 0
Let t(w) be the second derivative of -w**6/12 - w**5/20 + 7*w. What is m in t(m) = 0?
-2/5, 0
Find w such that -6/11*w**2 + 2/11*w + 6/11 - 2/11*w**3 = 0.
-3, -1, 1
Let a(r) be the second derivative of -6*r + 0 - 1/18*r**4 - 16/3*r**2 + 8/9*r**3. Factor a(s).
-2*(s - 4)**2/3
Let r(k) be the third derivative of k**6/300 - k**5/30 + k**4/20 + 3*k**3/5 + 6*k**2. Factor r(p).
2*(p - 3)**2*(p + 1)/5
Let x(b) be the third derivative of -b**6/30 + 8*b**5/15 - 10*b**4/3 + 32*b**3/3 - 29*b**2. Factor x(i).
-4*(i - 4)*(i - 2)**2
Factor 2/9*s**2 + 0 + 2/9*s.
2*s*(s + 1)/9
Let c(z) be the first derivative of -z**7/315 - z**6/180 + z**5/90 + z**4/36 - 2*z**2 - 4. Let r(x) be the second derivative of c(x). Solve r(p) = 0.
-1, 0, 1
Let l = 977/654 + 2/327. Factor 0*z**2 + l*z - 1/2*z**3 - 1.
-(z - 1)**2*(z + 2)/2
What is w in 24/7*w + 40/7*w**3 - 48/7*w**2 - 12/7*w**4 - 4/7 = 0?
1/3, 1
What is y in 5*y - 3*y**5 - 12*y**2 - 2/3 + 2*y**4 + 26/3*y**3 = 0?
-2, 1/3, 1
Factor -28*g**2 - 16*g - 16/7.
-4*(7*g + 2)**2/7
Let j be -1*3 - (15 - -2). Let l be (j/25)/(8/(-20)). Suppose 1/2*d**l + 1/2 - d = 0. Calculate d.
1
Suppose 2*s + 4 = 10. Suppose s*v = -v + 12. Factor -2/9*x**v + 2/3*x**2 + 0 - 4/9*x.
-2*x*(x - 2)*(x - 1)/9
Let l(z) = -2*z - 4. Let u be l(-3). Let i(a) be the first derivative of -7/3*a**6 + 0*a**u + 4/5*a**5 - 1 + 0*a + 0*a**3 + 0*a**4. Factor i(b).
-2*b**4*(7*b - 2)
Let p = -46 + 47. Factor 1/2*h - p + 1/2*h**2.
(h - 1)*(h + 2)/2
Let u = 1259/1700 + 4/425. Solve -3/4*t - u*t**4 + 0 + 3/4*t**3 + 3/4*t**2 = 0 for t.
-1, 0