*3 - d**2 + 1. Let o(u) = 3*u**4 + 5*u**3 - 19*u**2 - 25*u + 4. Let g(n) = 4*a(n) - o(n). Factor g(m).
m*(m - 5)**2*(m + 1)
Suppose 0 = 5*o - 2*w - 41, 3*o - 36 = 2*w + 3*w. Let x = o - 3. Suppose -x*d + d + 2*d + 4 - 3*d + d**2 = 0. What is d?
2
Let w be 7/2 - (-11 + 12). Let a(l) be the first derivative of -1 + w*l**4 + 4*l - 4/3*l**3 - 5*l**2. Suppose a(y) = 0. Calculate y.
-1, 2/5, 1
Let y(c) be the second derivative of c**5/120 - c**4/18 + 5*c**3/36 - c**2/6 + 15*c. Find b such that y(b) = 0.
1, 2
Solve -6/13*s**2 + 0 - 8/13*s**3 + 2/13*s = 0.
-1, 0, 1/4
Let g(u) = -u + 1. Let b(v) = 2*v**2 - v + 5. Let w(o) = o**3 - 3*o**2 - o + 4. Let h be w(3). Let f(x) = h*b(x) - 5*g(x). Factor f(y).
2*y*(y + 2)
Let g(b) be the second derivative of 2*b**6/15 - 4*b**5/5 + 5*b**4/3 - 4*b**3/3 - 12*b. Factor g(f).
4*f*(f - 2)*(f - 1)**2
Solve -4*j**3 + 541*j - 1073*j - 8 + 544*j = 0 for j.
-2, 1
Let l(y) be the second derivative of -y**7/168 - y**6/120 + y**5/16 + y**4/48 - y**3/3 + y**2/2 + 9*y. Factor l(s).
-(s - 1)**3*(s + 2)**2/4
Suppose 5*y = -2 + 17. Factor 2*c**2 - c**2 - 2*c**y + c**2.
-2*c**2*(c - 1)
Let b(j) be the third derivative of 0*j + 3*j**2 + 0*j**4 + 0 + 2/21*j**3 - 1/105*j**5. Factor b(a).
-4*(a - 1)*(a + 1)/7
Let a(v) be the first derivative of v**6/200 - 7*v**5/200 + v**4/20 - v**3/3 - 3. Let x(n) be the third derivative of a(n). Suppose x(m) = 0. What is m?
1/3, 2
Let h(u) be the third derivative of 0 - 4*u**2 + 0*u + 1/12*u**3 + 1/96*u**4 - 1/480*u**6 - 1/120*u**5. Factor h(r).
-(r - 1)*(r + 1)*(r + 2)/4
Suppose 2/13*c - 2/13*c**3 + 0*c**2 + 0 = 0. What is c?
-1, 0, 1
Let y be 0/(-32) - (-12)/14. Solve 9/7*z**2 - y*z - 3/7 = 0 for z.
-1/3, 1
Let p(d) = -26*d - 48. Let k be p(-2). Let 0*y**3 + 0 + 0*y**2 - 6/5*y**k + 0*y + 3/5*y**5 = 0. What is y?
0, 2
Let -8/3*s**5 + 2/3*s**3 + 0 + 0*s + 0*s**2 - 2*s**4 = 0. What is s?
-1, 0, 1/4
Let b(k) be the third derivative of 7*k**6/60 + k**5/6 - 4*k**4/3 + 4*k**3/3 + 4*k**2. Factor b(i).
2*(i - 1)*(i + 2)*(7*i - 2)
Let c - 3*c**2 - c - 73*c**3 + 76*c**3 = 0. What is c?
0, 1
Suppose -a + 6 = 2*a. Factor -f**4 + f**a + f**4 - f - f**4 + f**3.
-f*(f - 1)**2*(f + 1)
Let c be 3 + (1 - -1)*(-11 - -12). Let 1/4*f**c + 2*f**3 + 0 + f**2 + 0*f + 5/4*f**4 = 0. Calculate f.
-2, -1, 0
Let o be (-26)/(-180)*7 - 1. Let l(j) be the second derivative of -3*j + 1/60*j**5 + 0 + 1/12*j**4 - 1/18*j**3 - o*j**6 - 1/3*j**2. Factor l(p).
-(p - 2)*(p - 1)*(p + 1)**2/3
Factor 8/3 - 8/3*w + 2/3*w**2.
2*(w - 2)**2/3
Factor 6 + 0 + 3*a**5 + 24*a**2 + a**3 - 21*a - 7*a**3 - 6*a**4.
3*(a - 1)**4*(a + 2)
Let m(y) = -y - 1. Let l(r) = 2*r + 1. Let x(n) = 5*l(n) + 15*m(n). Let w be x(-2). Suppose -2/7*q - 4/7*q**2 + 0 + w*q**3 + 2/7*q**5 + 4/7*q**4 = 0. What is q?
-1, 0, 1
Let i(m) be the second derivative of -m**5/35 + m**4/28 + m**3/42 - 5*m. Solve i(z) = 0 for z.
-1/4, 0, 1
Let h = 38 - 3. Let g be 20/(-3)*(-6)/h. Solve 2/7*v**2 - g*v + 8/7 = 0.
2
Let l(m) be the first derivative of m**4/24 + m**3/18 - m**2/12 - m/6 - 9. Factor l(z).
(z - 1)*(z + 1)**2/6
Let v(i) be the second derivative of -i**7/5040 - i**6/480 - i**5/120 + 5*i**4/12 + 3*i. Let j(g) be the third derivative of v(g). Let j(s) = 0. What is s?
-2, -1
Let x be 5/2*(-16)/(-10). Factor j + 0*j**x - j + 2*j**2 - 2*j**4.
-2*j**2*(j - 1)*(j + 1)
Factor -1/7*b + 1/7*b**2 - 2/7.
(b - 2)*(b + 1)/7
Suppose 3*i + 7 = 16. Determine j so that 2/3*j - 1/3*j**i + 1/3*j**2 + 0 = 0.
-1, 0, 2
Let i be (-1)/(-5) + 6/120. Factor i + 1/2*q + 0*q**2 - 1/2*q**3 - 1/4*q**4.
-(q - 1)*(q + 1)**3/4
Let d be (-1)/((3/2)/(-3)). Let u**5 + 2*u**4 + 0*u - u + 3*u**d - 5*u**2 + 0*u**2 = 0. Calculate u.
-1, 0, 1
Let c(q) be the first derivative of -4 + 1/6*q**3 + 3/2*q**2 + 9/2*q. Find b, given that c(b) = 0.
-3
Factor x**3 + 90*x - 2*x**2 - 90*x.
x**2*(x - 2)
Factor -6/13*q + 10/13*q**2 - 4/13.
2*(q - 1)*(5*q + 2)/13
Solve -3*j**2 + 0*j + 3/4*j**4 + 0 - 3/8*j**5 + 3/2*j**3 = 0.
-2, 0, 2
Let l(f) = -f**3 - f**2 - f - 1. Let v(y) = 2*y**4 + 6*y**3 + 12*y**2 + 10*y + 10. Let q(h) = 20*l(h) + 2*v(h). Factor q(x).
4*x**2*(x - 1)**2
Let s be (-8)/3 - (-6)/9. Let w be (-6)/(2*(s - -1)). Find l, given that 0 - 5*l - w*l**3 - 3 - 7*l - 9*l**2 + 3*l = 0.
-1
Let n(m) = -m**2 - m - 1. Let y(h) = 3*h**3 + 15*h**2 + 12*h + 3. Let z(w) = 3*n(w) + y(w). Find a such that z(a) = 0.
-3, -1, 0
Let u(j) be the second derivative of 3*j**7/28 + 7*j**6/20 + 2*j**5/5 + j**4/6 + 6*j. Let u(t) = 0. Calculate t.
-1, -2/3, 0
Suppose -3*z - 461 = 4*k + 2*z, 3*k = -2*z - 344. Let n be (-6)/15 - k/135. Suppose -2/9*v**2 - 2/9 - n*v = 0. Calculate v.
-1
Suppose -5*h + 1 = -3*p, 4*h + 15 - 17 = 2*p. Suppose p*u**3 - 3/2 - 3/2*u + 3*u**2 - 3/2*u**5 - 3/2*u**4 = 0. What is u?
-1, 1
Let l = 37/4 + -161/20. Let 9/5 + 1/5*j**2 - l*j = 0. What is j?
3
Let u(s) be the first derivative of -s**9/756 - s**8/140 + 2*s**6/45 - 7*s**3/3 - 5. Let w(l) be the third derivative of u(l). Let w(i) = 0. What is i?
-2, 0, 1
Suppose -4*z = -4 - 16. Let s(v) = 6*v**2 - 7*v + 6. Let h(c) = 3*c**2 - 3*c + 3. Let t(d) = z*h(d) - 3*s(d). Let t(f) = 0. Calculate f.
1
Suppose 0 = -5*x + 20, x = -4*i - 3*x + 44. Suppose 2*c = 1 + i. Determine m, given that -2 - c*m + 2*m - 4*m + 8*m**2 = 0.
-1/4, 1
Let a be (-3)/((-9)/(-15))*(-70)/75. Find t such that a*t**5 - 26/3*t**2 + 0 + 18*t**3 - 46/3*t**4 + 4/3*t = 0.
0, 2/7, 1
Let n = -7 + -10. Let c = n - -35/2. Find l such that 1/2*l**2 - 1/2 + c*l**3 - 1/2*l = 0.
-1, 1
Let p be (1 - 1/(-2))*2. Let r be 6/14*2/p. Factor -r*l**2 + 4/7*l - 2/7.
-2*(l - 1)**2/7
Let j(g) be the first derivative of -1/21*g**6 + 2/35*g**5 - 4/21*g**3 + 1/7*g**4 + 2/7*g - 1/7*g**2 - 2. Factor j(h).
-2*(h - 1)**3*(h + 1)**2/7
Let y(w) = w**2 + w. Let j(n) = -9*n**2 - 9*n + 2. Let d(x) = 3*j(x) + 24*y(x). Suppose d(t) = 0. Calculate t.
-2, 1
Let l(n) be the third derivative of n**6/1080 - n**5/108 + n**4/36 - 10*n**2. Determine w, given that l(w) = 0.
0, 2, 3
Let x = -4 - -6. Solve 34*a**2 + 6*a**3 - 9*a**4 - 34*a**x + 3*a**5 = 0.
0, 1, 2
Let v(i) = i**3 - 7*i**2 + 5*i + 6. Let s be v(6). Let h(q) be the third derivative of -1/3*q**4 + 1/30*q**5 + 0 + 4/3*q**3 + s*q + 4*q**2. Factor h(u).
2*(u - 2)**2
Solve 0*t**2 + 3/5*t - 3/5*t**3 + 0 = 0.
-1, 0, 1
Factor 6/13 + 10/13*c**2 + 2/13*c**3 + 14/13*c.
2*(c + 1)**2*(c + 3)/13
Factor 2/11*q**2 + 18/11 + 20/11*q.
2*(q + 1)*(q + 9)/11
Let p(t) = -9*t**3 - 31*t**2 - 74*t - 44. Let n(v) = -19*v**3 - 61*v**2 - 149*v - 89. Let q(d) = 4*n(d) - 9*p(d). Suppose q(b) = 0. What is b?
-4, -2, -1
Find x, given that 3/2*x**2 + 9/2*x + 0 = 0.
-3, 0
Let q be (-74)/(-28) - 3/1. Let f = 1/7 - q. Determine m, given that -7/2*m**4 - 19/2*m**2 - f - 15/4*m - 39/4*m**3 = 0.
-1, -1/2, -2/7
Let a = 14/39 - -86/195. Factor 0*l - 2*l**3 + 0 - 6/5*l**4 - a*l**2.
-2*l**2*(l + 1)*(3*l + 2)/5
Let n(d) = 2*d - 2. Let h be n(7). Find a, given that 10*a + 1 - h*a**2 - 43*a + 8 = 0.
-3, 1/4
Let g(i) be the third derivative of -i**5/20 - 3*i**4/8 - i**3 - 3*i**2. Factor g(d).
-3*(d + 1)*(d + 2)
Let m = 1/126 + 5/18. Suppose -m*a + 2/7*a**3 - 2/7*a**4 + 2/7*a**2 + 0 = 0. What is a?
-1, 0, 1
Let u(g) be the first derivative of -g**6/15 + g**5/10 + g**4/6 - g**3/3 - 4*g - 4. Let m(d) be the first derivative of u(d). Solve m(l) = 0.
-1, 0, 1
Determine y, given that -2*y**3 + 0*y - 2/5*y**2 + 0 - 16/5*y**4 - 8/5*y**5 = 0.
-1, -1/2, 0
Let o be 0 + 2 + -1 - -2. Suppose -2*m - m + x = -o, 21 = 3*m + 5*x. Let 4*r + 1 - 1 - 2*r**2 + 4*r**m + 2 = 0. What is r?
-1
What is s in 1/3*s**2 - 2/3*s + 0 = 0?
0, 2
Let f = -32 + 32. Factor 2/5*z - 2/5*z**2 + f.
-2*z*(z - 1)/5
Let u = -17 + 17. Let j(w) be the third derivative of -1/4*w**4 + 3/20*w**5 + 1/6*w**3 + 0*w - 2*w**2 + u. Suppose j(y) = 0. What is y?
1/3
Let h(b) be the first derivative of -b**6/900 + b**4/60 - 4*b**3/3 - 2. Let f(m) be the third derivative of h(m). Suppose f(u) = 0. Calculate u.
-1, 1
Let z = 9 - 9. Let n be 3 - z*3/(-9). Find o such that 3*o + 0*o + 9*o**n + 2*o**2 - 11*o**2 - 3*o**4 = 0.
0, 1
Let u(f) = -3*f**2 + 2*f + 1. Let t be u(-1). Let y(m) = -7*m**2 + 3*m. Let s(p) = -20*p**2 + 9*p. Let n(o) = t*s(o) + 11*y(o). Determine j so that n(j) = 0.
0, 1
Factor 4*t + 51 - 2*t + 4*t - 2*t**3 - 55.
-2*(t - 1)**2*(t + 2)
Let a(u) = -10*u**2 + 10*u + 13. Let w(o) = 