45*i**5 + 4 - d*i**4 + 0*i + 1/9*i**2. Factor z(y).
-2*y*(y - 1)*(y + 1)**2/9
Suppose 7 = -2*g + g. Let q be (g/(-4))/(15/20). Factor -q*z**2 + 2/3*z + 0.
-z*(7*z - 2)/3
Let m(g) be the first derivative of g**9/5292 - g**7/1960 + g**6/2520 - 7*g**3/3 - 1. Let u(w) be the third derivative of m(w). Factor u(y).
y**2*(y + 1)*(2*y - 1)**2/7
Solve -1/2*t - 1 + t**3 + 2*t**2 - t**4 - 1/2*t**5 = 0.
-2, -1, 1
Factor 5 + 12*h**2 - 29*h**2 + 22*h**2 - 10*h.
5*(h - 1)**2
Let d be (-5)/(-55)*(0 + 4). Factor -6/11*z + 2/11*z**3 + 0*z**2 - d.
2*(z - 2)*(z + 1)**2/11
Let m(h) be the first derivative of 0*h + 1/9*h**6 - 1/3*h**2 + 4/15*h**5 - 2 + 0*h**4 - 4/9*h**3. Find b such that m(b) = 0.
-1, 0, 1
Let u(s) be the second derivative of -s**8/3360 + s**7/560 - s**6/360 + s**3 + 2*s. Let m(b) be the second derivative of u(b). Factor m(l).
-l**2*(l - 2)*(l - 1)/2
Let d(p) = 3*p**2 + 5*p. Let x(a) be the second derivative of -a**4/3 - a**3 + 4*a. Let q(l) = -6*d(l) - 5*x(l). Solve q(u) = 0.
0
Let q(k) = -4*k**4 + 64*k**3 - 152*k**2 + 112*k - 36. Let u(x) = -x**4 + 21*x**3 - 51*x**2 + 37*x - 12. Let y(i) = 3*q(i) - 8*u(i). Factor y(v).
-4*(v - 3)*(v - 1)**3
Let i(h) be the second derivative of h**4/54 - h**3/9 - 4*h**2/9 + 27*h. Solve i(q) = 0.
-1, 4
Let u = 2 - -1. Let y(o) = -o**4 - o**3 - o**2 - o + 1. Let n(c) = -4*c**4 - 6*c**3 - 5*c**2 - 5*c + 5. Let r(z) = u*n(z) - 15*y(z). Let r(h) = 0. What is h?
0, 1
Let k(p) = 5*p**5 + 6*p**3 - 3*p - 4. Let q(d) = 4*d**5 - d**4 + 6*d**3 - d**2 - 2*d - 3. Let t(b) = 3*k(b) - 4*q(b). Factor t(j).
-j*(j - 1)**4
Let w(o) = o**2 - o. Suppose 21 = -4*v - 5*s, 6*v - 2*v + 4*s = -16. Let a(m) = -7*m**2 + 5*m + 2. Let j(p) = v*a(p) + 5*w(p). Suppose j(z) = 0. Calculate z.
-1, 1
Suppose 0 - 245/4*u**4 + 5*u + 5*u**2 - 245/4*u**3 = 0. What is u?
-1, -2/7, 0, 2/7
Determine d so that 10 + 2/5*d**2 + 4*d = 0.
-5
Determine s so that -40*s**3 + 128*s**3 - 4*s + 48*s**4 + 54*s**2 + 10*s**2 + 20*s + 9*s**5 = 0.
-2, -2/3, 0
Let y(j) be the first derivative of -j**6/45 - 2*j**5/25 + 8*j**3/45 - 8. Factor y(w).
-2*w**2*(w - 1)*(w + 2)**2/15
Suppose -3*a - a = -32. Let l(g) = -11*g**3 - 5*g + 8. Let t(p) = -7*p**3 - 3*p + 5. Let y(o) = a*t(o) - 5*l(o). Let y(w) = 0. What is w?
-1, 0, 1
Let -16*m + 4/3*m**2 + 44/3 = 0. Calculate m.
1, 11
Suppose -13*p = -25 - 1. Solve -2*y**3 - y + 1/2 - 7/2*y**p = 0 for y.
-1, 1/4
Let h(t) = -11*t**3 - 8*t**2 + 3*t + 7. Let l(c) = -5*c**3 - 4*c**2 + c + 3. Let v(m) = 3*h(m) - 7*l(m). Solve v(y) = 0.
-1, 0
Let u(q) be the first derivative of 5*q**6/24 + 3*q**5/2 + 35*q**4/8 + 20*q**3/3 + 45*q**2/8 + 5*q/2 - 46. Solve u(t) = 0 for t.
-2, -1
Let s(r) = 2*r**3 + 3*r**2 - 2*r. Let t(g) = -5*g**3 - 6*g**2 + 5*g - 1. Let h(f) = -7*s(f) - 3*t(f). Factor h(l).
(l - 3)*(l - 1)*(l + 1)
Suppose -5*h - 4*z = -30 - 16, 0 = 2*h - 4*z + 4. Suppose 4*x**2 - 2*x**2 - 2*x**5 - h*x**3 - x + 6*x**4 + x = 0. What is x?
0, 1
Let z(v) be the first derivative of 1 + 1/2*v**2 + 2/9*v**3 - 2/3*v - 1/4*v**4. Factor z(y).
-(y - 1)*(y + 1)*(3*y - 2)/3
Let s(t) be the third derivative of 0*t + 0 + 2*t**2 - 1/30*t**4 - 1/300*t**5 - 2/15*t**3. Determine b, given that s(b) = 0.
-2
Let l(a) be the second derivative of a**4/6 + 2*a**3/3 + a**2 - 11*a. What is d in l(d) = 0?
-1
Let n = -25 + 16. Let b = -6 - n. Solve -2*g**b - 2*g**3 + 10*g**2 - 2*g - 4*g**3 = 0 for g.
0, 1/4, 1
Suppose -30*z**3 + 5*z**4 - 9*z**2 + 18*z + 54*z**2 - 60 + 2*z = 0. What is z?
-1, 2, 3
Let p(i) = i. Let d be p(5). Suppose 0 + 20 = d*q. Suppose 0 + 4/9*w + 28/9*w**q + 2/9*w**2 - 34/9*w**3 = 0. What is w?
-2/7, 0, 1/2, 1
Factor 0 - 2*s**4 - 164/7*s**3 + 144/7*s - 456/7*s**2.
-2*s*(s + 6)**2*(7*s - 2)/7
Let o(g) be the second derivative of g**5/4 - 75*g**4/4 + 1125*g**3/2 - 16875*g**2/2 - 2*g - 2. Factor o(h).
5*(h - 15)**3
Factor -1/3*w - 1/6*w**3 + 0 + 1/2*w**2.
-w*(w - 2)*(w - 1)/6
Let 2/11*a**2 - 6/11 - 4/11*a = 0. Calculate a.
-1, 3
Let a(o) be the first derivative of -3/16*o**4 + 1/2*o**2 + 1 + 1/3*o**3 - 1/24*o**6 - 1/5*o**5 + 0*o. Let a(u) = 0. What is u?
-2, -1, 0, 1
Let z(x) = -5*x**2 - 2*x + 1. Let u(j) = -6*j**2 - 2*j. Let c(a) = -3*u(a) + 4*z(a). Find m, given that c(m) = 0.
-2, 1
Factor -5/2*n**2 + 5*n - 5/2.
-5*(n - 1)**2/2
Determine b, given that 0*b**3 + 0 - b**4 + 1/2*b + b**2 - 1/2*b**5 = 0.
-1, 0, 1
Let i(k) be the first derivative of -7*k**6/6 - 16*k**5/5 - 11*k**4/4 - 2*k**3/3 - 7. Factor i(t).
-t**2*(t + 1)**2*(7*t + 2)
Factor 0*b + 3/2*b**3 + 0 - 1/2*b**2.
b**2*(3*b - 1)/2
Factor 4/3*o + 0 - 1/3*o**2.
-o*(o - 4)/3
Let m = -14 + 6. Let y(k) = k**3 + 7*k**2 - 10*k - 12. Let w be y(m). Factor 6*j**3 + 0*j - 8*j**w + 0 + 10/3*j**5 - 4/3*j**2.
2*j**2*(j - 1)**2*(5*j - 2)/3
Let p(g) be the first derivative of -g**6/4 + g**5/2 + g**4/4 - g**3 + g**2/4 + g/2 + 1. Solve p(w) = 0 for w.
-1, -1/3, 1
Let i(r) be the third derivative of 7*r**2 + 0 + 0*r**3 + 0*r**5 + 1/40*r**6 - 1/8*r**4 + 0*r. Factor i(g).
3*g*(g - 1)*(g + 1)
Suppose p = -7 + 15. Suppose 2*z**4 + 11*z**2 + 10*z**3 - p*z - 6 - 2*z**3 - 7*z**2 = 0. What is z?
-3, -1, 1
Let c(v) = v + 4. Let z be c(-4). Suppose -1/3*x**2 + z*x + 0 = 0. Calculate x.
0
Let g(x) be the second derivative of 9/4*x**3 - x - 3/2*x**4 + 3/8*x**5 - 3/2*x**2 + 0. Suppose g(o) = 0. Calculate o.
2/5, 1
Find c such that -22*c**2 + 40*c**2 + 0 - 3*c**3 + 0 - 15*c = 0.
0, 1, 5
Let y(p) = 0 - 2*p**3 - 3*p - 3*p**2 + 3 - 1. Let b(i) = -3*i**3 - 4*i**2 - 3*i + 2. Let u(o) = 3*b(o) - 4*y(o). Factor u(g).
-(g - 1)**2*(g + 2)
Let g(m) = -m - 1. Let s(k) = 5*k**2 - 37*k + 38. Let i(l) = -3*g(l) - s(l). Determine o, given that i(o) = 0.
1, 7
Let i(o) be the first derivative of 2/3*o**3 - 2*o**2 + 2*o + 1. Factor i(n).
2*(n - 1)**2
Let g be -32 + 30 - -1*(3 - -1). Factor -2*z - g - 1/2*z**2.
-(z + 2)**2/2
Let z(o) be the third derivative of o**7/210 - o**6/120 - 6*o**2. Factor z(n).
n**3*(n - 1)
Let l = 110/21 - 14/3. What is f in l*f**3 + 0 + 0*f - 4/7*f**2 = 0?
0, 1
Let o(m) be the second derivative of m**7/3360 - m**6/720 - m**5/120 + m**4/12 + 2*m. Let p(k) be the third derivative of o(k). Factor p(n).
(n - 2)*(3*n + 2)/4
Let k be 125/(-220) - 4/((-32)/6). Let 2/11*p**2 + k - 4/11*p = 0. What is p?
1
Let d(y) be the second derivative of -y**5/25 + 2*y**4/5 - y - 13. Find k such that d(k) = 0.
0, 6
Let j(m) be the first derivative of -4*m**5/5 + 6*m**4 - 52*m**3/3 + 24*m**2 - 16*m + 1. Determine x so that j(x) = 0.
1, 2
Let w(r) be the first derivative of 1/45*r**5 + 8 + 1/18*r**4 - 1/9*r - 1/9*r**2 + 0*r**3. Determine o so that w(o) = 0.
-1, 1
Let n(o) be the second derivative of -3*o**5/20 - 15*o**4/4 - 75*o**3/2 - 375*o**2/2 + 5*o. Factor n(b).
-3*(b + 5)**3
Let 4*d**2 + 0 - 1/2*d**3 - 8*d = 0. What is d?
0, 4
Let g(m) be the third derivative of m**7/560 - m**6/160 + 11*m**2. Let g(z) = 0. Calculate z.
0, 2
Let d(r) be the first derivative of -3 - 3/10*r**4 - 4/5*r + 1/5*r**2 + 8/15*r**3. Find w such that d(w) = 0.
-2/3, 1
Factor -48 + u + 13*u + 11*u - u - 3*u**2.
-3*(u - 4)**2
Let q = 5 - -2. Factor -3 + 6*p - 2*p**4 - q*p**3 - 9*p**4 - p**4 - 5*p**3 + 9*p**2.
-3*(p + 1)**2*(2*p - 1)**2
Let b(l) be the second derivative of 1/2*l**2 - 1/84*l**4 + 1/210*l**5 + 0 + 0*l**3 - 4*l. Let g(w) be the first derivative of b(w). Find c such that g(c) = 0.
0, 1
Suppose -v = -4*a + 9, 4*a - 5*v + 3*v = 6. Factor -m**2 + 0*m**2 + 0*m**3 + 2*m**a - m**3.
m**2*(m - 1)
Let u(a) = 7*a**5 + 2*a**4 + a**3 - 4*a**2 + 2*a + 7. Let o(y) = -6*y**5 - 2*y**4 + 4*y**2 - 2*y - 6. Let b(s) = 5*o(s) + 4*u(s). Factor b(i).
-2*(i - 1)**2*(i + 1)**3
Let n(s) = 27*s**2 - 78*s + 78. Suppose 0 = 4*f - 3*m - 5 + 2, 3 = m. Let c(a) = -a**3 + 27*a**2 - 79*a + 79. Let z(l) = f*c(l) - 2*n(l). Factor z(v).
-3*(v - 3)**3
Let f(r) be the third derivative of -1/1365*r**7 + 0 + 0*r**6 + 0*r**4 + 0*r**5 - 4*r**2 + 0*r + 0*r**3. Let f(h) = 0. What is h?
0
Let w(v) be the second derivative of v**7/105 - 4*v**6/75 + 2*v**5/25 + v**4/15 - v**3/3 + 2*v**2/5 - 12*v. Suppose w(y) = 0. Calculate y.
-1, 1, 2
Suppose w + 3*w = -5*h + 15, -2*h + w - 7 = 0. Let j be h/2*(-6)/1. Find o such that -2*o - 8*o**3 + 3*o + 6*o - 14*o**2 - j*o = 0.
-2, 0, 1/4
Let m(w) = -9*w**3 + 243*w**2 - 2180*w + 6561. Let x(l) = 6*l**3 - 162*l**2 + 1453*l - 4374. Let p(n) = 5*m(n) + 7*x(n). Factor 