3*z**4 + 8*z + 61 + 58.
-z*(z - 2)*(z + 2)*(3*z + 2)
Let t = -99959/84 - -1190. Let f(h) be the second derivative of 0*h**2 + 0*h**3 + 0*h**4 + 1/30*h**6 + 0 + 1/40*h**5 - h + t*h**7. Factor f(x).
x**3*(x + 1)**2/2
Let c(p) = 5*p**2 - 5*p - 3. Suppose -5*k + 0 = -15. Let x(r) = -4*r**2 + 4*r + 2. Let u(n) = k*x(n) + 2*c(n). Factor u(f).
-2*f*(f - 1)
Let h = -33 + 173/5. Factor -7/5*r**3 + 19/5*r**2 - 4/5 - h*r.
-(r - 2)*(r - 1)*(7*r + 2)/5
Suppose -11*g - g = -3*g. Suppose -10 + 0 = -5*h. Factor g*n**h + 0 + 2/3*n**3 - 2/3*n.
2*n*(n - 1)*(n + 1)/3
Suppose 4*y**3 - 72/5 - 74/5*y**2 + 24*y - 2/5*y**4 = 0. Calculate y.
2, 3
What is w in 8/5*w**3 - 12/5*w + 8/5*w**2 - 12/5*w**4 + 4/5 + 4/5*w**5 = 0?
-1, 1
Let g = -2/475 + 483/1900. Factor 1/4*a + 1/4*a**2 - g*a**3 - 1/4*a**4 + 0.
-a*(a - 1)*(a + 1)**2/4
Let a = 313 - 937/3. Factor -1/3*g**2 + 0 + a*g.
-g*(g - 2)/3
Let a(r) be the third derivative of r**5/80 + 3*r**4/32 + r**3/4 - 3*r**2. Factor a(i).
3*(i + 1)*(i + 2)/4
Factor -7/3*j**2 + 1/3*j**3 - 3 + 5*j.
(j - 3)**2*(j - 1)/3
Suppose 5*i + 9 = -11, 2*i = -3*b + 4. Let a(q) be the second derivative of -1/3*q**3 - 1/10*q**5 - b*q + 1/3*q**4 + 0 + 0*q**2. Let a(u) = 0. Calculate u.
0, 1
Let v be -1*(0 - (2 + -1)). Factor v + 7*b**3 + 2*b**5 - 1 - 3*b**3 + 6*b**4.
2*b**3*(b + 1)*(b + 2)
Let f(p) = -3*p**2 + 9*p - 13. Let k(r) = 2*r**2 - 6*r + 6. Let x(q) = 2*q**2 - 6*q + 7. Let c(v) = 2*k(v) - 3*x(v). Let o(s) = 7*c(s) - 5*f(s). Factor o(h).
(h - 2)*(h - 1)
Suppose -3*c + 0 + 12 = 0, -5*f - 5*c = -55. Let t = f - 5. Solve -3*o**2 + 2*o**2 + t - 4*o**2 - 3*o = 0 for o.
-1, 2/5
Let c(x) be the third derivative of x**5/90 - x**4/18 - 11*x**2. Solve c(r) = 0 for r.
0, 2
Factor 3/8*z**5 + 0 + 3/2*z**4 + 3/2*z**2 + 9/4*z**3 + 3/8*z.
3*z*(z + 1)**4/8
Let t be (12/18)/((-44)/(-3)). Let w = 47/66 - t. Factor -2/3*l - w*l**2 + 0.
-2*l*(l + 1)/3
Let y(d) = -3*d**3 + d**2 + 1. Let j(n) = 0 - 2 + n**3 + n**4 + 1. Let b = 7 - 8. Let w(v) = b*j(v) - y(v). Determine i, given that w(i) = 0.
0, 1
Let n(f) = -8*f**2 + 59*f - 21. Let i be n(7). Find g, given that -3/2*g**4 + i*g**3 - 3/2 + 3*g**2 + 0*g = 0.
-1, 1
Let o be 2/8 - (-1)/(-4). Suppose o = 3*t - 6 - 6. Factor -q + t*q - q - 2*q**3.
-2*q*(q - 1)*(q + 1)
Suppose 4*s = -16 - 16. Let p(g) = g + 12. Let m be p(s). Let d(r) = -6*r**2 + 3*r - 5. Let i(j) = 5*j**2 - 2*j + 4. Let l(f) = m*d(f) + 5*i(f). Factor l(q).
q*(q + 2)
Factor -32*m - 1 - 9 - 24*m + 21*m - 45*m**2 - 25*m**3 - 5*m**4.
-5*(m + 1)**3*(m + 2)
Let n(b) be the second derivative of -b**4/78 + 2*b**3/39 - 4*b. Let n(r) = 0. What is r?
0, 2
Let q(g) be the third derivative of -g**7/4200 + g**6/1800 - g**3 - 3*g**2. Let p(x) be the first derivative of q(x). Suppose p(y) = 0. What is y?
0, 1
Let z(l) be the third derivative of -l**8/50400 - l**5/60 - l**2. Let f(r) be the third derivative of z(r). Factor f(j).
-2*j**2/5
Let m(j) = j**2 - j + 1. Let l(y) = -y**2 - 24*y - 16. Let s(b) = l(b) - 4*m(b). Factor s(h).
-5*(h + 2)**2
Suppose -4*a + 8 = 3*u, -5*u = -5*a + 18 + 27. Suppose -p = 2 - a. Find o such that -o**4 - 3*o**3 + o**2 + 5*o**2 - p*o**4 + o**4 = 0.
-2, 0, 1
Let f(t) = t**2 + 2*t + 2. Let a be f(-2). Let -3 - a*s - 5 + s**2 - 2*s**2 + 7 = 0. Calculate s.
-1
Solve 8*w + 1 - 4*w**2 + 3 + 8*w**2 = 0.
-1
Let p(b) = -b**2 + 8*b - 12. Let o be p(3). Let a(w) be the second derivative of 1/54*w**4 - 1/9*w**2 + 2*w + 0 + 0*w**o. Factor a(g).
2*(g - 1)*(g + 1)/9
Let s be (-2*1/(-105))/(4/2). Let b(l) be the second derivative of 0*l**6 + s*l**7 + 0*l**3 + 0*l**4 - 3*l + 0*l**2 + 0 + 0*l**5. Suppose b(i) = 0. What is i?
0
Let q(v) be the second derivative of -63*v**5/10 + 95*v**4/6 - 12*v**3 + 4*v**2 - 8*v. What is t in q(t) = 0?
2/9, 2/7, 1
Let d = 15 - 9. Factor z**3 + 2*z**3 + 2*z**2 + 0*z - d*z + z**2.
3*z*(z - 1)*(z + 2)
Factor 2/7 + 4/7*i + 2/7*i**2.
2*(i + 1)**2/7
Let -2/11*x - 10/11*x**2 - 8/11*x**4 + 0 - 16/11*x**3 = 0. What is x?
-1, -1/2, 0
Let h = 4 - 2. Let y be (35/(-42))/((-5)/3). Determine w, given that 1/2*w + y*w**h - 1 = 0.
-2, 1
Let s(x) be the second derivative of -x**6/6 - x**5/2 + 5*x**3/3 + 5*x**2/2 + 3*x - 4. Factor s(t).
-5*(t - 1)*(t + 1)**3
Let r(t) be the first derivative of t**4/24 - t**3/4 + t**2/2 + 2*t - 7. Let v(o) be the first derivative of r(o). Factor v(i).
(i - 2)*(i - 1)/2
Let n(v) be the second derivative of v**4/3 - 2*v**3/3 - 12*v**2 - 13*v. Solve n(r) = 0 for r.
-2, 3
Suppose 0 = 2*m - 0 - 6. Suppose m*g = 7*g. Factor g*d - 2/5 + 2/5*d**2.
2*(d - 1)*(d + 1)/5
Find b, given that 4/9*b - 2/9*b**2 - 2/9 = 0.
1
Factor -15*p**4 - 4*p**3 + 29*p**3 - p**3 - 3*p**2 - 9*p**2 + 3*p**5.
3*p**2*(p - 2)**2*(p - 1)
Let a(m) be the first derivative of 1/4*m**2 + 3 - 1/8*m**4 + 1/2*m - 1/6*m**3. Factor a(o).
-(o - 1)*(o + 1)**2/2
Let f = 47/80 + -3/16. Factor -4/5*o - f*o**2 - 2/5.
-2*(o + 1)**2/5
Let 10*d**3 - 2 + 6*d**2 + 7*d**3 + 7*d - 4*d**4 - 24*d**3 = 0. Calculate d.
-2, -1, 1/4, 1
Suppose 0 = -h - 5*z + 13, -3*z + 31 - 10 = 5*h. Let t be ((-3)/12)/(3/(-6)). Factor 1/2*x**h + t*x**4 - 1/2*x**2 - 1/2*x + 0.
x*(x - 1)*(x + 1)**2/2
Let f be -3 - -10 - (-3)/(-1). Factor -1/2*u**f + 1/2*u**5 + 1/2*u**2 - 5/2*u**3 + 2 + 4*u.
(u - 2)**2*(u + 1)**3/2
Let d(b) be the third derivative of -b**8/1176 + b**7/735 + b**6/140 - b**5/42 + b**4/42 - 2*b**2. Determine t, given that d(t) = 0.
-2, 0, 1
Let x(f) = -6*f**2 + 41*f + 45. Let j = -16 - -18. Let z(s) = s**2 - 8*s - 9. Let d(n) = j*x(n) + 11*z(n). Let d(k) = 0. Calculate k.
-3
Factor 5/4*p + 1/4*p**3 + 1/2 + p**2.
(p + 1)**2*(p + 2)/4
Let u be ((-40)/48)/(1/(-6)). Let t(i) be the first derivative of 8/5*i - 2/5*i**3 + 2/25*i**u + 1/5*i**4 + 2 - 4/5*i**2. Suppose t(r) = 0. What is r?
-2, 1
Let f(t) = t**2 + 7*t + 7. Let g be f(-6). Let q = g - -3. Factor 5*n**2 - 2 - 6*n**2 + n + q.
-(n - 2)*(n + 1)
Suppose -d + 1 = -2. Factor -t**2 + d*t**2 - 4*t + 2 - 3 + 3.
2*(t - 1)**2
Let f = 319 + -217. Let m be f/30 + (-2)/5. Find n, given that -1/3*n**4 - n**m - 1/3*n - n**2 + 0 = 0.
-1, 0
Let q be (-32)/56 - (-222)/315. Factor 2/15*x**3 + 0 + 0*x**2 - q*x.
2*x*(x - 1)*(x + 1)/15
Let s be 2*2*5/2. Let o be (5/(s/(-28)))/(-2). Let -2*q**4 + 0*q - 3*q**2 - o*q**2 - 8*q**3 - 4*q = 0. Calculate q.
-2, -1, 0
Factor 16*l + 49*l + 10*l**3 - 11*l**2 - 44*l**2 - 20.
5*(l - 4)*(l - 1)*(2*l - 1)
Suppose 0 = 22*z - 26*z + 12. Let f(h) be the third derivative of 1/42*h**8 + 0*h**z + 1/60*h**6 + 0 + 0*h**5 + 0*h + 0*h**4 - 1/21*h**7 - 2*h**2. Factor f(d).
2*d**3*(d - 1)*(4*d - 1)
Let g be (-58)/(-70) + 4/(-10). Let s = 1/14 + g. Factor -1/2*w + 0 + s*w**3 + 0*w**2.
w*(w - 1)*(w + 1)/2
What is f in 20/3*f**3 - 10/3*f**4 - 2/3 + 10/3*f + 2/3*f**5 - 20/3*f**2 = 0?
1
Let r be (3/(-9))/((-1)/18). Let h(y) be the second derivative of -125/147*y**7 - 55/21*y**r + 0 - 2*y - 3*y**5 - 8/21*y**3 + 0*y**2 - 34/21*y**4. Factor h(v).
-2*v*(v + 1)*(5*v + 2)**3/7
Suppose -4/11 + 2/11*c**2 + 6/11*c + 2/11*c**4 - 6/11*c**3 = 0. Calculate c.
-1, 1, 2
Suppose 3*t - 1 = d, 0 = 7*d - 2*d + 5*t - 15. Let c(g) be the second derivative of 1/36*g**4 + 2/9*g**3 - 2*g + 2/3*g**d + 0. Suppose c(f) = 0. What is f?
-2
Let a(r) be the third derivative of 0*r**3 - 1/12*r**4 - 5/84*r**7 - 1/48*r**6 + 0*r + 0 + 2/15*r**5 - 4*r**2. Suppose a(x) = 0. What is x?
-1, 0, 2/5
Let f(z) = -2*z**2 - 4*z + 6. Let a(c) = -c**2 - 2*c + 3. Let n(u) = -11*a(u) + 6*f(u). Factor n(j).
-(j - 1)*(j + 3)
Suppose 9*r - r = 0. Factor 0 + 1/4*b**2 + r*b.
b**2/4
Let k = 12 + -5. Factor 5 + 21*w**2 + 11*w + 17*w**3 + k*w**4 + 0 - 2*w**4 - 3.
(w + 1)**3*(5*w + 2)
Let f = 0 - 0. Suppose -6 = -4*o + 2. Factor 0*k + k + k**o + f*k.
k*(k + 1)
Suppose -3*d = -10 + 1. Find h, given that -3*h**d + 3*h + 0 - 2*h**5 - 3*h**4 - 10*h**3 - 5*h**2 - 6*h**4 + 2 = 0.
-2, -1, 1/2
Let x(o) be the third derivative of o**6/540 - 2*o**5/135 + 5*o**4/108 - 2*o**3/27 - 17*o**2. Factor x(j).
2*(j - 2)*(j - 1)**2/9
Let v(h) = h**4 + h**2 - h. Let t(c) = -2*c**4 - 16*c**3 - 10*c**2 + 14*c + 16. Let d(r) = t(r) - 2*v(r). What is a in d(a) = 0?
-2, -1, 1
Let h(n) be the second derivative of -4*n + 0*n**3 + 1/60*n**6 + 0*n**4 - 1/80*n**5 - 1/168*n**7 + 0 + 0*n**2. Factor h(p).
-p**3*(p - 1)**2/4
Factor -27*y**2 - 84*y**3 - 34*y**2 + 54*y - 20*y**4 + 162 - 47*y**2 - 2*y**4 - 2*y**5.
-2*(y -