**3 - 5*x**2 + 5*x. Let f(p) = 6*d(p) - 5*v(p). Factor f(t).
-t**3*(t + 1)
Factor -2/3*q + 4/9 + 2/9*q**2.
2*(q - 2)*(q - 1)/9
Let q(x) be the second derivative of 3*x**5/80 + x**4/8 + x**3/8 - 2*x. Determine j, given that q(j) = 0.
-1, 0
Let g = 2073/5 + -414. Factor 6/5*x + 9/5 - g*x**2.
-3*(x - 3)*(x + 1)/5
Let n(w) = 2*w**2 + 3*w. Let d be n(-2). Let 0 + 4 - 2*c**2 + 0*c + 2*c + 0*c**d = 0. What is c?
-1, 2
Let r be 4/(-12) + (-26)/(-6). Find z such that -5*z**r - 8*z**4 - z**5 + 12*z**4 = 0.
-1, 0
Let n be (0/(-1))/(37 - 36). Solve -6/7*v**4 + n*v**3 + 0 + 3/7*v + 6/7*v**2 - 3/7*v**5 = 0.
-1, 0, 1
Let p = -17 + 21. Suppose -3*r = p*r. Factor 0 - 1/2*b**2 + 1/2*b**5 + r*b - 1/2*b**3 + 1/2*b**4.
b**2*(b - 1)*(b + 1)**2/2
Let w(i) be the third derivative of 23/840*i**7 + 0 - 1/192*i**8 + 0*i**3 + 0*i + 13/240*i**5 - 9/160*i**6 - 2*i**2 - 1/48*i**4. Suppose w(z) = 0. What is z?
0, 2/7, 1
Find b, given that 2/5*b + 9/5*b**2 + 0 - 11/5*b**3 = 0.
-2/11, 0, 1
Let d(t) = -10*t**3 - 30*t**2 - 36*t - 6. Let j(g) = -9*g**3 - 29*g**2 - 36*g - 5. Suppose 5*f = -1 + 26. Let y(u) = f*d(u) - 6*j(u). Solve y(a) = 0.
-3, 0
Let r(o) be the third derivative of 0 - 1/96*o**4 - 1/80*o**5 - 1/160*o**6 + 0*o + 0*o**3 - 1/840*o**7 - o**2. Factor r(c).
-c*(c + 1)**3/4
Let b(d) be the first derivative of -d**6/40 + d**5/40 + 2*d**3/3 - 5. Let m(w) be the third derivative of b(w). What is y in m(y) = 0?
0, 1/3
Let p(l) be the third derivative of 3*l**2 - 1/105*l**7 + 0*l + 0*l**3 + 0*l**4 + 0 + 1/15*l**5 - 1/60*l**6. Let p(d) = 0. Calculate d.
-2, 0, 1
Suppose 4*h = 4*m + 8, m + 7 + 1 = 4*h. Suppose -h*z + 2 + 2*z + 6*z + 2*z**3 + 0*z**3 + 6*z**2 = 0. What is z?
-1
Let y = 1/37 + 109/74. Suppose -2*o + 2 - y*o**2 = 0. Calculate o.
-2, 2/3
Let d(x) be the second derivative of -1/18*x**4 + 0*x**2 - 2/45*x**6 + 0 + 0*x**3 - 1/10*x**5 + 7*x. Factor d(c).
-2*c**2*(c + 1)*(2*c + 1)/3
Suppose -2*b - 5*a = 10, -6*a + 8*a + 4 = -b. Factor -2/3*j - 8/3*j**2 + b.
-2*j*(4*j + 1)/3
Let i be (94/(-64))/(15/(-10)). Let a = i - 5/16. Determine m so that -a*m**3 - 2/3*m**4 + 2/3*m**2 + 2/3*m + 0 = 0.
-1, 0, 1
Solve -4*r**2 - r - 16 + 0 - 5*r - 10*r = 0 for r.
-2
Let o = 14 + -139/10. Let d(t) be the third derivative of -2*t**2 + 1/210*t**7 + 0*t + 1/6*t**3 + 1/6*t**4 + 1/30*t**6 + 0 + o*t**5. Factor d(i).
(i + 1)**4
Let x = -28/11 - -240/77. Let v = -2/9 - -32/63. Factor 2/7*h**3 + v*h - x*h**2 + 0.
2*h*(h - 1)**2/7
Determine m so that -83*m + m**2 - 3 + 0 + 81*m = 0.
-1, 3
Let m(d) = -d + 5. Let p be m(-4). Suppose -5*t = -p - 1. Factor -2*y**3 - y - 3*y**2 + y**2 + t + 3*y.
-2*(y - 1)*(y + 1)**2
Let f = 161/85 - 22/17. Determine s, given that 0*s**3 + 0*s + 1/5*s**5 + 0 + f*s**4 - 4/5*s**2 = 0.
-2, 0, 1
Let u(g) = g**3 - 5*g**2 - 4*g + 20. Let m be u(5). Factor 0*k - 1/2*k**3 + 0 + m*k**2.
-k**3/2
Let v(u) be the first derivative of 2*u**3/45 - u**2/15 - 4*u/15 - 2. Determine d, given that v(d) = 0.
-1, 2
Let y(k) be the third derivative of k**11/332640 - k**9/30240 + k**7/5040 - k**5/10 - 2*k**2. Let h(x) be the third derivative of y(x). Factor h(c).
c*(c - 1)**2*(c + 1)**2
Let a(p) be the third derivative of p**5/15 + p**3/2 - 3*p**2. Let x(g) = 7*g**2 + 5. Let n(q) = 5*a(q) - 3*x(q). Factor n(j).
-j**2
Let r(o) = 24*o**3 - 24*o**2 - 34*o - 14. Let p(x) = -x**2 - 4*x**2 - 2 - 1 + 0 + 5*x**3 - 7*x. Let g(j) = 14*p(j) - 3*r(j). Let g(b) = 0. What is b?
-1, 0, 2
Suppose 3*v**2 - v - 7 + 34 + 19*v = 0. Calculate v.
-3
Let i(b) = -4*b**3 - 8*b**2 - 6*b. Let l = 21 + -34. Let v(x) = -8*x**3 - 4*x**3 + 8*x - 17*x**2 + 3*x**3 - 21*x. Let u(o) = l*i(o) + 6*v(o). Factor u(a).
-2*a**2*(a - 1)
Let p be (-75)/132 + (-5)/4 + 2. Suppose 2/11*w**3 + p*w**2 - 2/11*w**4 + 0 - 2/11*w = 0. Calculate w.
-1, 0, 1
Let k(g) be the third derivative of -g**5/270 + g**4/108 + 2*g**2. Determine p so that k(p) = 0.
0, 1
Let k(r) be the first derivative of -r**6/27 + 2*r**5/15 - r**4/6 + 2*r**3/27 + 16. Factor k(b).
-2*b**2*(b - 1)**3/9
Let m be (2 + 0)*(3 - 2). Let g be 15/10 - (-19)/m. Let w(a) = -5*a**2 - 6*a + 10. Let r(c) = c**2 + c - 2. Let i(k) = g*r(k) + 2*w(k). Factor i(o).
(o - 2)*(o + 1)
Factor 3 - 17*t**2 + t + 4*t + 20*t**2 + t.
3*(t + 1)**2
Let k(i) be the third derivative of -i**8/3192 - i**7/665 - i**6/1140 + i**5/190 + i**4/114 - 38*i**2. Find t, given that k(t) = 0.
-2, -1, 0, 1
Let a = 2 + 0. Factor 14 + a*w**2 - 14 - 2*w.
2*w*(w - 1)
Let m(x) = -x**3 - 2*x**2 - 3*x - 2. Let k be m(-1). Let f be 2 + 4 + k + -3. Factor 1/3*p**f + 2/3 - p + 0*p**2.
(p - 1)**2*(p + 2)/3
Let y(i) be the third derivative of -i**7/16380 + i**6/4680 + i**5/390 - i**4/24 - 3*i**2. Let z(v) be the second derivative of y(v). Factor z(k).
-2*(k - 2)*(k + 1)/13
Let r be 12/(-5) + (-10)/(-25). Let s be (-5)/(35/r)*7. Let -2*x**2 + 5*x - 3*x - 2*x + s = 0. Calculate x.
-1, 1
Let q = -40 - -37. Let u be 0*(14/(-4) - q). Factor u - 18/11*l**3 + 14/11*l**4 + 4/11*l**2 + 0*l.
2*l**2*(l - 1)*(7*l - 2)/11
Factor 15 + 165 - 24*g - 36*g + 13*g**2 - 8*g**2.
5*(g - 6)**2
Let -2 + 26*n - 62*n + 5*n**2 + 7 + 26*n = 0. Calculate n.
1
Find q such that 2/7*q**2 + 0 + 16/7*q = 0.
-8, 0
Let k = 574/3 - 190. Factor k*g**3 + 0 - 1/3*g**4 - 5/3*g**2 + 2/3*g.
-g*(g - 2)*(g - 1)**2/3
Suppose 15*p**3 + p**4 + 2 + 0 - 10*p**3 + 7*p + 9*p**2 = 0. Calculate p.
-2, -1
Let m = -48 - -50. Factor 0*p - 2/5*p**m + 2/5.
-2*(p - 1)*(p + 1)/5
Let l(a) be the first derivative of -a**5/30 + a**4/6 - a**3/3 + 2*a**2 - 3. Let t(x) be the second derivative of l(x). Factor t(w).
-2*(w - 1)**2
Let c(i) = -4*i - 28. Let a be c(-7). Let -9/5*b**3 + 0 + 12/5*b**4 + a*b - 3/5*b**2 = 0. What is b?
-1/4, 0, 1
Suppose -o + 6*o + 5 = 0. Let n be -6*6/(-9) + o. Determine x so that -44/9*x**2 - 26/9*x + 20/3*x**4 + 14/9*x**n - 4/9 = 0.
-1/2, -2/5, -1/3, 1
Let a(g) be the second derivative of -g**6/60 - 3*g**5/40 + g**3/3 + 4*g - 2. Factor a(r).
-r*(r - 1)*(r + 2)**2/2
Let 36*h**2 - 9*h**4 + 13*h**3 - 3*h + 2*h**5 + 2 - 69*h**2 + 28*h**2 = 0. Calculate h.
-1/2, 1, 2
Let f(d) = 19*d**3 - 99*d**2 + 126*d - 20. Let p(x) = -20*x**3 + 100*x**2 - 125*x + 20. Let u(a) = -5*f(a) - 6*p(a). Find l such that u(l) = 0.
1/5, 2
Factor 8/17*k + 0 - 2/17*k**2.
-2*k*(k - 4)/17
Let l = 23 + -21. Let x(s) be the third derivative of 0*s**3 + s**l + 0*s**4 + 0*s - 1/30*s**5 + 0. Factor x(g).
-2*g**2
Let q(w) = -w + 5. Let o be q(3). Factor -2*f**2 - 4*f**3 + 2*f + o*f**3 + 2*f + 0*f**3.
-2*f*(f - 1)*(f + 2)
Let v(l) = -l**2 - 3*l - 1. Let f be v(-4). Let b = f + 7. Factor 0 - 1/4*z**b + 1/4*z**3 + 0*z.
z**2*(z - 1)/4
Let t be (-2)/3*18/(-30). Let q(v) be the first derivative of -2/3*v**3 + t*v**5 + 1/3*v**6 - 1/2*v**4 + 0*v + 1 + 0*v**2. Factor q(h).
2*h**2*(h - 1)*(h + 1)**2
Let q be 2/5*(3 - -17). Suppose -4 + q = a. Let -5*v + 1 - 2 + v**2 + v**3 + a*v = 0. What is v?
-1, 1
Let g(l) be the third derivative of -l**5/60 - l**4/24 + l**3/3 - 5*l**2. Factor g(v).
-(v - 1)*(v + 2)
Suppose 4*n + 5*q = 89, 8*n - 2*q - 38 = 5*n. Suppose n = 3*f + f. Factor 3*i**4 - i - 6*i**4 + f*i**4 + 3*i**2 - 3*i**3.
i*(i - 1)**3
Let j = 109 + -106. Factor 0 + 2/5*g**4 + 2/5*g + 7/5*g**2 + 7/5*g**j.
g*(g + 1)*(g + 2)*(2*g + 1)/5
Let p(g) = -g**3 - 3*g**2 - 3*g - 4. Let a be p(-3). Suppose a*y - 4*y - 5 = 0. Suppose 3*w**4 - 4*w**3 - w**4 + 3*w**y + w**3 + w**2 - 3*w**4 = 0. What is w?
-1, 0, 1/3, 1
Let q(r) be the first derivative of r**5/30 - 2*r**4/9 + 5*r**3/9 - 2*r**2/3 + 3*r - 1. Let a(v) be the first derivative of q(v). Factor a(t).
2*(t - 2)*(t - 1)**2/3
Factor 4/3 - 16/3*w + 7/3*w**4 - 19/3*w**3 + 25/3*w**2 - 1/3*w**5.
-(w - 2)**2*(w - 1)**3/3
Let u(x) = -2*x**3 - 5. Let o(k) = 3*k**2 - 3*k**2 + 2*k**3 + 4. Let q = 9 + -5. Let m(s) = q*u(s) + 5*o(s). Factor m(g).
2*g**3
Let y(p) = -6*p**4 + 6*p**3 + 2*p**2 - 2*p + 4. Let h = -13 + 9. Let u(o) = -17*o**4 + 17*o**3 + 6*o**2 - 6*o + 11. Let c(n) = h*u(n) + 11*y(n). Factor c(v).
2*v*(v - 1)**2*(v + 1)
Let g(r) be the third derivative of 0 + 4*r**2 + 0*r**6 + 0*r + 0*r**3 - 1/840*r**7 + 1/240*r**5 + 0*r**4. Let g(d) = 0. Calculate d.
-1, 0, 1
Let c = -15 + 83/5. Factor -2/5*s**2 + 8/5*s**3 - c*s + 2/5.
2*(s - 1)*(s + 1)*(4*s - 1)/5
Determine y, given that -10/7*y**2 + 2*y + 2/7*y**3 - 6/7 = 0.
1, 3
Let h = -179/2 - -90. Let -1 - h*u**2 - 3/2*u = 0. Calc