(k) = k**3 - 2*k**2 - 3*k + 2. Let p be l(3). Suppose p*c = -2*c + 12. Find h, given that 0 - 3*h + 21/2*h**c - 15/2*h**2 = 0.
-2/7, 0, 1
Let k(v) be the first derivative of -11*v**6/3 - 14*v**5 - 39*v**4/2 - 34*v**3/3 - 2*v**2 - 6. Factor k(t).
-2*t*(t + 1)**3*(11*t + 2)
Let v = 6 + 1. Let a = -3 + v. Factor 10/3*z - 10/3*z**a - 20/3*z**2 + 2/3*z**5 - 2/3 + 20/3*z**3.
2*(z - 1)**5/3
Suppose 2*r + 10 = -3*h + 5*h, -3*r + 1 = 5*h. Solve 2*v**3 + 2*v + 12*v**h + 2 + 22*v - 2 + 16 = 0.
-2
Let b(x) = -x**4 - x**3 - x**2. Let q(d) = 13*d**4 + 5*d**3 + 6*d**2 + 4*d - 1. Let i(c) = -18*b(c) - 2*q(c). Determine g, given that i(g) = 0.
-1, 1/2, 1
Let t = 133 - 133. Determine v so that t + 1/3*v + 1/3*v**2 = 0.
-1, 0
Let s(y) = 6*y**5 - 15*y**4 - 9*y**3 + 21*y**2 - 3*y. Let k(o) = o**5 - o**2. Let w be (7/14)/((-2)/24). Let j(m) = w*k(m) - s(m). Suppose j(u) = 0. What is u?
-1, 0, 1/4, 1
Factor -3*x**5 - 55*x**2 - 54*x**3 - 39*x - 18*x**4 - 177 - 3*x**4 + 168 - 11*x**2.
-3*(x + 1)**4*(x + 3)
Let c(p) be the first derivative of -p**6/540 - p**5/90 - p**3 - 2. Let k(s) be the third derivative of c(s). Factor k(m).
-2*m*(m + 2)/3
Let v = 47 + -45. Factor 8/3 + 0*m - 2*m**v - 2/3*m**3.
-2*(m - 1)*(m + 2)**2/3
Factor -3/2*y**3 - 1/2*y**5 + 0 - 3/2*y**4 - 1/2*y**2 + 0*y.
-y**2*(y + 1)**3/2
Let r(t) = 2*t**2 + 0*t**3 + 3*t - 2*t - t**3. Suppose -4 = 2*o + 4. Let v(x) = -x. Let y(n) = o*v(n) - 2*r(n). Find h, given that y(h) = 0.
0, 1
Let n(a) be the first derivative of 2*a**3/15 - 12*a**2/5 + 22*a/5 + 31. Solve n(b) = 0 for b.
1, 11
Let b be ((-105)/(-210))/((2 - 4) + 4). Let g be (-6)/4*1/(-6). Factor -g*k + 0 + b*k**2.
k*(k - 1)/4
Let g(y) be the third derivative of -1/54*y**4 - 1/540*y**6 - 4*y**2 + 0 + 1/90*y**5 + 0*y + 0*y**3. Factor g(x).
-2*x*(x - 2)*(x - 1)/9
Factor 359*m**2 - 2*m**3 - 349*m**2 + 8 + 0*m**3 - 16*m.
-2*(m - 2)**2*(m - 1)
Solve p**4 + 1/3*p**3 + 0 - p**2 - 1/3*p = 0 for p.
-1, -1/3, 0, 1
Let k(z) be the third derivative of -z**6/1020 + z**5/170 - z**4/102 - 8*z**2. Factor k(c).
-2*c*(c - 2)*(c - 1)/17
Let u = 111/2 + -551/10. Find d such that 2/5*d**3 - u*d**4 + 0*d**2 + 0*d + 0 = 0.
0, 1
Suppose 0*z**2 + 4/11*z**3 + 0 - 14/11*z**4 - 18/11*z**5 + 0*z = 0. What is z?
-1, 0, 2/9
Suppose 0*r = 2*r - 18. Factor 0*t**3 - 2*t**3 - 7*t + r*t.
-2*t*(t - 1)*(t + 1)
Let i(z) be the third derivative of -z**6/300 - z**5/50 - z**4/20 - z**3/15 - 4*z**2. Determine c so that i(c) = 0.
-1
Let t be 16*184/2940 - 1. Let r(k) be the third derivative of 2*k**2 + t*k**7 + 0 + 0*k**4 + 1/210*k**6 + 0*k + 1/210*k**5 + 0*k**3. Factor r(c).
2*c**2*(c + 1)**2/7
Let w(b) = -b + 3. Let o be w(-3). Let q(i) = 2*i**3 - 13*i**2 + 7*i - 3. Let a be q(o). Let -2/3*y**2 + 0 + 0*y - 1/3*y**a = 0. Calculate y.
-2, 0
Let s be -3 + (183/186 - -2). Let m = 119/310 - s. Factor 2/5*u**3 + 4/5*u**2 + 0 + m*u.
2*u*(u + 1)**2/5
Let b(a) = 24*a**3 - 9*a**2 - 27*a + 3. Let o(f) = 12*f**3 - 4*f**2 - 13*f + 1. Let v(x) = 4*b(x) - 9*o(x). Solve v(z) = 0 for z.
-1/2, 1
Solve -3*f**4 - f + 3*f**3 - 2*f + 3*f**2 + 0*f**3 = 0.
-1, 0, 1
Let t(c) be the first derivative of 0*c + 1/3*c**3 + 1/2*c**2 - 2. Let k(s) = 9*s**2 - 3*s - 2. Let a(l) = 2*k(l) - 4*t(l). Factor a(q).
2*(q - 1)*(7*q + 2)
Determine h so that -28*h**3 - 267*h**2 + 2*h + 287*h**2 + 6*h = 0.
-2/7, 0, 1
Let j(i) be the second derivative of -2/63*i**7 + 2/15*i**5 + 0*i**2 + 2/45*i**6 + 0 + 0*i**3 + i + 0*i**4. Factor j(a).
-4*a**3*(a - 2)*(a + 1)/3
Let y(n) be the second derivative of -n**9/6048 + n**7/560 + n**6/360 - n**3/6 + n. Let z(r) be the second derivative of y(r). Factor z(v).
-v**2*(v - 2)*(v + 1)**2/2
Let p(m) = -10*m**4 + 56*m**3 - 60*m**2 + 40*m - 26. Let z(g) = -2*g**4 + 11*g**3 - 12*g**2 + 8*g - 5. Let v(d) = 3*p(d) - 16*z(d). Factor v(b).
2*(b - 1)**4
Let y(g) be the third derivative of -4*g**7/105 - g**6/10 - g**5/15 + 6*g**2. Factor y(h).
-4*h**2*(h + 1)*(2*h + 1)
Let b = 14 + -15. Let x be b - 3*9/(-21). Factor 4/7 + x*r**2 + 6/7*r.
2*(r + 1)*(r + 2)/7
Let a = 7/3 - 29/15. Let p(v) be the first derivative of 1 + 0*v - 2/5*v**3 + a*v**2. Let p(u) = 0. What is u?
0, 2/3
Factor 24*a**2 + 13*a**3 + 71*a**3 + 59*a**4 + 23*a**5 - 8*a**5 + 7*a**4.
3*a**2*(a + 2)**2*(5*a + 2)
Let j(y) be the third derivative of -y**7/108 + y**6/540 + y**5/270 + y**3/6 - 2*y**2. Let c(v) be the first derivative of j(v). What is d in c(d) = 0?
-1/5, 0, 2/7
Let b(c) = -4*c**3 - 12*c**2 - 8*c + 5. Let m(l) = 10*l**3 + 30*l**2 + 20*l - 12. Let j(k) = 12*b(k) + 5*m(k). Solve j(o) = 0 for o.
-2, -1, 0
Let 1/4*b**3 + 3/4*b**2 + 0*b - 1 = 0. What is b?
-2, 1
Let s = 3 - -1. Let q be 3/(-6) - 22/(-4). Factor -3*b**5 - 2*b**2 + b + s*b**2 + b**q - 2*b**4 + b**5.
-b*(b - 1)*(b + 1)**3
Suppose -o = 2*o - 12. Suppose 2*b - 4 = -4*g + 8*g, -g + 2*b - o = 0. Let 1/2*v**5 + 3/2*v**4 + 3/2*v**3 + 0*v + 1/2*v**2 + g = 0. What is v?
-1, 0
Factor 0*x - 2/3*x**5 - 2*x**3 + 2*x**4 + 2/3*x**2 + 0.
-2*x**2*(x - 1)**3/3
Let k(h) be the third derivative of h**8/168 + 12*h**2. Determine r, given that k(r) = 0.
0
Let s be 2/6 + (-22)/(-6). Factor -3 + 3*x**2 + s*x + 6 + 5*x - 3*x.
3*(x + 1)**2
Let y be (-2 + 4/2)/2. Solve -m**4 - 2*m**2 - 8 - 2*m**4 - 24*m**3 + 24*m - 5*m**4 + y*m**4 = 0 for m.
-2, 1/2
Let s(r) be the second derivative of -3*r**5/140 + 3*r**4/28 - 3*r**3/14 + 3*r**2/14 - 3*r. Let s(t) = 0. What is t?
1
Let o(g) be the third derivative of 0*g**3 + 0 + 1/8*g**4 + g**2 + 0*g + 1/20*g**5. Solve o(z) = 0 for z.
-1, 0
Let z be (-4)/(-6) + (-3)/(-9). Let k(b) = b + 1. Let d be k(z). Suppose 0 - 1 + x + x**4 - 3*x + d*x**3 = 0. What is x?
-1, 1
Let n(v) = -3*v**4 + 5*v**3 + 27*v**2 + 13*v - 1. Let t(f) = f**4 - 3*f**3 - 14*f**2 - 6*f + 1. Let j be 2*3*(-5)/(-6). Let q(y) = j*t(y) + 3*n(y). Factor q(z).
-(z - 2)*(z + 1)*(2*z + 1)**2
Let m(o) = 4*o**3 + 80*o**2 + 389*o - 11. Let r(k) = k**3 + 20*k**2 + 97*k - 3. Let h(j) = -6*m(j) + 22*r(j). Let h(f) = 0. What is f?
-10, 0
Suppose -3*c**3 + 14 - 32*c**2 - 161 + 2*c**2 - 15*c**2 - 189*c = 0. Calculate c.
-7, -1
Let x(o) = -o**4 + o**3 + o**2. Let z(s) = 4*s**4 - 16*s**3 - 12*s**2. Suppose 0 = 4*b - 8*b + 4. Let q(l) = b*z(l) + 8*x(l). Factor q(c).
-4*c**2*(c + 1)**2
Let r = 7 + -5. Let d = -211/2 - -106. What is o in d*o**r + 1/2 - o = 0?
1
Factor 4/9*o**2 - 4/9*o**3 + 0 + 4/9*o**5 + 0*o - 4/9*o**4.
4*o**2*(o - 1)**2*(o + 1)/9
Let 8/15 + 2/15*r**3 + 16/15*r + 2/3*r**2 = 0. Calculate r.
-2, -1
Factor 3*w - w**2 - 209 + 207 + 0*w**2.
-(w - 2)*(w - 1)
Let m(v) be the third derivative of 0*v - v**2 - 2/9*v**3 + 0 + 1/180*v**6 - 1/12*v**4 + 0*v**5. Solve m(z) = 0 for z.
-1, 2
Let u be 2/4 - ((-56)/7 - -8). Solve 0 - 1/6*y**5 + 0*y + u*y**3 + 0*y**2 + 1/3*y**4 = 0.
-1, 0, 3
Let h = 3 - 6. Let z be 10/21 - 2/h. Factor 2/7*n**5 + 0 + 2/7*n + 12/7*n**3 + z*n**4 + 8/7*n**2.
2*n*(n + 1)**4/7
Let h(w) = -w - 5. Let g be h(-6). Suppose 3*j + g = 10. Factor j - 1 + 10*f**2 - 12*f + 4*f - 4*f**3.
-2*(f - 1)**2*(2*f - 1)
Let l = -137/6 - -23. Let r(q) be the second derivative of -l*q**3 + 0 + 0*q**2 + 1/20*q**5 - 2*q + 0*q**4. Let r(y) = 0. Calculate y.
-1, 0, 1
Find d, given that 2/5*d**5 + 16/5*d**4 + 64/5*d**2 + 0 + 32/5*d + 48/5*d**3 = 0.
-2, 0
Let h be (0 - 0)/2*1/(-2). Suppose -10 + 2 = -4*u. Factor h*g - 1/2*g**u + 0.
-g**2/2
Let z = 20/71 + -1450/2627. Let p = 78/259 - z. Factor 2/7*b**5 + 6/7*b**4 - p*b**2 + 4/7*b**3 - 6/7*b - 2/7.
2*(b - 1)*(b + 1)**4/7
Suppose -4*j + 3*j + 9 = 0. Let k(q) = q - 6. Let s be k(j). Factor -2*w + 2*w**s + 8*w**4 + 0*w + 0*w - 8*w**2.
2*w*(w - 1)*(w + 1)*(4*w + 1)
Suppose 3*p - 214 = 4121. Let y = -7187/5 + p. Factor 8/5 - 2/5*l**5 - 32/5*l + 14/5*l**4 + 10*l**2 - y*l**3.
-2*(l - 2)**2*(l - 1)**3/5
Solve 48*c**4 - 3*c + 5*c**3 - 36*c**5 - c + 3*c**3 - 16*c**2 + 0*c = 0 for c.
-1/3, 0, 1
Find b, given that 35*b**3 + 3*b**2 + 37*b**3 - 75*b**3 + 3*b - 3 = 0.
-1, 1
Let g(o) be the second derivative of 5*o**4 + 32*o**3/3 + 8*o**2 + 5*o. Find t such that g(t) = 0.
-2/3, -2/5
Suppose 3*i + 6 = 0, i + 0*i - 1 = -t. Suppose -3*v + t = 2*c - 3, 3*c + 8 = 4*v. Factor 2/3*u**v + 4/3 + 2*u.
2*(u + 1)*(u + 2)/3
Factor -20/3*y**2 - 5*y**3 + 5/3*y + 10/3.
-5*(y + 1)**2*(3*y - 2)/3
Let b(d) be the second derivative of d**5/20 + d**4/2 + 3*d**3/2 - 2*d**2 + 3*d. Let x(y) be the first derivativ