2*d - 16. Factor 1/2*i**w - 1/2*i - 1/4 + 1/4*i**4 + 0*i**2.
(i - 1)*(i + 1)**3/4
Let n(k) = k**3 + 5*k**2 - 4*k + 14. Let r be (3 + (-22)/6)*9. Let d be n(r). What is z in 3/4*z**d + 1/4 - 1/4*z**3 - 3/4*z = 0?
1
Suppose 10 = 452*v - 447*v. Factor -1/7*a**v - 2/7*a + 3/7.
-(a - 1)*(a + 3)/7
Factor 3/4 - 9/8*c + 3/8*c**2.
3*(c - 2)*(c - 1)/8
Let o = 191/3 - 63. Factor o*b**3 - 4/3*b - 2/3*b**2 + 0.
2*b*(b - 2)*(b + 1)/3
What is x in -2/7*x**3 - 6/7*x - 2/7 - 6/7*x**2 = 0?
-1
Let i = 389/254 - 4/127. Factor 0*d - i*d**5 + 3/2*d**3 + 3/2*d**4 + 0 - 3/2*d**2.
-3*d**2*(d - 1)**2*(d + 1)/2
Let h(x) = -4*x**2 + x - 3. Let o be (-20)/15*3/(-2). Let c(u) = u**o + 2 + 2 - 3. Let i(r) = 6*c(r) + 2*h(r). Factor i(v).
-2*v*(v - 1)
Let b(n) be the first derivative of n**8/1008 - n**7/315 + n**2 - 2. Let l(q) be the second derivative of b(q). Let l(o) = 0. What is o?
0, 2
Let w be 2*((-6)/(-4))/1. Factor -l - 6*l + 8*l**2 + 2 - w*l.
2*(l - 1)*(4*l - 1)
Let j(v) be the third derivative of 7*v**5/60 + 11*v**4/24 - 5*v**3/3 - 6*v**2. Let p(c) = -c**2 - c + 1. Let m(n) = 3*j(n) + 24*p(n). Factor m(z).
-3*(z - 2)*(z - 1)
Let j(n) = -n**2 + 8*n + 2. Let h be j(8). Let y be (3/3*0)/h. Factor -2/3*l**2 + y + 2*l**3 + 0*l.
2*l**2*(3*l - 1)/3
Suppose 5*v + 0*c = 2*c + 6, 0 = -2*v - 2*c + 8. Determine j, given that 21*j**v + 13*j + 21*j + 2*j - 12 = 0.
-2, 2/7
Let l(k) = 3*k**2 - 2*k + 3. Let x(r) be the third derivative of 7*r**5/20 - 5*r**4/8 + 7*r**3/2 + 8*r**2. Let m(h) = 27*l(h) - 4*x(h). Factor m(j).
-3*(j - 1)**2
Suppose -3*y**2 - y**3 - 3*y + 0*y + 2*y - y**3 = 0. Calculate y.
-1, -1/2, 0
Let h(m) be the first derivative of m**6/120 - 3*m**5/40 + m**4/4 + m**3 - 4. Let o(w) be the third derivative of h(w). Factor o(z).
3*(z - 2)*(z - 1)
Let x(y) = -y**3 - 5*y**2 + 4*y - 7. Let d be x(-6). Suppose d*a - 10 = -0*a. Factor p**3 - p**2 + p**2 + p**4 - 2*p**3 - 2*p**a.
p**2*(p - 2)*(p + 1)
Determine m so that 2*m**4 + 100*m**2 - 6*m**3 + 0*m**4 - 104*m**2 + 4*m**3 = 0.
-1, 0, 2
Factor -32/7*s**4 - 4/7*s - 48/7*s**3 + 0 + 30/7*s**2.
-2*s*(s + 2)*(4*s - 1)**2/7
Let d(x) be the third derivative of -x**5/20 + 3*x**4/8 - x**3 + 5*x**2. Determine h, given that d(h) = 0.
1, 2
Let l(z) be the second derivative of -z**4/42 + 6*z. Factor l(g).
-2*g**2/7
Let s(i) = 6*i**5 - 10*i**4 + 2*i**3 + 6*i**2 - 8*i + 4. Let r(v) = v**5 - v**4 - v**3 + v**2. Let p(k) = -5*r(k) + s(k). Suppose p(y) = 0. What is y?
-1, 1, 2
Suppose -9*h - 48 = -5*h. Let w(l) = 5*l**2 + l - 4*l**2 - 2*l**2 - 1. Let k(q) = 14*q**2 - 18*q + 16. Let x(i) = h*w(i) - k(i). Let x(m) = 0. Calculate m.
1, 2
Let r(s) = -7*s**2 - 37*s - 133. Let v(x) = 11*x**2 + 56*x + 200. Let a(q) = 8*r(q) + 5*v(q). Solve a(m) = 0.
-8
Let a = -12/11 - -58/33. Suppose -a*b**3 + 0 + 4/3*b**2 - 2/3*b = 0. What is b?
0, 1
Let m(q) be the first derivative of q**5/210 - q**3/21 + 3*q**2/2 - 3. Let d(n) be the second derivative of m(n). Factor d(y).
2*(y - 1)*(y + 1)/7
Solve 0*r - 25/2*r**3 + 15/2*r**2 + 5/2*r**4 + 0 + 5/2*r**5 = 0 for r.
-3, 0, 1
Let y(q) be the third derivative of -1/420*q**8 - 2/525*q**7 - 6*q**2 + 0 - 1/30*q**4 + 1/75*q**6 + 0*q + 2/75*q**5 - 2/15*q**3. Factor y(l).
-4*(l - 1)**2*(l + 1)**3/5
Let o(m) be the first derivative of -2*m**3 - 3*m**2 - 4. Let j(q) = 2*q**2 + 2*q. Let v(u) = -8*j(u) - 3*o(u). Factor v(d).
2*d*(d + 1)
Let g be ((-4)/10)/((-1)/5). Let 3*o**2 - 7*o**2 + 2 + 0*o**2 + 2*o**g = 0. Calculate o.
-1, 1
Suppose 9 = -21*c + 24*c. Factor 1/2*x**2 - 1/2*x**c + 0 + 0*x.
-x**2*(x - 1)/2
Suppose 13*z = 9*z + 20. Let k(t) be the second derivative of -1/5*t**2 + t + 0 + 1/75*t**6 - 2/15*t**3 + 1/25*t**z + 0*t**4. Factor k(m).
2*(m - 1)*(m + 1)**3/5
Let c(i) be the first derivative of -i**7/21 + 2*i**6/15 - i**5/10 - 2*i - 3. Let v(w) be the first derivative of c(w). Factor v(s).
-2*s**3*(s - 1)**2
Let n(b) be the third derivative of b**5/24 + 5*b**4/48 + 32*b**2. Factor n(t).
5*t*(t + 1)/2
Let s(a) be the first derivative of a**3/3 - a**2/2 - a + 5. Let u(x) = 3. Let w(o) = -3*s(o) - u(o). What is k in w(k) = 0?
0, 1
Suppose -2*w = 10*c - 13*c + 2, 5*c = -3*w + 16. Factor -4*h**c - 2*h - 5/2*h**3 + 0 - 1/2*h**4.
-h*(h + 1)*(h + 2)**2/2
Let x = 1 - -6. Let p = 0 + -2. Let k(y) = -4*y**5 + 3*y**4 + 7*y**3 + 7. Let d(w) = -w**5 + w**4 + 2*w**3 + 2. Let a(i) = p*k(i) + x*d(i). Factor a(m).
m**4*(m + 1)
Factor 0 + 0*y**3 - 1/6*y**4 - 1/3*y + 1/2*y**2.
-y*(y - 1)**2*(y + 2)/6
Find h such that 3 + 18*h**2 + 14*h + 4*h**3 + 3 - 2*h**3 - 8*h**2 = 0.
-3, -1
Let v(s) be the third derivative of s**6/180 + s**5/30 - s**4/36 - s**3/3 - 33*s**2. Factor v(h).
2*(h - 1)*(h + 1)*(h + 3)/3
Suppose -21 = -5*x - 2*c, 21 = 4*x + 4*c - 3. Find i, given that 3*i - 2*i - 2*i**2 - 4 + x + 2*i = 0.
1/2, 1
Let n be 3*1*(-3)/(12/(-4)). Factor 0*v + 1/4*v**n + 0 - 1/4*v**2.
v**2*(v - 1)/4
Let x(y) be the first derivative of y**4/18 + 2*y**3/27 - 8*y**2/9 - 8*y/3 + 21. Find c such that x(c) = 0.
-2, 3
Let k(q) be the third derivative of -q**7/168 - q**6/48 - 4*q**2. Solve k(w) = 0.
-2, 0
Let t be (-3)/(-9) - 14/6. Let v be -3 + 2 - t/2. Find f such that v*f**2 + 0*f + 2/7*f**3 + 0 = 0.
0
Let r(k) = -2 + 1 + k**2 + 1 - 2*k - 2. Let i(v) = -2*v**2 + 5*v + 5. Let u(w) = -w**2 - w + 5. Let n be u(0). Let c(o) = n*r(o) + 2*i(o). Solve c(t) = 0 for t.
0
Let a(z) be the third derivative of 1/840*z**7 - 1/96*z**4 + 1/80*z**5 + 0*z + 0*z**3 - 1/160*z**6 + 0 - 7*z**2. Factor a(n).
n*(n - 1)**3/4
Factor -9/7*t - 3/7 + 0*t**2 + 12/7*t**3.
3*(t - 1)*(2*t + 1)**2/7
Let r(n) be the third derivative of 0*n + 1/20*n**6 + 0*n**3 + 0 - 2/105*n**7 - 1/12*n**4 + 0*n**5 + n**2. Determine l so that r(l) = 0.
-1/2, 0, 1
Let r(o) be the first derivative of -2*o**2 + 3/4*o**4 + 0*o - 1/5*o**5 + 0*o**3 + 5. Factor r(i).
-i*(i - 2)**2*(i + 1)
Let y(n) be the first derivative of n**8/2240 + n**7/420 + n**6/240 - n**4/96 - 2*n**3/3 + 4. Let p(k) be the third derivative of y(k). Factor p(m).
(m + 1)**3*(3*m - 1)/4
Solve -28*s**2 + 331*s**3 - 161*s**3 - 158*s**3 + 16 = 0.
-2/3, 1, 2
Suppose a = 2*s - 4*s + 7, 4*a - 4 = 4*s. Factor 4 - s*i**3 + i**2 - 8*i + 0*i**3 + i**3 + 4*i**2.
-(i - 2)**2*(i - 1)
Let f(a) be the third derivative of a**7/63 + 29*a**6/540 - 7*a**5/135 - 5*a**4/27 + 8*a**3/27 + 8*a**2. Let f(u) = 0. Calculate u.
-2, -1, 2/5, 2/3
Let n be (-1472)/(-1242) - (-2)/(-27). Find y such that -n*y + 8/3*y**2 - 4/9 = 0.
-1/4, 2/3
Suppose -3*l + v + 2 = -0, -2 = 5*l - 3*v. Suppose -6 = -l*p - 2. Factor -x**2 - 8*x - 2*x**p + 11*x - 7*x + 4.
-(x + 2)*(3*x - 2)
Let i(u) = u + 1. Suppose -2*z + z + 6 = 0. Let x(q) = -q**2 + 8*q - 7. Let k(f) = z*i(f) - 3*x(f). Solve k(o) = 0.
3
Let z(a) be the third derivative of -a**7/525 - a**6/75 - a**5/50 + a**4/15 + 4*a**3/15 - 6*a**2 - 4*a. Determine r, given that z(r) = 0.
-2, -1, 1
Let u(t) be the second derivative of 5*t**4/72 + 65*t**3/18 + 845*t**2/12 + 31*t. Factor u(c).
5*(c + 13)**2/6
Suppose -2*v - 41 = -3*k - 2*k, -37 = v + 3*k. Let b(a) = 8*a**2 - 53*a + 67. Let z(p) = -44*p**2 + 292*p - 368. Let d(s) = v*b(s) - 5*z(s). Factor d(h).
-4*(h - 3)**2
Factor 0 - 8/5*j**2 + 4/5*j**3 - 12/5*j.
4*j*(j - 3)*(j + 1)/5
Let x be -1 - (-4 + 8/3). Let 1/6 + 1/6*n**2 + x*n = 0. Calculate n.
-1
Let l(x) be the third derivative of -x**7/420 + x**6/60 - x**5/20 + x**4/12 - 2*x**3/3 - 2*x**2. Let a(z) be the first derivative of l(z). Factor a(c).
-2*(c - 1)**3
Let z(r) be the third derivative of -r**8/112 + 17*r**7/315 - 23*r**6/180 + 2*r**5/15 - r**4/72 - r**3/9 + 7*r**2. Determine x, given that z(x) = 0.
-2/9, 1
Let l(r) be the second derivative of -r**7/1260 + r**6/270 - r**5/180 - r**3/6 + r. Let z(f) be the second derivative of l(f). Solve z(b) = 0 for b.
0, 1
Let y(n) be the first derivative of n**4/12 - n**2/6 + 7. Determine r so that y(r) = 0.
-1, 0, 1
Let u(y) = 8*y**2 - 2. Let a(b) = -7*b**2 - b + 1. Let f(i) = 6*a(i) + 5*u(i). Factor f(c).
-2*(c + 1)*(c + 2)
Solve 5/2*w**2 + 1 - 7/2*w = 0 for w.
2/5, 1
Let g(c) be the second derivative of -c**7/840 - c**4/6 + c. Let t(r) be the third derivative of g(r). Factor t(v).
-3*v**2
Let n(t) be the third derivative of t**6/420 + t**5/70 - 4*t**3/21 - 22*t**2. Suppose n(z) = 0. Calculate z.
-2, 1
Let y(s) be the second derivative of -s**9/22680 - s**8/10080 + s**7/3780 + s**6/108