- 1)*(i + 1)**2/11
Let r(z) be the second derivative of 1/30*z**6 + 0 - 1/12*z**4 + 1/6*z**3 - 1/20*z**5 + 0*z**2 + 3*z. Factor r(v).
v*(v - 1)**2*(v + 1)
Let j(s) = 2*s + 12. Let f be j(-4). Let i(r) be the first derivative of 8/9*r**2 - 3 - 5/18*r**f - 14/27*r**3 + 8/9*r. Factor i(t).
-2*(t - 1)*(t + 2)*(5*t + 2)/9
Let w(a) be the third derivative of 0 + 1/112*a**8 + 0*a + 2*a**2 + 1/70*a**7 + 0*a**3 - 1/40*a**6 + 0*a**4 - 1/20*a**5. Factor w(l).
3*l**2*(l - 1)*(l + 1)**2
Let x(o) be the first derivative of -3 + 0*o + 0*o**2 + 1/4*o**4 - 1/10*o**5 - 1/6*o**3. Find z, given that x(z) = 0.
0, 1
Suppose -2*d + 0*l + 5*l = -15, 9 = -3*l. Suppose 0 = 3*u - 3 - d. Solve 1 - 2*x**3 - u = 0.
0
Solve 0 + 9/5*x + 3/5*x**3 + 12/5*x**2 = 0 for x.
-3, -1, 0
Determine t so that 0 + 0*t**2 + 0*t - 6/11*t**5 - 4/11*t**4 + 0*t**3 = 0.
-2/3, 0
Suppose -10*s = -3*s - 9*s. Factor s - 2/5*c**2 - 2/5*c.
-2*c*(c + 1)/5
Let m(z) be the third derivative of z**7/1260 + z**4/6 + 5*z**2. Let h(y) be the second derivative of m(y). Factor h(r).
2*r**2
Suppose 0 = 5*k - 3*k + 10. Let r(x) = 9*x**4 + 8*x**3 - 5*x**2 - 13*x + 1. Let s(m) = -4*m**4 - 4*m**3 + 2*m**2 + 6*m. Let t(a) = k*s(a) - 2*r(a). Factor t(q).
2*(q - 1)*(q + 1)**3
Suppose -4*s - 2*r = -8, -2*r = -3*s - 12 + 4. Suppose s*d = 3*d - 9. Factor -2/3*f - 2/3*f**d + 0 - 4/3*f**2.
-2*f*(f + 1)**2/3
Factor -27/2 + 3/2*a**3 + 57/2*a - 33/2*a**2.
3*(a - 9)*(a - 1)**2/2
Solve 14*p**3 - 4 + 0*p**3 - 6*p - 2*p**3 + 10*p**2 = 0 for p.
-1, -1/2, 2/3
Let s be (2 - (-20)/(-8))/((-1)/6). Factor 0*k + 1/3*k**2 - 2/3*k**4 - 1/3*k**s + 0.
-k**2*(k + 1)*(2*k - 1)/3
Let m be 2/(-1 + (-20)/(-16)). Suppose 0 = -4*t + 4*l + 8, -2 = 4*t - 5*l - 9. Factor -4*c**t - m*c**2 - 2*c**3 + 4*c + 4*c.
-2*c*(c + 2)*(3*c - 2)
Let l = 65 + -45. Let w = 101/5 - l. Factor 0 - 2/5*s + w*s**2.
s*(s - 2)/5
Let u(s) be the first derivative of -s**5/150 - s**4/30 - s**3/15 - s**2 - 3. Let a(o) be the second derivative of u(o). Factor a(l).
-2*(l + 1)**2/5
Let r = -2 + 7. Suppose -3*x - 7 + 2 = 5*c, r*c = 2*x + 20. Factor 2*j + j - 5*j + 2*j**c.
2*j*(j - 1)
Let x(y) be the first derivative of 0*y**2 + 2 + 4/3*y**3 - 4*y. Suppose x(d) = 0. What is d?
-1, 1
Let i = -6 - -10. Determine y, given that -25*y**2 - 6*y**5 + 8*y**3 - 2*y + 21*y**2 + 0*y**4 + i*y**4 = 0.
-1, -1/3, 0, 1
Let o(v) = -v**2 - v + 1. Let n be o(2). Let w be (-8)/(-5) + (-2)/n. Factor -4/3*s - 1/3*s**w - 4/3.
-(s + 2)**2/3
Let o(k) = -k + 12. Let l be o(9). Find d, given that -4*d**3 + 3*d**5 + 9*d**3 - 11*d**l + 3*d = 0.
-1, 0, 1
Let r(k) be the first derivative of 2*k**3/33 - 2*k**2/11 - 6*k/11 - 3. Factor r(f).
2*(f - 3)*(f + 1)/11
Suppose j**3 - j - 3198*j**2 + 3198*j**2 = 0. Calculate j.
-1, 0, 1
Let r(c) = -c**3 + 3*c**2 + 5*c + 2. Let i be r(4). Let o + 13*o**5 + 4*o**2 - o - 19*o**5 - 4*o**4 + i*o**3 = 0. Calculate o.
-1, -2/3, 0, 1
Let k(d) be the second derivative of -d**7/4620 - d**6/1980 + d**5/660 + d**4/132 + 7*d**3/6 + 6*d. Let b(t) be the second derivative of k(t). Factor b(s).
-2*(s - 1)*(s + 1)**2/11
Let m be (2/(-9))/((-3)/27). Factor 2/3*p**m + 0 + 2/3*p**3 - 4/3*p.
2*p*(p - 1)*(p + 2)/3
Factor -14*u**2 - 2*u**2 + 0*u**3 + 12*u**3 + 4*u**4.
4*u**2*(u - 1)*(u + 4)
Suppose 4*z - 40 = -4*i, -z - 2*i - 5 = -4*i. Factor 1/2*y**z + 0*y + 0 - 1/2*y**3 + 1/2*y**4 - 1/2*y**2.
y**2*(y - 1)*(y + 1)**2/2
Factor -3*d - 3/2*d**2 + 3/2*d**3 + 0.
3*d*(d - 2)*(d + 1)/2
Suppose -5*n + 2 = -18. Determine c, given that 4*c**2 + 0*c**3 + c**3 - 4*c**4 + 3*c**3 - n*c**5 = 0.
-1, 0, 1
Let k(i) = -i**2 + 5*i + 8. Let r be k(6). Suppose -7*s**2 + s**r + 2*s + 2*s**2 = 0. What is s?
0, 1/2
Let i(a) be the third derivative of a**9/8400 - a**8/2800 + a**7/4200 + a**4/8 + 4*a**2. Let u(b) be the second derivative of i(b). Factor u(t).
3*t**2*(t - 1)*(3*t - 1)/5
Let z = 10 - 10. Suppose -3*a - 2*a + 10 = z. Factor 1/2*c + 0 - c**a + 1/2*c**3.
c*(c - 1)**2/2
Determine z so that -12*z**2 + 3*z**4 + 3*z**3 + 21/2*z - 3/2*z**5 - 3 = 0.
-2, 1
Let k(b) be the second derivative of -b**4/6 - b**2 + 3*b. Let v(d) = d. Let r(w) = -k(w) + 4*v(w). Factor r(m).
2*(m + 1)**2
Let v(k) be the first derivative of k**3/2 - 3*k**2/2 - 9*k/2 - 4. Determine s, given that v(s) = 0.
-1, 3
Let w be 63/102 + (-2)/17. Let h(d) be the first derivative of w*d**6 + 12/5*d**5 + 9/2*d**4 + 3/2*d**2 + 4*d**3 + 0*d - 1. Find m such that h(m) = 0.
-1, 0
Let w = -816 + 2591/3. Let c = 48 - w. Factor 0 + 0*h**4 + 0*h**2 + 0*h - 1/3*h**5 + c*h**3.
-h**3*(h - 1)*(h + 1)/3
Let q(y) = y**5 - y**3 + y - 1. Let w(v) = 3*v**5 - 14*v**4 + 35*v**3 - 40*v**2 + 17*v - 1. Let o(l) = 2*q(l) - 2*w(l). Solve o(f) = 0 for f.
0, 1, 2
Let t = 8 - 5. Let a(i) = i**4 - i**3 - i**2 - i. Let b(d) = 3*d**4 - 3*d**3 - 3*d**2 - d. Let u(k) = t*b(k) - 6*a(k). Suppose u(q) = 0. What is q?
-1, 0, 1
Let j(w) = -w**3 - 3*w**2 - 2*w. Let f be j(-1). Let y(z) be the first derivative of f*z**3 + 2 + 0*z**5 + 0*z**2 + 0*z + 0*z**4 - 1/6*z**6. Factor y(m).
-m**5
Let o(v) be the second derivative of v**7/420 + v**6/80 + v**5/40 + v**4/48 + v**2 + 4*v. Let l(t) be the first derivative of o(t). Let l(w) = 0. Calculate w.
-1, 0
Let f(v) = -8*v**3 - 4*v**2 + 4*v. Let p be ((-12)/(-15))/(2/15). Let c(r) = 23*r**3 + 12*r**2 - 11*r. Let l(m) = p*c(m) + 17*f(m). Factor l(j).
2*j*(j + 1)**2
Let o be 1 + (18/(-5))/6. Factor -o*x**3 + 0*x + 2/5*x**4 - 2/5*x**2 + 0 + 2/5*x**5.
2*x**2*(x - 1)*(x + 1)**2/5
Let j be -1*(3 - 3) + 1. Suppose 3*k - s + j = -3*s, 3*s + 12 = -k. Factor 0*r**2 - r + 7*r - 3*r**2 - k.
-3*(r - 1)**2
Let h(d) = d**3 + 4*d**2 + 2*d + 1. Let a be h(-3). Factor -9 + 9 + 2*z**3 + 8*z**a.
2*z**3*(4*z + 1)
Let s(j) = 1. Let v(x) = x**2 - 4. Let w(p) = -5*s(p) + v(p). Find c such that w(c) = 0.
-3, 3
Let z = 91/22 + 4/11. Factor -3*v + 1/2*v**2 + z.
(v - 3)**2/2
Suppose -j - 1 = 0, -c - 6 = -5*c - 2*j. Factor 1/5*t**3 + 3/5*t - 1/5 - 3/5*t**c.
(t - 1)**3/5
Let a(t) be the third derivative of -t**5/20 + 3*t**4/8 + 8*t**2. Suppose a(o) = 0. What is o?
0, 3
Let d = 13/17 + -35/68. Factor 1/2 - 1/4*n**2 + d*n.
-(n - 2)*(n + 1)/4
Let y(s) be the first derivative of -1/180*s**5 + 1/72*s**4 - 2*s**2 + 0*s**3 + 0*s + 3. Let k(j) be the second derivative of y(j). Factor k(h).
-h*(h - 1)/3
Let a(i) be the second derivative of 3*i**5/140 - i**4/28 - i**3/7 - 7*i. Find w such that a(w) = 0.
-1, 0, 2
Let c(u) be the first derivative of 5 + 5/4*u**3 + 1/4*u**2 + 0*u. Solve c(y) = 0.
-2/15, 0
Suppose -3*p - 2*v = -6*v + 34, 4*v = 4. Let a be (48/300)/((-4)/p). Find f, given that 0 - 2/5*f**3 - a*f**2 + 4/5*f = 0.
-2, 0, 1
Let t(k) be the second derivative of -k**7/210 + k**6/80 + k**5/40 - k**4/24 + 2*k**2 + 5*k. Let w(j) be the first derivative of t(j). Factor w(c).
-c*(c - 2)*(c + 1)*(2*c - 1)/2
Let p(i) be the second derivative of -1/10*i**5 + 0 + 1/120*i**6 + 1/2*i**3 + 0*i**2 + i + 1/2*i**4. Let y(f) be the second derivative of p(f). Solve y(a) = 0.
2
Factor -7*b**2 + 6*b**2 + 3*b - 42*b**3 + b**4 + 39*b**3.
b*(b - 3)*(b - 1)*(b + 1)
Let d = 7 - 4. Factor 5*m**3 - 2*m + m**4 - 4 - 3*m**d + 3.
(m - 1)*(m + 1)**3
Suppose -5*f + 40 = -f. Let z = f - 8. Factor 0 - 1/3*n**4 + 2/3*n**3 - 1/3*n**z + 0*n.
-n**2*(n - 1)**2/3
Let a be (-1 - -4)*(1 - (-5)/(-6)). Factor -1 + 1/2*t**3 + 3/2*t**2 - a*t**4 - 1/2*t.
-(t - 2)*(t - 1)*(t + 1)**2/2
Let o(v) be the first derivative of -v**6/140 + v**5/42 - v**4/84 - v**3/21 - 2*v**2 + 4. Let t(i) be the second derivative of o(i). Factor t(q).
-2*(q - 1)**2*(3*q + 1)/7
Suppose -d**2 - d - 3*d**3 + 4*d**3 + 0*d + 1 = 0. Calculate d.
-1, 1
Factor -p + 4*p**3 - 3*p**3 - 2*p**3 - 2*p**2.
-p*(p + 1)**2
Let -w**2 + 0 - w**4 + 1/4*w**5 + 1/4*w + 3/2*w**3 = 0. What is w?
0, 1
Let s(i) be the first derivative of -2 + 0*i + 0*i**4 + 2/21*i**3 - 2/35*i**5 + 0*i**2. Solve s(u) = 0 for u.
-1, 0, 1
Suppose -n + 3*i = n - 10, -4*i = -5*n + 11. Let u be -5 - n - 34/(-8). Factor 0*r**2 - u*r**3 - 1/2 + 3/4*r.
-(r - 1)**2*(r + 2)/4
Let b = -5 - -5. Let o = b - -2. Find d, given that 0*d + 2/9*d**o + 2/9*d**3 - 2/9*d**4 - 2/9*d**5 + 0 = 0.
-1, 0, 1
Solve -9/4*k**2 - 9/4*k - 3/4*k**3 - 3/4 = 0.
-1
Let z = -1/515 - -3101/5665. Solve -2/11*j**2 - z - 8/11*j = 0 for j.
-3, -1
Let r(k) be the first derivative of k**6/3 + 14*k**5/15 + k**4/3 + 10. Factor r(b).
2*