1 = -g. Factor -a**2 + 4 - 18*a + 4*a**s + g*a**2.
2*(a - 1)*(7*a - 2)
Let w(p) be the second derivative of -p**6/360 + p**4/24 + 2*p**3/3 - 6*p. Let b(l) be the second derivative of w(l). Factor b(o).
-(o - 1)*(o + 1)
Suppose 3*o + 26 = 16*o. Factor -2/7*j**4 + 0*j**o + 3/7*j**3 - 1/7*j + 0.
-j*(j - 1)**2*(2*j + 1)/7
Let o be 1/2*(1 + 3). Suppose -4*t + o*t + 6 = 0. Factor -4/3*l**5 + 0*l + 5/3*l**4 + 0*l**2 - 1/3*l**t + 0.
-l**3*(l - 1)*(4*l - 1)/3
Let y(s) be the second derivative of -2*s**7/3 - 4*s**6/15 + 14*s**5/5 + 4*s**4/3 - 14*s**3/3 - 4*s**2 - 12*s. Let y(b) = 0. What is b?
-1, -2/7, 1
Let m be ((-4)/10)/(3/(-30)). Suppose 5*j - m*w - 7 = -7*w, -2*j - 2*w + 2 = 0. Factor -2*s**j + 0*s**2 + 0*s**2 + 3*s**2 - 2*s.
s*(s - 2)
Let f(u) = u**3 - u**2 - 2*u - 1. Let q(j) = -21*j**4 - 156*j**3 + 129*j**2 + 54*j + 3. Let l(c) = 3*f(c) + q(c). Factor l(g).
-3*g*(g - 1)*(g + 8)*(7*g + 2)
Let f(h) be the second derivative of 1/50*h**5 + 0*h**3 + 0*h**2 - 2*h + 1/30*h**4 + 0 - 1/105*h**7 - 1/75*h**6. Factor f(v).
-2*v**2*(v - 1)*(v + 1)**2/5
Let u(m) = m + 4. Suppose -2*h - 5 + 1 = 0. Let o be u(h). Solve -2/7*j**o - 2/7*j + 4/7 = 0.
-2, 1
Let x(l) be the first derivative of 16*l**5/5 - 2*l**4 - 5*l**3 + 4*l**2 - l + 5. Factor x(j).
(j - 1)*(j + 1)*(4*j - 1)**2
Suppose -2*r + 0*s - 21 = -5*s, s = -2*r + 9. Let n(u) = -u - 1. Let v(a) = -a**2 + a - 7. Let f(j) = r*v(j) - 6*n(j). Determine g, given that f(g) = 0.
2
Suppose -5*t = -6*t. Suppose -5*o - 3*o - o**2 + t*o**2 - 3*o**2 = 0. Calculate o.
-2, 0
Let o be (1 - 438/436)*22. Let u = o + 5483/327. Find a, given that 0 - 22/3*a**3 + 8/3*a + u*a**5 + 8*a**2 - 20*a**4 = 0.
-2/5, 0, 1
Let a(z) be the second derivative of -1/42*z**4 + 0 - z + 0*z**3 + 0*z**2. Factor a(k).
-2*k**2/7
Let o(z) be the first derivative of 5*z**4/4 - 5*z**3/3 - 10. Find s such that o(s) = 0.
0, 1
Let v be (-1 - 0)*10/(-5). Let q(d) = 39*d**2 - 2*d - 1. Let t be q(-1). Solve 71/3*o**v + t*o**3 - 4/3 - 4*o - 400/3*o**4 = 0 for o.
-1/4, 2/5
Let o be (4 + 41)*(-2)/5. Let w = o - -21. Factor 0 - 2/3*t**w - 2/3*t**2 + 0*t.
-2*t**2*(t + 1)/3
Factor -22*y + 5*y**2 - 18*y**2 - 10 - y**2 - 2*y**3.
-2*(y + 1)**2*(y + 5)
Suppose -5*c + 2*g + 17 = g, -2*g - 10 = -4*c. Suppose -5*n = -c - 6. Factor -4/5*a + 0 + 6/5*a**n - 2/5*a**3.
-2*a*(a - 2)*(a - 1)/5
Let v(s) be the third derivative of 3*s**8/112 - 4*s**7/35 + s**6/40 + 2*s**5/5 - s**4/2 - 42*s**2. Solve v(h) = 0 for h.
-1, 0, 2/3, 1, 2
Let f(y) = -y**3 + y**2. Let w(s) = -3*s**2 - s. Let p = 2 - 0. Let i(c) = p*f(c) + 2*w(c). Factor i(x).
-2*x*(x + 1)**2
Suppose -2*b - 4 = -0*b. Let g be (-8)/(-2) + b + 1. Factor -3*o**3 + o**4 + 7*o**g - 1 - 2*o**3 - 2*o.
(o - 1)*(o + 1)**3
Let s(r) = 235*r + 1 - 234*r + 5. Let k be s(-6). Factor 0*f + 1/2*f**2 + k.
f**2/2
Determine f so that 44*f - 141 - 2*f**2 + 75 - 34 - 142 = 0.
11
Let u(r) be the second derivative of -r**4/60 - r**3/10 - r**2/5 + r. Let u(x) = 0. What is x?
-2, -1
Let a(h) = -h**3 - 9*h**2 + 21*h - 9. Let f be a(-11). Factor -1/3 - 2/3*u - 1/3*u**f.
-(u + 1)**2/3
Let n(k) be the second derivative of k**2 - 1/5*k**5 - 4*k + 0 - 1/3*k**3 + 1/7*k**7 + 1/3*k**6 - k**4. Factor n(a).
2*(a - 1)*(a + 1)**3*(3*a - 1)
Let u = -2 - -5. Let b(g) be the first derivative of -1/4*g**4 + 0*g + 0*g**u + 1 + 1/2*g**2. Factor b(t).
-t*(t - 1)*(t + 1)
What is t in 2/11*t**4 + 0*t + 0 + 4/11*t**3 + 2/11*t**2 = 0?
-1, 0
Let i(k) be the first derivative of k**4/48 - k**3/9 + k**2/8 - 54. Let i(m) = 0. Calculate m.
0, 1, 3
Let j(w) be the third derivative of 1/36*w**4 + 0*w - 2*w**2 + 0 + 2/45*w**6 + 0*w**3 - 11/180*w**5 - 1/90*w**7. What is g in j(g) = 0?
0, 2/7, 1
Let g be (9/12)/((-216)/(-64)). Let s(o) be the first derivative of 1/18*o**4 + 1 + 1/3*o**2 - 2/9*o - g*o**3. Let s(v) = 0. What is v?
1
Let f(c) be the third derivative of -1/3*c**5 + 0*c + 0 + 0*c**3 + 1/3*c**4 + 5*c**2 + 2/15*c**6 - 2/105*c**7. Factor f(u).
-4*u*(u - 2)*(u - 1)**2
Let u = 134725/4907 - 19/701. What is s in 1812/7*s**3 - 244*s**4 + u*s - 16/7 - 124*s**2 + 84*s**5 = 0?
2/7, 1/3, 1
What is i in 3*i + 3/2*i**3 + 13/4*i**2 + 1 + 1/4*i**4 = 0?
-2, -1
Let m(v) be the second derivative of v**4/48 + v**3/4 + v**2 + 21*v. Factor m(a).
(a + 2)*(a + 4)/4
Suppose 0 = o + o + 4*t - 8, -5*t = 2*o - 9. Factor 29*w**3 + 8*w**4 - w**o - w**2 - 35*w**3.
2*w**2*(w - 1)*(4*w + 1)
Let y(r) be the first derivative of 2*r**3/15 - 2*r**2/5 - 6*r/5 - 25. Factor y(q).
2*(q - 3)*(q + 1)/5
Let y(s) = -s**2 + 16*s + 8. Let a be 1/(2/(-6)*-1). Let o = a + 1. Let j(z) = 2*z**2 - 47*z - 25. Let n(x) = o*j(x) + 11*y(x). Determine m so that n(m) = 0.
-2
Let v(n) be the second derivative of 9*n**4/7 - 6*n**3/7 + 3*n**2/14 + 7*n. Factor v(o).
3*(6*o - 1)**2/7
Suppose -21 = -3*u - 15. Let v**2 - 3*v - v**3 + 0 + 4*v - 3*v**u + 2 = 0. Calculate v.
-2, -1, 1
Let d(b) be the first derivative of -b**4/28 - b**3/7 - 3*b**2/14 - b/7 - 17. Factor d(m).
-(m + 1)**3/7
Let z(o) be the third derivative of -o**7/945 - o**6/540 + o**5/270 + o**4/108 + o**2. Factor z(l).
-2*l*(l - 1)*(l + 1)**2/9
Suppose -4*d**3 + 6*d**3 - 6*d - 4*d**2 + 8*d = 0. Calculate d.
0, 1
Let o(z) be the second derivative of -2/27*z**3 + 0 - 3*z - 3/2*z**2 - 1/270*z**5 + 1/36*z**4. Let j(g) be the first derivative of o(g). Factor j(q).
-2*(q - 2)*(q - 1)/9
Let p(m) be the third derivative of -m**7/3024 - m**6/360 - m**5/180 + m**4/3 - 6*m**2. Let q(d) be the second derivative of p(d). Factor q(g).
-(g + 2)*(5*g + 2)/6
Let m(f) be the third derivative of -f**8/16 + 3*f**7/7 - 5*f**6/4 + 2*f**5 - 15*f**4/8 + f**3 + 4*f**2. Suppose m(c) = 0. Calculate c.
2/7, 1
Let g(b) = 8*b**2 - 3*b - 5. Let j(q) = 15*q**2 - 6*q - 9. Let n(l) = 9*g(l) - 5*j(l). Solve n(d) = 0 for d.
0, 1
Let a = 62 + -554/9. Factor -2/9*j**3 + a - 10/9*j + 8/9*j**2.
-2*(j - 2)*(j - 1)**2/9
Let n be 125/15 + (-1)/3. What is b in 14*b**3 + n*b**2 + 15*b**3 + 4*b**4 - 17*b**3 = 0?
-2, -1, 0
Suppose -12*t + 24 = -4*t. Let -3/5*n**t - 1/5*n - 3/5*n**2 + 0 - 1/5*n**4 = 0. Calculate n.
-1, 0
Let t(i) be the third derivative of -i**5/180 - i**4/36 - i**3/18 - 6*i**2. Factor t(r).
-(r + 1)**2/3
Factor 0*n**2 + 22*n**2 + 27*n + 12*n**2 + 16 + 25*n - 12*n**3.
-2*(n - 4)*(2*n + 1)*(3*n + 2)
Let v(l) be the first derivative of -1/14*l**4 + 1 + 0*l + 4/21*l**3 - 2/35*l**5 + 0*l**2. Factor v(y).
-2*y**2*(y - 1)*(y + 2)/7
Let w be 0/((1*(-2 + 1))/(-1)). Factor 0*l**2 + 0*l - 2/3*l**3 + 4/3*l**5 + 2/3*l**4 + w.
2*l**3*(l + 1)*(2*l - 1)/3
Let t(y) = -y**3 + 4*y + 3. Let p be t(-2). Factor 5*k**3 - 3*k**2 - 6*k + k**p - 2*k**3 - k**3.
3*k*(k - 2)*(k + 1)
Let l(d) be the second derivative of 3*d**5/80 + 3*d**4/16 + 3*d**3/8 + 3*d**2/8 + 24*d. Factor l(x).
3*(x + 1)**3/4
Let a(j) = -j**2 - 5*j - 3. Let d = 8 + -11. Let o be a(d). Factor -t**3 + t**2 - 2*t**3 + 4*t**o.
t**2*(t + 1)
Suppose -2*m + 0*h - 3*h + 2 = 0, 4*m - 2*h = 20. Suppose 3 = 3*i + 3*n, -m*i - n + 13 = i. Let k**4 + k**3 + i*k**2 - 3*k**2 = 0. What is k?
-1, 0
Let x(i) be the second derivative of i**8/10080 - i**6/1080 + i**4/4 - 2*i. Let k(u) be the third derivative of x(u). Find f, given that k(f) = 0.
-1, 0, 1
Let l(x) = -3*x**2 + 16*x - 5. Let i be l(5). Factor i*j + 1/3*j**5 - 1/3*j**3 + 0*j**4 + 0*j**2 + 0.
j**3*(j - 1)*(j + 1)/3
Suppose 0*j = -2*q - 5*j, 0 = 3*q - 3*j. Let h(d) be the third derivative of 2*d**2 + 1/6*d**4 + 0 + 0*d**3 + 7/30*d**5 + q*d. Factor h(v).
2*v*(7*v + 2)
Let l(n) = -n**3 + n + 4. Let c be l(0). Suppose -2 - c = -2*g, -o - 3*g = -11. Factor 3*d**2 - o*d + 2 - 8*d**3 + 9*d**3 - 3*d - d**4.
-(d - 1)**3*(d + 2)
Let l = 3 + 0. Let y(m) = -36*m - 13*m**2 + 42*m - 100*m**3 - 9 + 65*m. Let q(g) = 50*g**3 + 7*g**2 - 35*g + 5. Let c(r) = l*y(r) + 7*q(r). Factor c(a).
2*(a + 1)*(5*a - 2)**2
Let y(n) = n**4 - n**3 + n + 1. Let a be (6/(-3) + 1)*-4. Let x(j) = -7*j**4 - 5*j**3 - 3*j**2 + 5*j + 2. Let g(v) = a*y(v) + x(v). Factor g(d).
-3*(d - 1)*(d + 1)**2*(d + 2)
Let o(q) = -q**2 + 6*q + 1. Let f be o(7). Let u(a) = -a**3 - 7*a**2 - 5*a + 6. Let r be u(f). Factor r + 1/2*m + 1/2*m**2.
m*(m + 1)/2
Suppose 3*x = x + 4. Let l be (-57)/(-15) + -3 - -4. Let -16/5*k**x - l*k**3 + 36/5*k**4 + 0*k + 0 - 2*k**5 = 0. Calculate k.
-2/5, 0, 2
Let d(q) be the third derivative of q**8/2184 - q**7/455 - q**6/390 + q**5/6