 + 1)*(y + 7)/10
Let a(t) = t**2 - 2*t + 4. Let f be a(3). Determine g, given that -1 + f*g - 2*g**2 + 6*g**2 + 5 - 15*g = 0.
1
Let d(l) be the third derivative of l**5/60 - 7*l**4/24 + 4*l**3/3 - 3*l**2. Let p be d(6). Factor -p - 4*q - 2*q + 5*q + 2*q + q**2.
(q - 1)*(q + 2)
Suppose -5*g = -5*o + 15, o - 3 = -0*o - 4*g. Factor m**4 - 13 + 13 + m - m**2 - m**o.
m*(m - 1)**2*(m + 1)
Let y(w) be the first derivative of -45*w**4/4 + 10*w**3/3 + 45*w**2/2 - 10*w + 10. Let y(f) = 0. Calculate f.
-1, 2/9, 1
Let q(w) be the second derivative of -3*w**5/20 - w**4/4 + w**3 + 2*w. Factor q(a).
-3*a*(a - 1)*(a + 2)
Let z(d) be the third derivative of 1/525*d**7 + 0*d + 0*d**6 - d**2 + 0*d**5 + 0*d**4 + 0*d**3 + 0. Factor z(i).
2*i**4/5
Let c(p) be the second derivative of 5*p**7/6 + 25*p**6/6 + 15*p**5/2 + 25*p**4/6 - 25*p**3/6 - 15*p**2/2 - 9*p. Factor c(u).
5*(u + 1)**4*(7*u - 3)
Let r(i) = 2*i**3 + 8*i**2 + 6*i + 2. Let f(x) = 10*x**3 + 41*x**2 + 30*x + 10. Let o(a) = -2*f(a) + 11*r(a). Factor o(h).
2*(h + 1)**3
Let -3/2*t**3 + 9/4*t**4 - 3/4 + 9/4*t - 3/4*t**5 - 3/2*t**2 = 0. Calculate t.
-1, 1
Let p(s) = 7*s**4 + s**3 - 4*s**2 - 7*s - 3. Let c(x) = -6*x**4 - 2*x**3 + 4*x**2 + 6*x + 2. Let f(l) = -3*c(l) - 2*p(l). Factor f(v).
4*v*(v - 1)*(v + 1)**2
Let r(s) be the second derivative of s**7/420 - s**6/60 + s**4/3 - s**3/6 + 3*s. Let q(y) be the second derivative of r(y). Find d such that q(d) = 0.
-1, 2
Let z(v) be the first derivative of v**7/210 + v**6/40 + v**5/20 + v**4/24 - 2*v**2 - 4. Let k(q) be the second derivative of z(q). Factor k(s).
s*(s + 1)**3
Let h(f) be the second derivative of -f**7/3360 + f**5/480 - f**3/6 + f. Let g(t) be the second derivative of h(t). Factor g(v).
-v*(v - 1)*(v + 1)/4
Let y be (-98)/(-4)*(4 - 2). Factor -3*p + y*p**3 + 35*p + 4 + 35*p**2 + 42*p**2.
(p + 1)*(7*p + 2)**2
Let z(r) = -r + 7. Let i be z(5). Factor 3*p**2 + 4*p - 4 + 8 - p**2 - p**i.
(p + 2)**2
Let s(c) = -c**2 - 7*c - 12. Let o be s(-6). Let m be 1/6 + (-3)/o. Factor 5/3*v + m + v**2.
(v + 1)*(3*v + 2)/3
Let f(c) be the second derivative of -5*c - 49/40*c**5 + 0 - 5*c**3 - 21/4*c**4 - 2*c**2. Factor f(s).
-(s + 2)*(7*s + 2)**2/2
Suppose 5*u = -1 + 86. Factor -1 - u*y**2 - 12*y**3 + 0*y + 3 + 2*y - 5*y.
-(y + 1)*(3*y + 2)*(4*y - 1)
Let n(m) be the second derivative of m**6/45 + m**5/15 - 21*m. Factor n(u).
2*u**3*(u + 2)/3
What is s in -7*s**3 + 4*s**2 - s**3 + 11*s**4 - 7*s**4 = 0?
0, 1
Let n(o) be the third derivative of -o**5/150 - 2*o**4/15 + 3*o**3/5 + 33*o**2. Factor n(k).
-2*(k - 1)*(k + 9)/5
Suppose 6*j - j = 25. Factor -2*w**5 + 0*w**3 + w**4 + 2*w**2 + 3*w**j - w**3 - 3*w**2.
w**2*(w - 1)*(w + 1)**2
Let c be (3/336)/(2 - (-8)/(-7)). Let v(j) be the third derivative of -c*j**4 + 0 + 0*j + 3*j**2 + 1/240*j**5 + 0*j**3. Factor v(f).
f*(f - 1)/4
Suppose 2*y - 3*y = -2. Factor 4 - 3*v - 3*v**3 - y + 4*v**3.
(v - 1)**2*(v + 2)
Let q(w) = -15*w**2 + 15*w - 11. Let a(z) = 4*z**2 - 4*z + 3. Let t(h) = 22*a(h) + 6*q(h). Let t(u) = 0. What is u?
0, 1
Let d(q) be the second derivative of 7/100*q**5 + 7*q - 23/60*q**4 + 2/3*q**3 - 2/5*q**2 + 0. Factor d(z).
(z - 2)*(z - 1)*(7*z - 2)/5
Let v(a) = a - 4 - 6*a - 3 + 4*a. Let t be v(-10). Let 0 + 0*j + 2/3*j**4 - 2/3*j**2 - 2/3*j**5 + 2/3*j**t = 0. Calculate j.
-1, 0, 1
Find i such that 2/7*i**4 + 0*i + 0 - 2/7*i**3 + 0*i**2 = 0.
0, 1
Let t = -561 - -2245/4. Find z such that -1/4*z**2 - 1/4*z**3 + t*z + 1/4 = 0.
-1, 1
Let b(z) be the first derivative of -3 - 1/6*z**4 + 2/3*z**3 + 0*z - 2/3*z**2. Factor b(v).
-2*v*(v - 2)*(v - 1)/3
Solve -29*m**2 + 41*m**2 + 48*m - 3*m**5 + 4*m**3 - 40*m**3 - m**4 - 20*m**4 = 0.
-4, -2, 0, 1
Suppose -1/3*u**2 + 1 + 2/3*u = 0. Calculate u.
-1, 3
Let l = -2 - -4. Factor l - 3*f**2 - 1 - 6*f - 1.
-3*f*(f + 2)
Let j(p) = 4*p**4 - 10*p**3 - 16*p**2 + 10*p. Let w(x) = -x**3 - x. Let q(o) = j(o) - 6*w(o). Determine i so that q(i) = 0.
-2, 0, 1, 2
Let m = 979/205 - -1/41. Factor 21/5*z + 9/5*z**3 + m*z**2 + 6/5.
3*(z + 1)**2*(3*z + 2)/5
Suppose 3*x + 2*x + 3*p - 9 = 0, 5*p = x - 13. Factor 0*k**2 - 2/3*k + 2/3*k**x - 1/3*k**4 + 1/3.
-(k - 1)**3*(k + 1)/3
Let x(r) be the third derivative of -r**7/5040 - r**4/12 - r**2. Let i(w) be the second derivative of x(w). Factor i(g).
-g**2/2
Let w = -14 - -17. Determine t so that t**2 - t**2 + 2*t**2 - t**w + t + 1 - 3*t**2 = 0.
-1, 1
Let d(p) = -p**2 - 8*p - 8. Let t be d(-6). Let z = t + -1. Solve 2/3 - 5/3*a**3 + 1/3*a**4 - 7/3*a + z*a**2 = 0 for a.
1, 2
Let h(z) be the first derivative of -z**5/10 - z**4/8 - 5. Factor h(v).
-v**3*(v + 1)/2
Suppose -2*b - 7 = 1, 0 = 5*o - 4*b - 26. Suppose o*k = -k + 6. Let -3*q**k + 1 + q**2 - 1 - 4*q = 0. Calculate q.
-2, 0
Let m(d) be the first derivative of -2*d**3/39 + 10*d**2/13 - 50*d/13 + 16. Factor m(p).
-2*(p - 5)**2/13
Let m = 47/4 - 1547/132. Let k(l) be the second derivative of m*l**3 + 0*l**2 - 1/66*l**4 + 0 + l. Factor k(f).
-2*f*(f - 1)/11
Let b be (-12)/10*(-11)/((-1089)/(-55)). Determine x so that 16/3 - 4/3*x**2 + 8/3*x - b*x**3 = 0.
-2, 2
Let n(i) be the first derivative of -i**7/210 - i**6/120 + 2*i**2 + 4. Let a(o) be the second derivative of n(o). Let a(f) = 0. Calculate f.
-1, 0
Let s = 19 + -17. Let z(r) be the third derivative of 1/840*r**8 + 0*r + 1/15*r**4 + 0 + 2/25*r**5 + s*r**2 + 0*r**3 + 2/175*r**7 + 13/300*r**6. Factor z(t).
2*t*(t + 1)**2*(t + 2)**2/5
Suppose 3*b - n = -6*n + 35, 2*b = 5*n + 40. Let i be (-10)/(-4)*4/b. Factor -i*l + 0*l**3 + 2/3*l**5 + 4/3*l**2 - 4/3*l**4 + 0.
2*l*(l - 1)**3*(l + 1)/3
Let v(z) be the second derivative of -z**8/10080 + z**7/1680 - z**6/1080 + z**3/6 - 5*z. Let d(s) be the second derivative of v(s). Factor d(u).
-u**2*(u - 2)*(u - 1)/6
Let p(x) = 4*x**3 - 4*x**2 + 6*x - 3. Let g(f) = -f**3 - f + 1. Let b(l) = -3*g(l) - p(l). Let w be b(2). Let 1/2*z**w - 1/4*z**3 + 0 - 1/4*z = 0. What is z?
0, 1
Let u = 4 + -23/6. Let h(t) be the second derivative of -1/20*t**5 - 1/6*t**3 - 2*t + 0*t**2 + 0 + u*t**4. Factor h(v).
-v*(v - 1)**2
Let m(q) be the second derivative of q**4/4 + 7*q**3/2 + 9*q**2 + 4*q. Factor m(a).
3*(a + 1)*(a + 6)
Let p = 258 - 256. Solve 0 + 1/2*m + 1/4*m**p = 0.
-2, 0
Let d(j) be the third derivative of j**7/5040 - j**6/720 + j**5/240 + j**4/24 + 2*j**2. Let v(f) be the second derivative of d(f). Solve v(t) = 0 for t.
1
Suppose 3*s + 9 = 0, -6 = -5*x - 5*s - 1. Suppose 5*n = 2*q - 3*q, 4*n = -x*q. Determine w, given that 1/2*w**3 - 3/2*w**2 + w + q = 0.
0, 1, 2
Let g(y) be the second derivative of y**7/210 + y**6/120 - y**5/60 - y**4/24 + y**2 - 3*y. Let s(w) be the first derivative of g(w). Let s(x) = 0. Calculate x.
-1, 0, 1
Let i(d) be the second derivative of -2*d**7/21 - 2*d**6/15 + 3*d**5/5 + d**4/3 - 4*d**3/3 + 15*d + 3. Suppose i(z) = 0. What is z?
-2, -1, 0, 1
Let z(h) = h**4 + h**2 + h - 1. Let a(q) = 5*q**5 - q**4 - 30*q**3 + 24*q**2 + 44*q - 4. Let o(f) = -a(f) + 4*z(f). What is k in o(k) = 0?
-2, -1, 0, 2
Let k(r) be the first derivative of -2*r**3 - 1/2*r**4 - 3 - 2*r**2 + 0*r. Let k(n) = 0. Calculate n.
-2, -1, 0
Let s(t) be the first derivative of -t**6/24 + 3*t**5/20 + 3*t**4/8 - 5*t**3/6 - 21*t**2/8 - 9*t/4 + 2. Factor s(k).
-(k - 3)**2*(k + 1)**3/4
Suppose 0 = -3*k - k + 12. Let g be (-6)/(-21) + k/14. Factor -1/2*p - g*p**2 + 0.
-p*(p + 1)/2
Let j be (-2)/9 - 6/(-27). Let k be ((-6)/(-4) + 0)*20/135. Factor k*x**4 + 2/9 + j*x + 0*x**3 - 4/9*x**2.
2*(x - 1)**2*(x + 1)**2/9
Let z = -1/27 + 7/27. Let f be (-22)/(-8) - 2/(-8). Let -2/3*y**2 + 4/9 + 2/9*y**4 - z*y + 2/9*y**f = 0. Calculate y.
-2, -1, 1
Suppose -57*u = -59*u + 4. Factor 6*o**u - 7/2*o**3 - 3/2*o - 1.
-(o - 1)**2*(7*o + 2)/2
Let w(p) be the third derivative of p**6/780 - p**5/390 - p**4/156 + p**3/39 + 3*p**2. Factor w(o).
2*(o - 1)**2*(o + 1)/13
Factor 2/5*z**4 - 2*z**2 + 0 + 6/5*z + 2/5*z**3.
2*z*(z - 1)**2*(z + 3)/5
Let t = 319/6 + -53. Let j(c) be the first derivative of -2 + 0*c - 1/8*c**4 + t*c**3 + 1/4*c**2 - 1/10*c**5. Factor j(i).
-i*(i - 1)*(i + 1)**2/2
Let h be 4/20 - (-42)/15. Let v(b) = -b**3 + 4*b**2 - b - 2. Let k be v(h). Solve -31*y - 16*y**3 + 4*y**2 + 21*y**5 + 31*y + y**k = 0 for y.
-1, 0, 2/7, 2/3
Let 1/2*z**2 + 9/2 - 3*z = 0. Calculate z.
3
Let b(t) = -t**2 - 6*t + 8. Let f be b(-6). Suppose 20 = i - 0. Factor 9*x**3 + i*