 2*c. Let t(a) = 7*k(a) - 3*z(a). Factor t(l).
-5*(l - 7)*(l - 1)
Let y(i) = i**5 - i**4 + i**3 + 2*i + 3. Let n(c) = 12*c**5 + 54*c**4 + 81*c**3 + 58*c**2 + 15*c - 2. Let k(t) = 2*n(t) + 2*y(t). Let k(m) = 0. Calculate m.
-1, -1/13
Let c = 68 + -70. Let g be 3/c*(7 + -9). Solve 1/4*h**4 - 1/4*h**2 + 1/4*h**g - 1/4*h + 0 = 0 for h.
-1, 0, 1
Suppose -11/4*l**4 + 5/4*l**5 + 1/2*l**3 - 7/4*l + 5/2*l**2 + 1/4 = 0. Calculate l.
-1, 1/5, 1
Let f(t) = 2*t**3 + 534*t**2 + 47521*t + 1409968. Let u(z) = -3*z**3 - 801*z**2 - 71281*z - 2114955. Let i(l) = 8*f(l) + 5*u(l). Factor i(r).
(r + 89)**3
Let c(g) be the first derivative of -11 - 2/5*g**2 - 3/5*g**3 + 12/5*g - 1/25*g**5 + 3/10*g**4. Factor c(y).
-(y - 3)*(y - 2)**2*(y + 1)/5
Let u(g) be the third derivative of -3/40*g**5 + 0*g + 7/240*g**6 + 0 + 1/3*g**3 - 1/4*g**4 + 4*g**2. Suppose u(q) = 0. What is q?
-1, 2/7, 2
Let w(r) be the first derivative of 13 + 0*r**2 + 0*r + 15/28*r**4 + 4/7*r**3 + 3/35*r**5. Factor w(n).
3*n**2*(n + 1)*(n + 4)/7
Let o(p) be the second derivative of 2*p**7/21 - 22*p**6/3 + 727*p**5/5 + 839*p**4/3 - 1456*p**3/3 - 1568*p**2 + 148*p. Find c, given that o(c) = 0.
-1, 1, 28
Let f = -2/5087 - -7086197/15261. Let t = f - 456. Find q such that -1/3*q**2 + 10/3*q - t = 0.
5
Let w(y) be the third derivative of 0*y - 2/5*y**4 + 2/25*y**5 - 1/200*y**6 + 0 + 0*y**3 - 9*y**2. Suppose w(b) = 0. What is b?
0, 4
Let w(o) be the first derivative of -o**6/39 - 2*o**5/65 + 4*o**4/13 + 8*o**3/13 - 94. Determine z, given that w(z) = 0.
-2, 0, 3
Let o(k) be the second derivative of k**6/6 - k**5/2 - 15*k**4/4 + 5*k**3/3 + 20*k**2 + 158*k. Let o(u) = 0. What is u?
-2, -1, 1, 4
Let s be 28/7 - 1/((-9)/(-32)). Determine f, given that -4/9*f**2 - 4/9*f + s + 4/9*f**3 = 0.
-1, 1
Let o(l) be the second derivative of l**6/30 - 2*l**5/15 - 11*l**2/2 + 7*l. Let b(c) be the first derivative of o(c). Factor b(i).
4*i**2*(i - 2)
Suppose -3*k = -2*s + 107, -6*s + k - 61 = -7*s. Let i = s - 58. Suppose 0 + 4/3*p**2 + i*p - p**5 - 4*p**3 + 11/3*p**4 = 0. What is p?
0, 2/3, 1, 2
Let r = 39329/11 + -3569. Let s(n) = -n**2 - 4*n - 1. Let j be s(-2). Determine y, given that -16/11*y + r*y**j - 62/11*y**2 + 8/11 = 0.
-2/5, 2/7, 1
Let r = -306 - -314. Let t be ((-6)/63)/(r/(-72)). Factor -2/7*a**2 + t*a - 4/7.
-2*(a - 2)*(a - 1)/7
Suppose -41 = -y + 4*k, 5*k = -4*y + 108 - 7. Factor -y - 21 - 4*p**2 - 15*p + 5*p**2 + 29*p**2 - 5*p**3.
-5*(p - 5)*(p - 2)*(p + 1)
Determine q so that 1/3*q - 1/3*q**3 + 1/3 - 1/3*q**2 = 0.
-1, 1
Suppose 26 = 2*d - 4*f, -2*d + 4*d - 5*f = 29. Factor -3 - 47*p**2 - 4*p**4 - 8*p + d + 47*p**2 + 8*p**3.
-4*(p - 1)**3*(p + 1)
Let g(v) be the first derivative of -3*v**4/4 + 165*v**3 - 27225*v**2/2 + 499125*v + 56. Solve g(x) = 0 for x.
55
Factor -51/7*c - 36/7 + 15/7*c**2.
3*(c - 4)*(5*c + 3)/7
Suppose 5*a - 381 = -21. Let b be (2 + -1)*24/a. Factor 0 + b*o**2 - 4/3*o.
o*(o - 4)/3
Let t(x) = 6*x + 37. Let b be t(-5). Find f, given that 8*f**2 - 12 - 4*f - 4*f**4 + 8*f**3 - b - 4*f**5 + 15 = 0.
-1, 1
Let b(w) be the first derivative of 2*w**6/3 - 2*w**5 + w**4/2 + 4*w**3/3 - 364. Determine q so that b(q) = 0.
-1/2, 0, 1, 2
Let v(h) be the third derivative of -h**6/96 - h**5/8 + 275*h**4/96 + 3*h**2 - 60. Factor v(x).
-5*x*(x - 5)*(x + 11)/4
Let b(j) be the second derivative of 3/100*j**5 + 1/50*j**6 + 0 + 1/60*j**4 + 0*j**3 + 1/210*j**7 + 0*j**2 + 2*j. Factor b(v).
v**2*(v + 1)**3/5
Let j(l) be the first derivative of 0*l + 20 - 3/2*l**2 + 0*l**3 + 9/16*l**4 + 3/20*l**5. Solve j(g) = 0 for g.
-2, 0, 1
Suppose 32*v - 56*v = -48. Factor -1/2*r**v - 1/2 + r.
-(r - 1)**2/2
Let k = 51 - 70. Let t = -17 - k. Factor -1/8*q**3 + 0*q - 3/8*q**t + 1/2.
-(q - 1)*(q + 2)**2/8
Let h(o) = 31*o + 191. Let m be h(-6). Let w(s) be the second derivative of -2/3*s**2 + 2/9*s**3 - 1/36*s**4 - m*s + 0. Determine z so that w(z) = 0.
2
Let l(g) be the second derivative of -g**6/200 + g**5/50 + 7*g**2 + 12*g. Let m(n) be the first derivative of l(n). Find r, given that m(r) = 0.
0, 2
Suppose -4*b + 955 + 21 = 0. Solve -b*m + 4*m**2 + 2*m**3 + 244*m = 0 for m.
-2, 0
Factor 0 - 5*x**4 - 30*x**2 - 18*x - 37/2*x**3 - 1/2*x**5.
-x*(x + 2)**2*(x + 3)**2/2
Suppose -33*n + 5*n**3 + 0*n**3 + 35*n**2 - 4*n**3 + 4*n**3 + 83*n = 0. Calculate n.
-5, -2, 0
Let w(g) be the first derivative of -81*g**4/2 + 1320*g**3 - 868*g**2 + 192*g + 21. Factor w(l).
-2*(l - 24)*(9*l - 2)**2
Let g(x) be the first derivative of 0*x - 1/14*x**4 + 2/7*x**2 + 28 + 2/21*x**3. Let g(o) = 0. What is o?
-1, 0, 2
Let u(f) = -2*f - 4. Let g be u(0). Let z be -4 - (-8)/4 - g. Suppose 6/7*y - 2/7*y**z - 4/7 = 0. What is y?
1, 2
Let x(j) be the third derivative of 0*j**3 + 3*j**2 + 1/105*j**6 + 0*j**4 - 2/105*j**5 + 0*j + 0 - 1/735*j**7. Determine q so that x(q) = 0.
0, 2
Factor -2*b**3 - 35*b - 20*b**2 - 2*b**3 - 3*b + 14*b.
-4*b*(b + 2)*(b + 3)
Let u = -803 - -3213/4. What is y in -1/4*y**5 + 3/4*y**3 - u*y**4 + 0 + 1/4*y**2 - 1/2*y = 0?
-2, -1, 0, 1
Let y be 12/9*9 - 3. Let l = y - -1. Factor -8*d + 3 - 7 + 6 + l*d**2 - 4*d**3.
-2*(d - 1)**2*(2*d - 1)
Let -10/3 + 5/3*p + 5/3*p**2 = 0. What is p?
-2, 1
Let x(k) be the first derivative of -k**4/24 - k**3/9 + 4*k**2/3 + 16*k/3 - 413. Let x(s) = 0. Calculate s.
-4, -2, 4
Let h(p) be the third derivative of p**6/30 + 19*p**5/15 - 2*p**2 - 106. Determine k so that h(k) = 0.
-19, 0
Let v = -29 - -28. Let o(z) = 3*z**3 + 6*z**2 + 9*z. Let d(m) = m**2 + m. Let c(b) = v*o(b) + 9*d(b). Factor c(f).
-3*f**2*(f - 1)
Factor f + 0 - 1/2*f**4 - 1/2*f**5 + 3/2*f**3 + 5/2*f**2.
-f*(f - 2)*(f + 1)**3/2
Let z be ((-4)/(26 + 2))/(6/(-21)). Find a, given that 2*a - z*a**2 - 2 = 0.
2
Let q(b) be the first derivative of 2*b**5/25 - 3*b**4/5 + 26*b**3/15 - 12*b**2/5 + 8*b/5 + 3. Factor q(y).
2*(y - 2)**2*(y - 1)**2/5
Let b(g) = 2*g**2 + 12*g + 7. Let i(k) = -7*k**2 - 35*k - 20. Let u(s) = -8*b(s) - 3*i(s). Find a, given that u(a) = 0.
-1, -4/5
Let c(y) be the second derivative of 0 - 30*y - 1/180*y**6 + 0*y**2 + 1/24*y**4 + 1/60*y**5 + 0*y**3. Suppose c(h) = 0. Calculate h.
-1, 0, 3
Let o(b) = 14*b**2 - 2. Let h(a) = -a**3 + 1. Let u(v) = 4*h(v) + 2*o(v). Suppose u(s) = 0. Calculate s.
0, 7
Let o(r) = 11*r**2 + 17*r - 15. Let b = 21 - 13. Let f(q) = 13*q + 1 - 5*q - b + 5*q**2. Let p(n) = 13*f(n) - 6*o(n). Factor p(w).
-(w - 1)**2
Let x(k) be the third derivative of -k**5/60 + 17*k**4/12 - 31*k**3/2 - 911*k**2. Factor x(j).
-(j - 31)*(j - 3)
Factor -160/13*m - 2/13*m**3 + 34/13*m**2 + 128/13.
-2*(m - 8)**2*(m - 1)/13
Let h(m) be the third derivative of m**10/30240 - m**8/6720 - m**4/12 - 2*m**2. Let i(x) be the second derivative of h(x). Solve i(s) = 0 for s.
-1, 0, 1
Let m(a) be the third derivative of 0*a + 0 - 1/180*a**5 + 2*a**2 - 1/540*a**6 + 4/3*a**3 + 1/18*a**4. Let r(q) be the first derivative of m(q). Solve r(j) = 0.
-2, 1
Let d = 0 + 3. Let a = 6 - d. Factor g + g**4 + g - 3*g + g**a - g**2.
g*(g - 1)*(g + 1)**2
Let y(t) = -t**3 - t + 1. Let k(u) = 10*u**3 + 2*u - 6. Let o(i) = k(i) + 6*y(i). Let o(n) = 0. What is n?
-1, 0, 1
Let g(v) be the second derivative of 7*v**4/24 + 65*v**3/12 + 9*v**2/2 + 42*v. What is i in g(i) = 0?
-9, -2/7
Let q = 8 - 6. Suppose 1344*b = 1330*b. Solve b + 0*u - 1/2*u**q = 0 for u.
0
Factor 97*o**2 - 65*o**4 - 11*o - 1069*o + 39*o**2 - 123*o**3 + 5*o**5 + 44*o**2 + 333*o**3.
5*o*(o - 6)**2*(o - 3)*(o + 2)
Let m(p) be the second derivative of p**6/120 - p**4/8 + p**3/3 - 6*p**2 + 3*p. Let t(o) be the first derivative of m(o). Find u such that t(u) = 0.
-2, 1
Let h be ((-12)/3 + 1)*-1. Suppose -h*d + 4*m + 28 = 0, -2*m = 5*d - 7*m - 40. Let 9/2*t**5 + t + 53/4*t**3 - 51/4*t**d - 6*t**2 + 0 = 0. Calculate t.
0, 1/2, 2/3, 1
Let k(p) be the first derivative of -p**2 + 0*p**3 + 1/8*p**4 - 7 + 0*p. Factor k(q).
q*(q - 2)*(q + 2)/2
Suppose 3*m - 8*m + 65 = 0. Let l be (m/(-39))/(10/(-12)). Factor -2/5*j**3 + l*j**2 + 2/5*j - 2/5.
-2*(j - 1)**2*(j + 1)/5
Let x(p) = -p**3 + 24*p**2 + 22*p + 78. Let k be x(25). Let s(l) be the first derivative of 0*l - 1/2*l**3 + 0*l**2 + k. Let s(u) = 0. Calculate u.
0
Let o(b) be the second derivative of 39*b + 0 + 1/18*b**4 + 0*b**2 + 0*b**3. Find z, given that o(z) = 0.
0
Suppose 0 = 4*u - 16, 7*l - 4*l = -5*u + 29. Let m(c) be the second derivative of 0*c**l