etermine z so that f(z) = 0.
2/7, 1
Let x = 12 - 23/2. Let n = -43/2 + 22. Solve -1/2*b**2 + 1/2*b - x*b**3 + n = 0.
-1, 1
Let l(n) be the first derivative of 1/10*n**4 + 6/5*n**3 - 1 + 27/5*n**2 + 54/5*n. Let l(m) = 0. Calculate m.
-3
Let w be 3/(-12)*2*0. Let z(u) be the third derivative of 0*u + w - 1/80*u**6 + 0*u**3 + 1/60*u**5 + 1/48*u**4 - 2*u**2. Factor z(p).
-p*(p - 1)*(3*p + 1)/2
Let s(r) = -8*r**2 - 14*r + 2. Let t(j) be the third derivative of j**2 + 0*j + 1/24*j**4 + 1/60*j**5 + 0*j**3 + 0. Let p(z) = -s(z) - 10*t(z). Factor p(y).
-2*(y - 1)**2
Let q(y) = -13*y**4 + 24*y**3 - 21*y**2 - 5*y - 5. Let r(z) = 7*z**4 - 12*z**3 + 11*z**2 + 3*z + 3. Let s(b) = 3*q(b) + 5*r(b). Factor s(w).
-4*w**2*(w - 2)*(w - 1)
Let p(v) be the second derivative of 3/14*v**3 - 5/294*v**7 + 5/42*v**4 + 0 + 1/7*v**2 - 1/35*v**5 - 5*v - 2/35*v**6. What is j in p(j) = 0?
-1, -2/5, 1
Let m(l) = 7*l**3 + 8*l**2 + l + 5. Let k(i) = -8*i**3 - 8*i**2 - 6. Let d(u) = -5*k(u) - 6*m(u). Find o, given that d(o) = 0.
-3, -1, 0
Suppose -3*k = -9, 0 = -5*p - 4*k - 9 + 31. Let v be -1 + 6/(0 + p). Suppose m - m - m - 4*m**v = 0. Calculate m.
-1/4, 0
Let w(i) be the third derivative of 1/120*i**6 + 2*i**2 + 0 + 0*i**3 + 1/24*i**4 + 0*i - 1/30*i**5. Solve w(m) = 0.
0, 1
Let d be 30/10 + -2 - -1. Let 4/3*w**d - 5/3*w + 1/3 = 0. What is w?
1/4, 1
Let x = 28 - 25. Let n(m) be the first derivative of -3*m**2 + 3/4*m**4 - 4 - m**x + 0*m. Factor n(g).
3*g*(g - 2)*(g + 1)
Let b(j) = 8*j - 3 - 4 + 11*j**2 - 10*j**2. Let z be b(-9). Factor -d**z - 1/2*d**4 + 0 + 0*d + 3/2*d**3.
-d**2*(d - 2)*(d - 1)/2
Let u(v) be the first derivative of 0*v**3 + 1/2*v**4 + 1/3*v**6 + 0*v - 4/5*v**5 + 0*v**2 + 2. Solve u(l) = 0 for l.
0, 1
Let v(q) = -q**2 + q - 1. Let d(i) = 13*i**2 - i - 1. Let o(s) = -2*d(s) + 2*v(s). Find w, given that o(w) = 0.
0, 1/7
Let x(b) = -26*b**2 - 36*b - 12. Let m(j) = -j**2. Let g(l) = -m(l) - x(l). Solve g(p) = 0.
-2/3
Let x = 53/12 + -49/12. Factor 0 - 1/3*r**3 + x*r**4 + 0*r + 0*r**2.
r**3*(r - 1)/3
Let t(s) be the first derivative of -4*s**3/3 + 12*s**2 - 26. Find i such that t(i) = 0.
0, 6
Let h(g) be the second derivative of g**10/30240 + g**9/7560 + g**8/6720 - g**4/12 + 3*g. Let z(y) be the third derivative of h(y). Solve z(n) = 0 for n.
-1, 0
Let l(n) = n**3 - 13*n**2 + 13*n - 10. Let u be l(12). Suppose -u*j = 2 - 6. Factor -2/3*a**j - 4/3*a - 2/3.
-2*(a + 1)**2/3
Let t(u) = -u**3 - 2*u**2 - u - 3. Let n(r) be the second derivative of -1/2*r**2 + r + 0. Let j(z) = 3*n(z) - t(z). Factor j(i).
i*(i + 1)**2
Factor 0*i**2 + 6/7*i - 2/7*i**3 - 4/7.
-2*(i - 1)**2*(i + 2)/7
Suppose 2*w - 2*w = 3*w. Let n(t) be the second derivative of 0 - 2*t + w*t**2 + 1/16*t**4 - 3/80*t**5 - 1/24*t**3 + 1/120*t**6. Suppose n(a) = 0. Calculate a.
0, 1
Let k(m) be the first derivative of -5*m**3/3 + 10*m**2 - 15*m + 44. Solve k(n) = 0 for n.
1, 3
Let r(k) be the second derivative of k**4/28 - 2*k**3/7 + 9*k**2/14 + 6*k. Factor r(g).
3*(g - 3)*(g - 1)/7
Suppose -5*l = -14 - 11. Let y(v) be the first derivative of 0*v**2 + 1/14*v**4 - 1 - 2/35*v**l - 1/21*v**6 + 0*v + 2/21*v**3. Factor y(k).
-2*k**2*(k - 1)*(k + 1)**2/7
Let p = 11 - 11. Factor 2*f**3 + 1 - f - 3*f**2 - 4*f**3 + p*f + 2*f**4 + 3*f**3.
(f - 1)*(f + 1)**2*(2*f - 1)
Let m(z) = z - 3. Let o be m(0). Let j be (-15)/(-3) - (o + 4). Let 2/7*i + 6/7*i**2 + 0 + 6/7*i**3 + 2/7*i**j = 0. Calculate i.
-1, 0
Let m(o) = -7*o**4 - 22*o**3 - 50*o**2 - 27*o + 27. Let q(w) = -8*w**4 - 23*w**3 - 51*w**2 - 27*w + 27. Let p(t) = -6*m(t) + 5*q(t). Factor p(d).
(d + 3)**3*(2*d - 1)
Let f(n) be the third derivative of 8*n**7/105 + 3*n**6/5 - 13*n**5/20 + 5*n**4/24 + 23*n**2. Factor f(c).
c*(c + 5)*(4*c - 1)**2
Determine t so that -2*t**2 - 3*t**2 - 15*t - 85 - 40 + 65*t = 0.
5
Let o(n) = -2*n**4 + 2*n**3 + 8*n**2 + 4*n + 4. Let d(t) = 2*t**4 - t**3 - 8*t**2 - 5*t - 3. Let h(c) = 4*d(c) + 3*o(c). Factor h(b).
2*b*(b - 2)*(b + 1)*(b + 2)
Let r(q) be the first derivative of -3*q**5/5 + 7*q**4/2 - 19*q**3/3 + 2*q**2 + 4*q + 9. Determine v so that r(v) = 0.
-1/3, 1, 2
Let u(k) be the third derivative of k**9/60480 - k**8/10080 + k**5/60 + 2*k**2. Let m(p) be the third derivative of u(p). Solve m(x) = 0 for x.
0, 2
Let y(i) be the first derivative of i**6/180 - i**5/90 - 3*i**2/2 + 2. Let x(f) be the second derivative of y(f). Factor x(s).
2*s**2*(s - 1)/3
Suppose 14*d = 7 - 7. Suppose 2/3 - c + d*c**2 + 1/3*c**3 = 0. What is c?
-2, 1
Let x(c) be the second derivative of 2*c + 0*c**4 - 1/900*c**6 + 0*c**2 - 1/3*c**3 + 0*c**5 + 0. Let d(u) be the second derivative of x(u). Solve d(m) = 0.
0
Let h(y) = 7*y**2. Let u(j) be the second derivative of -5*j**4/3 - 7*j. Let x(z) = -17*h(z) - 6*u(z). Factor x(i).
i**2
Let a(m) be the second derivative of 2*m**7/147 - 2*m**6/105 - 9*m**5/35 - 11*m**4/21 - 8*m**3/21 - 2*m - 13. Factor a(v).
4*v*(v - 4)*(v + 1)**3/7
Let q(o) = 7*o**3 - 4*o**2 - 5*o. Let t(c) = -22*c**3 + 12*c**2 + 14*c. Let w(x) = 10*q(x) + 3*t(x). What is v in w(v) = 0?
-1, 0, 2
Let d(y) be the first derivative of -1/4*y**4 + y**3 - 3 + 0*y - y**2. Factor d(p).
-p*(p - 2)*(p - 1)
Let b(n) be the third derivative of -n**5/80 - 3*n**4/32 + n**3/2 + 6*n**2. Factor b(a).
-3*(a - 1)*(a + 4)/4
Suppose -2*d = -4*i + 14, 4*d + 4 = -0*d. Suppose i*l - 9 = -3. Let -1 + 8*k**2 - k - 7*k**4 - l*k**3 - k + 0*k**3 + 4*k**5 = 0. Calculate k.
-1, -1/4, 1
Let a = 0 + 2. Suppose a*i - i - 3 = 0. Factor -4*c**3 + c**3 - i*c**2 - 3*c**2 - 2*c**4 - 3*c**3 - 2*c.
-2*c*(c + 1)**3
Let o(h) = h**3 - h. Let i(l) = 393*l**3 + 126*l**2 - 25*l - 8. Suppose 1 = 3*r - 2*r. Let p(q) = r*i(q) - o(q). Let p(s) = 0. What is s?
-2/7, 1/4
Let b = -2/495 + 4463/1980. Let h(l) be the second derivative of b*l**2 + 0 + 1/24*l**4 - 1/2*l**3 + 4*l. Let h(p) = 0. What is p?
3
Let j(f) be the second derivative of -f**6/60 - 7*f**5/80 - 3*f**4/16 - 5*f**3/24 - f**2/8 - 10*f. Factor j(k).
-(k + 1)**3*(2*k + 1)/4
Let v(n) be the first derivative of 3*n**4/5 + 28*n**3/15 - 16*n/5 + 1. Determine k so that v(k) = 0.
-2, -1, 2/3
Find g, given that -6/5*g**3 - 2/5*g + 8/5*g**5 + 0 - 2*g**2 + 2*g**4 = 0.
-1, -1/4, 0, 1
Factor -1/2*n**4 + 0 + 0*n**2 - 1/4*n**5 - 1/4*n**3 + 0*n.
-n**3*(n + 1)**2/4
Let n be (118/12)/((-24)/(-21)). Let i = n + -31/16. What is h in 20/3*h**3 + 2/3*h**5 + 10/3*h - 2/3 - 10/3*h**4 - i*h**2 = 0?
1
Factor -8/9*l**5 + 0 + 0*l**2 + 2/9*l**4 + 0*l**3 + 0*l.
-2*l**4*(4*l - 1)/9
Let d be (12/(-15))/((-4)/10). Let r(c) = -2*c**3 + 13*c + 0*c - 5*c**d - 12*c**2. Let o(y) = -y**3 - 8*y**2 + 6*y. Let x(w) = 13*o(w) - 6*r(w). Solve x(n) = 0.
-2, 0
Factor 6/11*n - 4/11 - 2/11*n**2.
-2*(n - 2)*(n - 1)/11
Suppose -38*y - 8*y + 14*y**2 - 12 - 58*y**2 - 10*y**3 = 0. Calculate y.
-3, -1, -2/5
Suppose -6*m = -m - 5*i - 10, -2*m + 11 = 5*i. Factor u**3 - 28*u + 26*u - m + u**2 + 3.
u*(u - 1)*(u + 2)
Suppose j = -4*j + 10. Factor -9 - v**j + 2*v + 0 + v - 9*v.
-(v + 3)**2
Let l(c) = c**3 - 10*c**2 + 9*c + 5. Let q be l(9). Let k = 9 - q. Suppose -2*o**5 - o - o**3 + k*o**5 + 3*o**3 - 3*o**5 = 0. Calculate o.
-1, 0, 1
What is t in -2*t**3 + 0 + 0*t + 2/3*t**4 + 0*t**2 = 0?
0, 3
Let w(t) be the first derivative of -t**8/1260 + t**7/504 - t**6/1080 + 2*t**3/3 - 3. Let r(h) be the third derivative of w(h). Let r(y) = 0. What is y?
0, 1/4, 1
Factor 0*a**5 + 3*a**4 + 2*a**4 + 3*a**5 - 4*a**5 + 4*a**2 - 8*a**3.
-a**2*(a - 2)**2*(a - 1)
Let g(n) be the first derivative of -n**4/4 + 2*n**3/3 - n**2/2 + 8. Find y, given that g(y) = 0.
0, 1
Let a be 2/4 + 7/(-14). Factor a + 5/6*p**2 - 2/3*p**3 - 1/6*p.
-p*(p - 1)*(4*p - 1)/6
Suppose -2*c + 2 = v - 3*c, 0 = 2*v + 3*c - 4. Factor -1/4*w**3 - 1/4*w**v + 0*w + 0.
-w**2*(w + 1)/4
Let r be (-3316)/8*2/1. Let f = r - -9127/11. Let 72/11*i**2 + 0 - 210/11*i**3 - f*i + 200/11*i**4 = 0. Calculate i.
0, 1/4, 2/5
Factor 0*u**2 + 12*u + 3*u**2 - 10*u + u**3.
u*(u + 1)*(u + 2)
Let u be (-6)/(-24) - (-515)/4. Let j be u/27 - 6/(-27). Factor 2*r**3 - 2 + r + 7*r**2 + 2*r - j*r**4 - 7*r**3 + 2*r**3.
-(r - 1)*(r + 1)**2*(5*r - 2)
Let i be (2 + 4)/(2/15). Let z be 39/i + (-1)/(-3). Determine v, given that 6/5*v**4 - z*v**3 + 2/5*v**2 - 2/5*v**5 + 0 + 0*v = 0.
0, 1
Let j(i) = i**2 - 3*i. Let r be j(4). Let w(x) be the second derivative of 1/18*x**3 + 2*x + 1/3*x*