2
Find h such that 8*h + 2 - 4*h**4 + 4*h**2 + 21*h**3 - 29*h**3 - 2 = 0.
-2, -1, 0, 1
Let g(w) be the third derivative of w**5/90 - w**4/12 + 2*w**3/9 - 10*w**2. Factor g(k).
2*(k - 2)*(k - 1)/3
Let h(g) = g**3 - 3*g**2 - 2*g - 5. Suppose 8*p + c - 25 = 3*p, 0 = -5*p + c + 15. Let y be h(p). Factor -2/7*x**y + 2/7*x + 0*x**2 + 0.
-2*x*(x - 1)*(x + 1)/7
Let j(u) be the third derivative of -u**10/529200 + u**9/52920 - u**8/17640 - u**5/30 + u**2. Let d(q) be the third derivative of j(q). Solve d(v) = 0.
0, 2
Let f(a) be the second derivative of -3*a**6/10 + 6*a**5/5 - a**4 + 10*a. Factor f(m).
-3*m**2*(m - 2)*(3*m - 2)
Let o = 225 + -674/3. Factor o*h**4 + 0 + 0*h + 0*h**2 + 1/3*h**3.
h**3*(h + 1)/3
Let m(p) be the second derivative of -7*p**7/30 + 427*p**6/75 - 1117*p**5/100 - 17*p**4/15 + 158*p**3/15 + 32*p**2/5 + 9*p. Find r, given that m(r) = 0.
-2/7, 1, 16
Suppose 2*p + 8 = -3*t, -2*t + 7*t + 24 = 2*p. Let m(s) be the first derivative of 1/3*s**p + 0*s - 1 + 1/6*s**4 - 4/9*s**3. Factor m(n).
2*n*(n - 1)**2/3
Factor 0 + 0*s + 3/4*s**3 - 9/4*s**2.
3*s**2*(s - 3)/4
Let g = 61/2 + -30. Factor g*m + 0 + 1/2*m**2.
m*(m + 1)/2
Let w(p) be the second derivative of 5*p**4/24 + 125*p**3/24 + 15*p**2/2 + 4*p + 1. Determine r, given that w(r) = 0.
-12, -1/2
Let m(z) be the first derivative of 5/8*z**4 - 1/4*z + 5/8*z**2 - 5/6*z**3 + 5 + 1/24*z**6 - 1/4*z**5. Factor m(h).
(h - 1)**5/4
Let k(o) = -o + 4. Let a be k(2). Determine j so that 0 + 2*j - 3*j - a*j**2 + j**3 + 2 = 0.
-1, 1, 2
Suppose 4*k + 138 = -3*x, 3*k + 106 = -3*x + 2*x. Let h be (-2)/((-9)/(k/(-40))). Suppose 0 + j**3 + 4/5*j**2 - h*j = 0. What is j?
-1, 0, 1/5
Let b(h) be the third derivative of 1/30*h**5 + 1/4*h**4 + 0 - 6*h**2 + 2/3*h**3 + 0*h. Determine a, given that b(a) = 0.
-2, -1
Let w(k) = k**2 - 5*k**3 + 4*k - 2*k - k**2 + 3*k**2. Let z(h) = 21*h**3 - 12*h**2 - 9*h. Let x(o) = -9*w(o) - 2*z(o). Factor x(f).
3*f**2*(f - 1)
Let h(i) = -5*i**3 + 7*i**2 + 8*i - 13. Let p(g) = 10*g**3 - 13*g**2 - 17*g + 27. Let q(s) = -7*h(s) - 3*p(s). Find d such that q(d) = 0.
-1, 1, 2
Factor 5*k**3 - 19*k**2 - 340 - 11*k**2 + 340 + 5*k**4.
5*k**2*(k - 2)*(k + 3)
Solve 45/2*v - 3/8*v**4 - 69/4*v**2 + 9/2*v**3 - 75/8 = 0 for v.
1, 5
Let i(p) = 2*p - 5. Let s be i(4). Let o(c) be the second derivative of 0 - 3*c - 1/60*c**5 - 1/18*c**4 - 1/18*c**s + 0*c**2. Find w, given that o(w) = 0.
-1, 0
Let o be (-5)/(-50) - 4/(-10). Factor -o*l - 1/2*l**2 + 1.
-(l - 1)*(l + 2)/2
Let w be 26/8 + 1/(-4). Determine i, given that -4*i - 6*i**2 - 1 + i**w - i**4 + 3*i**3 - 8*i**3 = 0.
-1
What is k in 0 + 2/13*k**4 + 0*k**3 - 2/13*k**2 + 0*k = 0?
-1, 0, 1
Let q = -7 + 4. Let x be 1/(-6)*(0 + q). Factor -x*v**4 + 3/2*v**2 + 0 + 0*v**3 + v.
-v*(v - 2)*(v + 1)**2/2
Let v(f) be the third derivative of f**8/2688 + f**7/840 - f**5/240 - f**4/192 + 10*f**2. Let v(a) = 0. What is a?
-1, 0, 1
Let z(b) be the first derivative of b**3/6 - b**2/2 + 6. Solve z(l) = 0 for l.
0, 2
Let k = 14 + -13. Factor 1 + 3*p**2 - k - 5*p**2 + 12*p - 18.
-2*(p - 3)**2
Suppose 0 = 4*z - 0*z. Suppose 4*u + 5*s - 1 = z, s - 10 = -2*u - 5. Factor a - a - 4*a**3 + 10*a**u.
2*a**3*(5*a - 2)
Let b = 202 - 199. Solve 4/5*x**b + 0 + 0*x**2 - 4/5*x = 0.
-1, 0, 1
Let 4*i + 6 + 2/3*i**2 = 0. Calculate i.
-3
Suppose -5*k + 5 = 0, 6*k - 3*k = -4*i + 67. Suppose r + i = 5*r. Factor 2 + z**4 - 7*z**r + 4*z**2 + 4*z**3 + 2*z**5 - 6*z + 0*z**2.
2*(z - 1)**4*(z + 1)
Let t = 110 - 78. Let -11*b**2 + 39*b**4 - 54*b**3 - 3*b + 9*b**3 + t*b**2 - 12*b**5 = 0. Calculate b.
0, 1/4, 1
Factor 8/13 + 2/13*y**2 + 10/13*y.
2*(y + 1)*(y + 4)/13
Let a be (-1 - 0)/(4/44). Let g(t) = t**2 - 5*t. Let w(y) = 3*y**2 - 14*y. Let c(v) = a*g(v) + 4*w(v). Find p, given that c(p) = 0.
0, 1
Suppose -4*l + 5*b + 97 = 0, 2*b - b = 3*l - 59. Let g = 18 - l. Factor 2/7*t**4 + 0*t**2 + 0*t**3 + 0 + g*t.
2*t**4/7
What is v in -32/7 - 2/7*v**2 + 48/7*v - 12/7*v**3 - 2/7*v**4 = 0?
-4, 1
Let w(z) be the second derivative of -z**4/60 + z**3/15 - 6*z. Solve w(l) = 0.
0, 2
Suppose j + 2*b - 12 = -0*j, 5*b = 20. Factor w**2 + 18*w**3 - 4*w**4 - 4*w**2 - 23*w**j + 12*w**5.
3*w**2*(w - 1)**2*(4*w - 1)
Suppose 12*q - 33 = -9. Factor 4/3 + 14/3*v**3 - 8*v**2 + q*v.
2*(v - 1)**2*(7*v + 2)/3
Let f(b) = b + 1. Let h(m) = -2*m**3 + 2*m**2 - 7*m - 11. Let z(o) = o**3 - 4*o**2 - 4*o - 7. Let r be z(5). Let i(d) = r*h(d) - 18*f(d). Factor i(w).
4*(w - 1)**2*(w + 1)
Let o be (-2)/(-20)*2 + 1. What is g in -4/5*g**2 + o*g**4 - 2/5 - 6/5*g + 2/5*g**5 + 4/5*g**3 = 0?
-1, 1
Let i(y) be the third derivative of 0 + 0*y + 0*y**3 + 0*y**5 + 4*y**2 - 1/210*y**7 + 0*y**4 + 1/120*y**6. Factor i(s).
-s**3*(s - 1)
Suppose 6*l - 3*l - 6 = 0. Let u(y) = -7*y**2 + 12*y - 6. Let o(n) = -34*n**2 + 60*n - 31. Let j(q) = l*o(q) - 11*u(q). Factor j(f).
(3*f - 2)**2
Let d be (-29)/(-35) + (-12)/15. Let j(c) be the third derivative of 0 + 0*c**5 + 0*c - d*c**7 + 0*c**3 + c**2 + 0*c**4 - 1/60*c**6 + 1/42*c**8. Factor j(q).
2*q**3*(q - 1)*(4*q + 1)
Let o(g) be the first derivative of -g**3/9 + 2*g**2/3 - 4*g/3 - 1. Suppose o(d) = 0. What is d?
2
Suppose -5*o = 5*h - 0*h - 35, 3*o - 6 = 0. Let z be (h/25)/((-2)/(-5)). Solve 1/2 - z*a + 1/2*a**3 - 1/2*a**2 = 0.
-1, 1
Suppose -1 = -4*y + 7. Let q(o) be the first derivative of 0*o + 4/9*o**3 - 1/3*o**y - 1/6*o**4 - 2. Let q(c) = 0. Calculate c.
0, 1
Let s(a) be the first derivative of -12*a + 7 + 3/4*a**4 - 6*a**2 + a**3. Factor s(p).
3*(p - 2)*(p + 1)*(p + 2)
Let k(s) be the first derivative of 5*s**4/4 + 5*s**3/3 - 15*s**2 + 27. Factor k(h).
5*h*(h - 2)*(h + 3)
Let w be (-2988)/(-81) + (-2)/9. Let o = w + -36. Factor -4*m**2 - 8/3*m - o*m**4 + 10/3*m**3 + 16/3.
-2*(m - 2)**3*(m + 1)/3
What is a in 2*a**4 + 4*a**4 - 9*a - 13*a**2 + 6*a**5 - 9*a**3 - 8*a**2 + 3*a**4 = 0?
-1, 0, 3/2
Let d(y) be the second derivative of y**7/280 + y**6/40 + 3*y**5/40 + y**4/8 - y**3/6 - 5*y. Let p(k) be the second derivative of d(k). Factor p(s).
3*(s + 1)**3
Solve -5*s**2 - 10*s + 8*s**2 + 22*s**2 = 0.
0, 2/5
Let -6*d**3 + 8*d**4 - 9*d**5 - d**4 + 8*d**3 = 0. What is d?
-2/9, 0, 1
Factor 2*c**2 - 28 + 23 - 4*c - c**2.
(c - 5)*(c + 1)
Let c be (-64)/36 + 2 + 52/90. Factor 2/5*i + 2/5*i**2 - c.
2*(i - 1)*(i + 2)/5
Let x = 2 + -2. Let s(f) be the first derivative of 0*f + 1/10*f**5 + x*f**2 - 1/6*f**3 + 0*f**4 + 1. Solve s(v) = 0 for v.
-1, 0, 1
Factor -8/11*j**2 + 2/11*j + 0.
-2*j*(4*j - 1)/11
Let p(u) be the second derivative of u**7/840 + u**6/240 - u**4/3 + 2*u. Let m(c) be the third derivative of p(c). Factor m(d).
3*d*(d + 1)
Let n be (-2)/(-6) - 195/(-1125). Let b = n - -4/25. Suppose 0*x + 0 + 0*x**4 + x**3 + b*x**2 - 1/3*x**5 = 0. Calculate x.
-1, 0, 2
Suppose -3*f = 3*k - 36, -49 = 5*k + f - 125. Solve -2*l**3 + 2*l**4 + k*l - 16*l - l**5 - 2*l**2 + 3*l**5 = 0.
-1, 0, 1
Solve -2 - 8*w - 311/2*w**4 + 63/2*w**2 + 165/2*w**5 + 103/2*w**3 = 0.
-1/3, -2/11, 2/5, 1
Let i(z) be the third derivative of -z**8/84 + 4*z**7/105 - 2*z**5/15 + z**4/6 - 4*z**2. Suppose i(k) = 0. What is k?
-1, 0, 1
Suppose 0*m = 4*m. Let y(k) be the first derivative of 1/12*k**3 + 0*k**4 - 2 - 1/20*k**5 + m*k + 0*k**2. Factor y(f).
-f**2*(f - 1)*(f + 1)/4
Factor 7*b + 10 - 25*b + 7*b + b**2.
(b - 10)*(b - 1)
Let z(u) be the second derivative of -u**6/45 - u**5/30 + u**4/9 - 10*u. Factor z(f).
-2*f**2*(f - 1)*(f + 2)/3
Suppose -h + 16 = 4*r, -h - 3 = r - 10. Let 0*o**2 - 2/11*o**5 + 0*o**3 + 0*o + 0 + 2/11*o**h = 0. Calculate o.
0, 1
Let v(x) be the third derivative of x**10/16800 - x**9/2880 + x**7/420 - x**5/30 + 2*x**2. Let j(r) be the third derivative of v(r). Factor j(h).
3*h*(h - 2)*(h - 1)*(3*h + 2)
Let p(j) be the first derivative of 1/360*j**6 - 2 - j**3 + 0*j**4 - 1/120*j**5 + 0*j**2 + 0*j. Let t(b) be the third derivative of p(b). Solve t(i) = 0.
0, 1
Let o = 42 + -208/5. Determine u, given that 0 - 2/5*u**3 - o*u + 4/5*u**2 = 0.
0, 1
Let o be 4 + 3 + -6 + 3. Let z(v) be the first derivative of -v**2 - 1/2*v**o - 2 - 4/3*v**3 + 0*v. Solve z(g) = 0.
-1, 0
Let d(t) be the third derivative of -t**8/1176 - 2*t**7/735 - t**6/420 + 12*t**2. Find j such that d(j) = 0.
-1, 0
Let h(o) be the third derivative of -o**6/480 + o**4/32 + o**3/12 + 7*o**2. What is f in h(f) = 0?
-1, 2
Let b(w) = -w. Let f(h) = -5*h - 1. Let o(y) = -