1)**2/9
Let z(r) be the third derivative of r**8/1512 + r**7/210 + r**6/108 - r**5/108 - r**4/18 - 2*r**3/27 + 131*r**2. Determine l so that z(l) = 0.
-2, -1, -1/2, 1
Let a(j) be the second derivative of 5*j**4/6 - 59*j**3/6 - 3*j**2 + 4*j + 17. Factor a(m).
(m - 6)*(10*m + 1)
Let h(i) be the first derivative of -i**6/12 + 4*i**5/5 - 25*i**4/8 + 19*i**3/3 - 7*i**2 + 4*i - 16. Suppose h(o) = 0. What is o?
1, 2
Let i(o) be the third derivative of -1/140*o**7 + 0*o - 44*o**2 + 1/8*o**4 + 0 - 1/224*o**8 + 1/8*o**5 + 3/80*o**6 + 0*o**3. Factor i(s).
-3*s*(s - 2)*(s + 1)**3/2
Let i be 93/180 - (12/(-8) - -2). Let w(f) be the third derivative of 0 - i*f**5 + 0*f + 1/6*f**4 - 1/2*f**3 - 5*f**2. Determine q, given that w(q) = 0.
1, 3
Let d = 8 + 30. What is v in -79 + 0*v**2 - 4*v**2 + d*v + 15 - 6*v = 0?
4
Let q(r) be the first derivative of -12 + 0*r + 2/11*r**2 - 2/11*r**3. Factor q(p).
-2*p*(3*p - 2)/11
Let v(j) be the third derivative of -j**5/72 + 5*j**4/16 - 5*j**3/2 - 2*j**2. Find k such that v(k) = 0.
3, 6
Suppose -7*k = 10 - 17. Let y be ((-3)/(-1) - k)/1. Determine f, given that 0 - 2/11*f**y + 2/11*f = 0.
0, 1
Let w be (360/110)/(-3)*8/(-24). Factor -10/11*v**2 + 0 + 6/11*v**3 + w*v.
2*v*(v - 1)*(3*v - 2)/11
Let j(o) = -4*o**2 - 4*o + 5. Let b = -74 - -71. Let a(m) = m**2 + m - 1. Let z(i) = b*a(i) - j(i). Factor z(r).
(r - 1)*(r + 2)
Suppose -2*y - 18*y + 50 = 10. Factor 0 - 2/3*f - 1/6*f**y.
-f*(f + 4)/6
Let w = -1/18 + 25/18. Let h = 8 + -6. Let -2/3*a**2 + 0 - 2/3*a**5 + h*a**3 + 2/3*a**4 - w*a = 0. Calculate a.
-1, 0, 1, 2
Suppose -4*j - 2*m = -40, -30 = -3*j + 2*m + 2*m. Suppose i + 2 = 4*a - j, -5*i + 3*a + 8 = 0. Factor 6*k**5 - 5*k**5 - 56*k**4 + 55*k**i.
k**4*(k - 1)
Let z(w) be the third derivative of w**8/588 - 16*w**7/735 - 3*w**6/70 + 36*w**5/35 + 18*w**4/7 - 383*w**2. Suppose z(m) = 0. What is m?
-3, -1, 0, 6
Let p(m) be the second derivative of 7*m**6/72 + 19*m**5/36 + 5*m**4/9 - 10*m**3/9 - 15*m**2 - 4*m. Let u(y) be the first derivative of p(y). Factor u(r).
5*(r + 1)*(r + 2)*(7*r - 2)/3
Let p(k) be the first derivative of 3*k**6/5 + 3*k**5/5 - 4*k**4/3 - 2*k**3 - k**2 + 26*k - 1. Let z(o) be the first derivative of p(o). Factor z(q).
2*(q - 1)*(q + 1)*(3*q + 1)**2
Let o = -19/70 + 39/70. Factor -1/7*n**2 + 1/7*n**5 + 0 - 3/7*n**3 + o*n + 1/7*n**4.
n*(n - 1)**2*(n + 1)*(n + 2)/7
Suppose -11*f**4 + 12*f**4 + 12 + 28*f**2 + 2*f**5 - f**4 - 34*f - 8*f**4 = 0. What is f?
-2, 1, 3
Let s(z) be the second derivative of z**4/4 - 3*z**3 - 81*z**2/2 + z - 56. Factor s(g).
3*(g - 9)*(g + 3)
Suppose -2 = -2*l, -4*l = -2*t - 6*l + 2. Suppose 3*y = -2*h + 21, 5 + 2 = 4*h - y. Find r, given that -r**2 + t*r**h - 1/4*r**5 + 0 + 3/4*r**4 + 0*r = 0.
-1, 0, 2
Factor -3/5*i**4 + 3*i**3 + 3/5*i**2 + 0 - 3*i.
-3*i*(i - 5)*(i - 1)*(i + 1)/5
Suppose -4*b - z - 2 + 16 = 0, -3*z - 3 = -3*b. Factor -30*r**2 - 23*r**3 - 21*r**3 - 5*r**4 + 30*r**3 - 18*r + b*r**4.
-2*r*(r + 1)*(r + 3)**2
Let r(n) = -n**2 + 13*n + 1. Let o be r(12). Let k = o + -11. Find b such that b**3 + b**4 + 8*b - 9*b + 1 - 1 - b**k = 0.
-1, 0, 1
Let a(g) = g**5 - g**2 - g + 1. Let n(b) = -5*b**5 + 100*b**4 - 55*b**3 - 40*b**2 - 10*b + 10. Let r(i) = -10*a(i) + n(i). Suppose r(l) = 0. What is l?
-1/3, 0, 1, 6
Let h(u) = -45*u**2 + 385*u - 4. Let k(l) = 78*l**2 - 769*l + 7. Let f(q) = 7*h(q) + 4*k(q). Factor f(a).
-3*a*(a + 127)
Let b(n) be the first derivative of 2/21*n**3 + 0*n - 15 + 3/7*n**2. Factor b(p).
2*p*(p + 3)/7
Let k = 1635 - 178213/109. Let o = 430/327 + k. Factor o - 2/3*q**3 + 2*q + 0*q**2.
-2*(q - 2)*(q + 1)**2/3
Suppose 3*b = -0*b + 6. Suppose 5*t = -b*g + 10, 6 = -t + 4*t + 2*g. Solve -i**2 + 4*i - t*i + 4*i**2 - 4*i**2 + 3 = 0 for i.
-1, 3
Factor -244*k - 4*k**2 - 6*k - 41616 + 1066*k.
-4*(k - 102)**2
Let o = 24257/11 - 2205. Factor -16/11*i**2 - 32/11*i + 0 - o*i**3.
-2*i*(i + 4)**2/11
Suppose 13 = 4*u + g, -2*u - 3*u - 5*g + 35 = 0. Let -13*n**u + n**2 - 7*n**3 - 5*n**3 + 4*n**4 - 4*n**2 = 0. Calculate n.
-1, 0, 4
Let z be -10 + (-1296)/(-112) + -1. Determine n so that -4/7*n + 4/7*n**4 + 0 - 4/7*n**2 + z*n**3 = 0.
-1, 0, 1
Let c be 2*(-10 + (-217)/(-21)). Suppose -c*v**4 - 98/3*v**2 + 28/3*v**3 + 0 + 0*v = 0. Calculate v.
0, 7
Suppose 4*g + g - 3*s = 34, g - 2*s - 11 = 0. Suppose -8*a**4 + 4*a**5 + 5*a**4 - 7*a**g = 0. Calculate a.
-1, 0
Let f(w) be the first derivative of 18 + 15*w**2 - 6*w - 9/2*w**3. Solve f(l) = 0.
2/9, 2
Let k(n) = -38*n**4 - 24*n**3 + 23*n**2 - 26*n - 13. Let a(l) = -6*l**4 - 4*l**3 + 4*l**2 - 4*l - 2. Let w(y) = 26*a(y) - 4*k(y). Find h, given that w(h) = 0.
-3, 0, 1
Let k(z) = 9*z**2 + 354*z + 6121. Let g(o) = 17*o**2 + 707*o + 12243. Let c(y) = -4*g(y) + 7*k(y). Determine b so that c(b) = 0.
-35
Suppose -23*v + 17*v = -60. Suppose 0*f - 5*f + 15 = 0. Find s such that s**f + v*s - s**2 - 3*s + 6*s**2 + 4 + s = 0.
-2, -1
Suppose g = 2*u + u - 9, 3*u - 3 = -g. Determine d so that -15*d + 3 - 1 + 3*d**u + 4 + 6*d = 0.
1, 2
Let p(g) = g**4 - g**3 - g**2 - g + 1. Let d(t) = -7*t**4 - 32*t**3 + 21*t**2 - 6*t + 2. Let o(x) = -d(x) + 2*p(x). Factor o(h).
h*(h + 4)*(3*h - 1)**2
Suppose -3*d = 3*k + 3, 2*d = 3*k - 14 + 17. Let z(h) be the third derivative of -1/15*h**5 + 0*h + 0 + d*h**3 + 2*h**2 - 1/6*h**4. Factor z(o).
-4*o*(o + 1)
Let s(y) be the second derivative of y**4/6 - y**3/6 + 75*y. Factor s(a).
a*(2*a - 1)
Let g(p) = 2*p**2 + 15*p - 22. Let i(f) = f**3 - f**2 - 8*f - 3. Let b be i(3). Let m be g(b). Solve 0 - 2/5*y**m + 0*y**2 + 0*y + 0*y**4 + 2/5*y**3 = 0.
-1, 0, 1
Factor -7/3*h**3 + 0 - 11/3*h - 35/6*h**2 - 1/6*h**4.
-h*(h + 1)*(h + 2)*(h + 11)/6
Factor 43 + 93*i**3 - 37*i**3 + 4*i**4 - 2*i**2 + 60 + 9 - 160*i - 10*i**2.
4*(i - 1)**2*(i + 2)*(i + 14)
Let m(g) be the second derivative of -21*g**5/4 + 29*g**4 + 46*g**3 + 24*g**2 - 2*g + 23. Factor m(b).
-3*(b - 4)*(5*b + 2)*(7*b + 2)
Let t(z) = -4*z**2 + 7*z + 2. Let h be t(2). Let f(c) be the second derivative of -1/6*c**4 - 1/10*c**5 + 1/15*c**6 + 0*c**2 + 1/3*c**3 - 8*c + h. Factor f(r).
2*r*(r - 1)**2*(r + 1)
Suppose f + 54 = 7*f. Suppose -3*c + 15 = f. Let 0 + 2/13*b**c + 0*b = 0. What is b?
0
Let m(a) = 4*a**2 + 11*a - 15. Let k(s) be the second derivative of s**4 + 16*s**3/3 - 22*s**2 - 10*s. Let l(j) = 3*k(j) - 8*m(j). Factor l(c).
4*(c - 1)*(c + 3)
Factor -134*a**2 - 156 + 58*a - 141*a**2 + 273*a**2.
-2*(a - 26)*(a - 3)
Factor -16/5*s - 18/5*s**2 - 1/5*s**4 - 8/5*s**3 - 1.
-(s + 1)**3*(s + 5)/5
Let m(c) be the second derivative of -c**4/78 + 10*c**3/39 - 25*c**2/13 + 270*c + 1. Factor m(z).
-2*(z - 5)**2/13
Let y = -30 + 33. Factor 3*o**y - 2*o**4 - 14*o**2 - 3*o - o**4 + 17*o**2.
-3*o*(o - 1)**2*(o + 1)
Let s(t) be the second derivative of 5*t**7/42 + 7*t**6/30 - 2*t**5/5 - t**4/3 - 2*t - 20. Determine z, given that s(z) = 0.
-2, -2/5, 0, 1
Suppose -w + 3 = u, 4*u - 6 + 8 = 3*w. Let k(d) be the first derivative of -5 - 2*d**3 + 8*d - 2/5*d**5 + w*d**4 - 4*d**2. Factor k(l).
-2*(l - 2)**2*(l - 1)*(l + 1)
Let z(y) be the third derivative of -3*y**5/140 + 101*y**4/168 - 11*y**3/21 - 5*y**2 + 1. Solve z(w) = 0 for w.
2/9, 11
Let g(d) be the first derivative of -9*d**5/10 - 3*d**4 - 5*d**3/2 + 291. Factor g(u).
-3*u**2*(u + 1)*(3*u + 5)/2
Factor 76*h**2 - 24*h**2 - 53*h**2 - 4*h + 2*h.
-h*(h + 2)
Let l = 61 - 60. Suppose -3*b + 0*c - 4*c + 25 = 0, 4*b = c + 8. Find n such that -l + 0 + 4*n**2 - b*n**2 = 0.
-1, 1
Let v(j) be the first derivative of 16/15*j**5 - 8/9*j**3 - 11 - 10/3*j**2 - 8/3*j + 4/3*j**4 + 2/9*j**6. Suppose v(q) = 0. Calculate q.
-2, -1, 1
Let j(a) be the third derivative of -a**9/90720 + a**8/20160 - a**7/15120 + 7*a**4/24 + 28*a**2. Let q(b) be the second derivative of j(b). Factor q(w).
-w**2*(w - 1)**2/6
Suppose 2*o + 28 = 32. Factor 3*w**4 - 8*w**2 - 48*w - 13*w**o + 6 + 51*w + 6*w**5 - 21*w**3.
3*(w - 2)*(w + 1)**3*(2*w - 1)
Let q(a) = -2*a**4 + 4*a**3 + a**2 - 3*a + 3. Let m(j) = -2*j + 30 + 4*j**3 - 58 + 30 - 2*j**4. Let w(o) = -3*m(o) + 2*q(o). Factor w(h).
2*h**2*(h - 1)**2
Let p(l) be the first derivative of -6/5*l**5 + 2*l**3 + 0*l - 18 + 0*l**2 - 3/4*l**4 + 1/2*l**6. Factor p(u).
3*u**2*(u - 2)*(u - 1)*(u + 1)
Factor 0 + 42/5*c + 3/5*c**3 - 27/5*c**2.
3*c*(c - 7)*(c - 2)/5
Let x(m) be the third derivative of m**5/240 + 3*m**4/4 + 54*m**3 - 108*