 6
Let h(v) be the third derivative of -v**5/720 + 19*v**4/144 - 361*v**3/72 + 83*v**2. Find l such that h(l) = 0.
19
Let d(q) = -2*q + 18. Let n be d(8). Factor -o + o + 17*o**2 - 2*o**n - 12*o - 3.
3*(o - 1)*(5*o + 1)
Let q = -165 + 170. Let r(u) be the third derivative of -1/90*u**q + 5/108*u**4 + u**2 + 0*u + 2/27*u**3 + 0. Determine t, given that r(t) = 0.
-1/3, 2
Let c(w) be the third derivative of -w**6/80 + w**5/40 - 80*w**2. Factor c(z).
-3*z**2*(z - 1)/2
Suppose 8*a - 3*a = -2*m + 15, -5*m - 10 = 3*a. Let i(n) be the second derivative of 0*n**2 + 1/10*n**4 + 0 - 1/75*n**6 + 0*n**5 + a*n - 2/15*n**3. Factor i(f).
-2*f*(f - 1)**2*(f + 2)/5
Let c(b) = -5*b**2 - 8*b - 3. Let o(f) = -f**3 - 6*f**2 - 3*f - 17. Let r be o(-6). Let t(w) = -w**2 + 1. Let p(h) = r*t(h) + c(h). Find n such that p(n) = 0.
-1, -1/3
Let h(x) = -13*x**5 + 88*x**4 - 24*x**3 - 114*x**2 + 41*x + 30. Let z(t) = -t**5 - 2*t**4 - t. Let y(c) = h(c) + 2*z(c). Suppose y(v) = 0. What is v?
-1, -2/5, 1, 5
Let x(a) be the second derivative of 3*a + 0*a**2 - 11/4*a**4 - 1/90*a**6 - 9/2*a**3 - 6 - 19/60*a**5. What is s in x(s) = 0?
-9, -1, 0
Suppose 5*t - 6 = -2*r - 2, t - 8 = 2*r. Factor -3 - 27/4*w**3 + 6*w + 9/4*w**t.
-3*(w + 1)*(3*w - 2)**2/4
Let k be (5 + 4/(-1))*0. Suppose 4*b - b - 15 = k. Let 0*o + 2/3*o**3 + 0 + 2/9*o**b - 2/9*o**2 - 2/3*o**4 = 0. What is o?
0, 1
Let u(b) = b**2 + 19*b - 20. Let j be u(-20). Let k(d) be the third derivative of 6*d**2 - 3/4*d**4 - 9/2*d**3 - 1/20*d**5 + j*d + 0. Factor k(r).
-3*(r + 3)**2
Let o(d) be the third derivative of -d**6/360 - d**5/60 - d**4/24 - d**3/6 + 6*d**2. Let z(u) be the first derivative of o(u). Find i such that z(i) = 0.
-1
Let m be (501/(-8))/((-15)/10). Let d = 85/2 - m. Solve 3/2 - 3/4*g**2 - d*g = 0 for g.
-2, 1
Let d be (198/(-4455))/(4/(-60)). Factor -2/9*k**3 + 4/9 - 2/9*k**4 + 10/9*k + d*k**2.
-2*(k - 2)*(k + 1)**3/9
Let m(t) be the third derivative of 1/12*t**4 - 13*t**2 + 1/735*t**7 + 2/21*t**3 + 1/84*t**6 + 0*t + 3/70*t**5 + 0. Let m(r) = 0. What is r?
-2, -1
Solve -1/3*k**4 - 261*k**2 + 0 - 55/3*k**3 - 243*k = 0 for k.
-27, -1, 0
Let u(q) = q**5 + 11*q**4 - 15*q**3 - 35*q**2 - 13*q. Let g(d) = -2*d**5 - 10*d**4 + 14*d**3 + 34*d**2 + 14*d. Let p(w) = -3*g(w) - 2*u(w). Factor p(o).
4*o*(o - 2)*(o + 1)**2*(o + 2)
Let v(b) be the third derivative of 0*b + 1/5*b**4 + 0 - 3/100*b**5 - 2/5*b**3 + 14*b**2. Factor v(g).
-3*(g - 2)*(3*g - 2)/5
Let j(n) be the second derivative of n**4/54 - 10*n**3/27 - 14*n - 1. Determine c, given that j(c) = 0.
0, 10
Let j = -5 - -7. Suppose -3*z + 2 = -j*z. Factor -4*r**z + 2*r**2 - 4*r**3 + 19*r**4 - 21*r**4.
-2*r**2*(r + 1)**2
Suppose 0 = 2*d + 4, 7*s - 12*s + 16 = -3*d. Let q(t) = 2*t**3 + 2*t**2 - 1. Let u be q(1). Let -1/5*y**u + 1/5*y**s + 0 + 0*y = 0. Calculate y.
0, 1
Let u(b) be the second derivative of -162/5*b**6 + 0 + 17*b**4 - 216/5*b**5 - 8*b**2 + 40/3*b**3 + 2*b. Find l, given that u(l) = 0.
-1, -1/3, 2/9
Let h be (-23)/3 + (-55)/(-33) - 4. Let a be (h/(-6))/((-70)/(-126)). Solve -2*c**4 - 8/7*c**5 + 16/7*c**2 - 2/7 + 4/7*c**a + 4/7*c = 0.
-1, 1/4, 1
Let j be 10/125 + (-3666)/(-1050) + -3. Find l such that -j*l + 2/7*l**2 + 2/7 = 0.
1
Let h(v) be the third derivative of -v**10/756000 - v**9/75600 - v**8/33600 - 11*v**5/60 - v**2. Let f(z) be the third derivative of h(z). Factor f(u).
-u**2*(u + 1)*(u + 3)/5
Suppose 4*k + 40 + 48 = 0. Let m be k/77 - 32/(-14). Factor 3*i + 3*i**3 - 6*i + 0*i**m + 3*i**2 + 0*i - 3.
3*(i - 1)*(i + 1)**2
Let f(d) be the second derivative of -d**5/60 - 5*d**4/18 - 7*d**3/18 + 3*d**2 + 504*d. What is s in f(s) = 0?
-9, -2, 1
Let n(c) be the third derivative of -2*c**7/105 - 11*c**6/30 - 2*c**5/3 - 31*c**2 + 3. Factor n(o).
-4*o**2*(o + 1)*(o + 10)
Let i(w) be the third derivative of 1/18*w**3 - 6*w**2 - 1/360*w**5 + 0*w + 1/144*w**4 + 0. Let i(z) = 0. What is z?
-1, 2
Let l(g) = -4*g**3 - 1. Let z be (-3)/(-15) + 6/(-5). Let k be l(z). Determine o so that k*o**4 + o**3 + 4*o**3 + 2*o**3 - 4*o**3 = 0.
-1, 0
Solve -5*g**2 + g**2 - 2*g**5 - 36*g**4 + 28*g**4 - 24*g**3 + 14*g**3 = 0 for g.
-2, -1, 0
Suppose -6*f + 5 + 13 = 0. Factor 2*x**2 + 0*x**3 + x**5 + 138*x - f*x**4 + 2*x**3 - 141*x + 1.
(x - 1)**4*(x + 1)
Let w = -142 - -142. Let h(m) be the third derivative of 0*m**6 + 0*m - 1/21*m**3 - 1/735*m**7 + 0*m**4 + 5*m**2 + 1/105*m**5 + w. Factor h(d).
-2*(d - 1)**2*(d + 1)**2/7
Let y(r) = -43*r + 21. Let h be y(-3). Factor h*j**4 - 70*j**4 + 592*j**4 - 495*j**3 - 105*j**2 - 5*j - 67*j**4.
5*j*(j - 1)*(11*j + 1)**2
Let b(p) be the first derivative of -p**3/18 + 61*p**2/6 - 3721*p/6 + 122. Factor b(d).
-(d - 61)**2/6
Let u(k) be the third derivative of k**7/210 - k**6/24 + k**5/10 + 2*k**2 + 7. Let u(m) = 0. What is m?
0, 2, 3
Let x(h) = -48*h**2 + 0 + 4*h + 4 + 49*h**2 + 0*h. Let v be x(-4). Solve -2*t**2 - 2*t**2 + 2*t**2 + 2*t**3 + t**3 + 20*t**v = 0 for t.
-2/5, 0, 1/4
Let k = -86 + 88. Let l(m) be the first derivative of 0*m - 8 + 4/3*m**3 - 4*m**k. Solve l(s) = 0 for s.
0, 2
Suppose 0 = -l + 3*v + 2 + 2, -3*l + 2 = v. Let d be l - (25/11)/5. Factor 2/11*m**4 - 2/11*m - d*m**3 + 0 + 6/11*m**2.
2*m*(m - 1)**3/11
Let x(s) = 906*s**2 + 138*s + 10. Let j(t) = 905*t**2 + 135*t + 9. Let q(r) = 6*j(r) - 5*x(r). Let q(n) = 0. Calculate n.
-1/15
Let g(y) be the first derivative of y**6/27 - 56*y**5/45 - y**4/18 + 56*y**3/27 - 759. Suppose g(k) = 0. What is k?
-1, 0, 1, 28
Let u(s) = -2*s**3 - s**2 - 2. Let c(k) = 4*k**3 + 180*k**2 + 364*k + 192. Let q(p) = c(p) + 4*u(p). What is x in q(x) = 0?
-1, 46
Suppose 36/5*p - 2/5*p**2 - 162/5 = 0. What is p?
9
Let l(s) = 16*s**3 + 4*s**2 + 12. Let f(d) = 3*d + 11. Let w be f(-4). Let u(q) = q**3 + q**2 + q + 1. Let i(a) = w*l(a) + 20*u(a). Factor i(t).
4*(t + 1)**2*(t + 2)
Determine d so that 5/4*d**2 - 30*d + 315/4 = 0.
3, 21
Let w(n) = -2*n**5 + 7*n**4 + 243*n**3 + 610*n**2 + 565*n + 183. Let q(p) = p**5 - p**4 + p**3 + 1. Let i(x) = -3*q(x) + w(x). Let i(j) = 0. Calculate j.
-4, -1, 9
Suppose 2*i - 10 = 3*r, -8 + 0 = -5*i - r. Factor m + 0*m + 3*m - 404 + i*m**2 + 398.
2*(m - 1)*(m + 3)
Let y = 28/23 - 145/138. Factor 1/6*w - y*w**3 + 0 - 1/6*w**2 + 1/6*w**4.
w*(w - 1)**2*(w + 1)/6
Suppose -2*g + 676 = 2*g - 2*y, -3*y + 666 = 4*g. Let 2*p + 169 - 340 + p**2 + g = 0. Calculate p.
-3, 1
Let p(s) be the first derivative of 3/2*s**4 - 6/5*s**5 + 0*s - 2/3*s**3 + 1/3*s**6 + 0*s**2 + 10. Factor p(x).
2*x**2*(x - 1)**3
Let v = 2909 + -2889. Suppose 5/2*m**2 - 45/2 + v*m = 0. Calculate m.
-9, 1
Let q be 0 + ((-15)/(-6)*2 - 3). Suppose 10 = 4*d - q. Find s such that 0*s**d - 1/3*s**4 - 2/3*s + s**2 + 0 = 0.
-2, 0, 1
Let g(t) = 2*t**3 + 80*t**2 + 514*t + 18. Let b be g(-8). Suppose 1/2*l**b - 11/6*l - 2/3 = 0. Calculate l.
-1/3, 4
Let b(q) be the first derivative of 28*q**5/5 + 312*q**4 + 99808*q**3/21 + 27456*q**2/7 + 7744*q/7 + 187. Factor b(u).
4*(u + 22)**2*(7*u + 2)**2/7
Let i(m) = -3*m**3 + 1. Let s be i(-2). Suppose s = -5*l, -l + 2*l - 5 = -2*b. Find w, given that 4*w - 3*w**2 + 4*w - b*w = 0.
0, 1
Let m = 1779 - 236604/133. Let p = m + 225/133. Let -2/7*q**3 - 18/7*q + 0 + p*q**2 = 0. What is q?
0, 3
Let m(k) = k - 2. Let y be m(-3). Let w be 12/10*y/(-2). Suppose 9*b - 4*b**2 + b**3 + 3*b**2 - w*b**2 - 2*b**2 = 0. Calculate b.
0, 3
Let 6*q - 15*q**5 + 30*q**2 + 3/2*q**4 + 81/2*q**3 + 0 = 0. What is q?
-1, -1/2, -2/5, 0, 2
Let d(x) be the third derivative of -x**7/60 + x**6/20 + 113*x**5/30 + 26*x**4 + 80*x**3/3 + 608*x**2. What is i in d(i) = 0?
-4, -2/7, 10
Let v be ((-1)/(-3) - -5)*2/8. Let u = -29/39 - -14/13. Suppose v*x - 5/3*x**3 - 8/3 + 2*x**2 + u*x**4 = 0. What is x?
-1, 2
Let v = 3192038/105 - 30400. Let u = v + -1/35. Factor -1/9*l**3 + 0 - u*l**2 - 2/9*l.
-l*(l + 1)*(l + 2)/9
Suppose -300 - 15/2*h**3 + 115/2*h + 51/2*h**2 + 1/2*h**4 = 0. Calculate h.
-3, 5, 8
Let g be (-2)/(-6) - (-408)/18. Suppose 24*i = g*i. Factor 0*b + 2/3*b**5 + 0 + 0*b**2 - 2/3*b**3 + i*b**4.
2*b**3*(b - 1)*(b + 1)/3
Let n = 3 + 3. Factor 5 - 2*a**4 - 2*a**2 + n*a**3 + 1 - 2 - 6*a.
-2*(a - 2)*(a - 1)**2*(a + 1)
Suppose -4*j + 53 = 3*x - 71, -16 = -4*j. Factor -4 - 8*d**5 - 4*d + 136*d**3 + 64*d**2 - 4 - x*d**5 + 104*d**4 + 72*d**5.
4*(d + 1)**4*(7*d - 2)
Let q(i) be the third derivative of i**5/35 + 11*i**4/56 + 1