 u(-9). Let -1/7*l**k - 5/7*l**3 - l - 9/7*l**2 - 2/7 = 0. What is l?
-2, -1
Let a(g) be the third derivative of g**8/420 - g**7/140 - g**6/90 + g**3/6 - 10*g**2. Let f(s) be the first derivative of a(s). Factor f(d).
2*d**2*(d - 2)*(2*d + 1)
Let j = 200/309 - -2/103. Let w(c) be the first derivative of -3 - j*c**3 + 0*c + 1/2*c**4 - 2*c**2. Factor w(t).
2*t*(t - 2)*(t + 1)
Let h(o) be the first derivative of -5 + 10*o + 25/2*o**2 - 5*o**3. Factor h(l).
-5*(l - 2)*(3*l + 1)
Let j(k) be the second derivative of -k**10/45360 + k**8/5040 - k**6/1080 - k**4/6 + k**3/2 + 40*k. Let h(r) be the third derivative of j(r). Factor h(c).
-2*c*(c - 1)**2*(c + 1)**2/3
Let y(s) be the first derivative of s**9/1176 - s**8/490 + s**7/735 - 7*s**3/3 + 4. Let r(h) be the third derivative of y(h). Suppose r(d) = 0. Calculate d.
0, 2/3
Let x = 1/6936 - -97099/34680. Factor 2/5*a**4 + 4/5 + 18/5*a**2 + 2*a**3 + x*a.
2*(a + 1)**3*(a + 2)/5
Let k(w) be the first derivative of 24 + 3/5*w**2 - 2/15*w**3 + 0*w. Let k(p) = 0. What is p?
0, 3
Determine m so that 4*m**3 - 2215*m**2 + 2*m**4 + 144*m + 1018*m**2 + 0*m**4 + 1119*m**2 = 0.
-8, 0, 3
Let j be ((-4)/6)/((-4)/30). Suppose 14 - 4 = j*z. Factor 3*p - 8*p**2 - 7*p**z + 18*p**2.
3*p*(p + 1)
Let b(t) = 4*t**2 - t + 6. Let k be b(0). Factor y**3 + 114 - 3*y**3 - 4*y**2 + k*y**2 - 122 + 8*y.
-2*(y - 2)*(y - 1)*(y + 2)
Let r = -143 - -143. Solve r + 2/5*u - 1/5*u**2 = 0.
0, 2
Let s(h) be the second derivative of -h**8/6720 - h**7/1260 + h**4/2 - 4*h. Let d(o) be the third derivative of s(o). Determine w so that d(w) = 0.
-2, 0
Let f(u) = 4*u**3 + 16*u**2 - 32*u + 12. Let n(a) = -2*a**3 - 16*a**2 + 30*a - 12. Let h(k) = -2*f(k) - 3*n(k). Factor h(t).
-2*(t - 6)*(t - 1)**2
Let x(a) = -2*a**3 + 7*a**2 + 7*a - 5. Let y = -19 + 14. Let f(p) = -9*p**3 + 36*p**2 + 36*p - 24. Let h(l) = y*f(l) + 24*x(l). Let h(j) = 0. Calculate j.
-2, 0
Factor 123/2*w - 3/2*w**3 + 0 + 60*w**2.
-3*w*(w - 41)*(w + 1)/2
Let s(p) be the third derivative of p**8/20160 - p**7/5040 - p**6/360 - p**5/30 + 18*p**2. Let q(x) be the third derivative of s(x). What is v in q(v) = 0?
-1, 2
Let o(l) be the third derivative of -l**6/30 - 2*l**5 + 22*l**4 - 272*l**3/3 - 177*l**2. Determine g, given that o(g) = 0.
-34, 2
Let l(r) be the first derivative of -2/35*r**5 + 4/7*r**4 - 32/7*r + 8 - 16/7*r**3 + 32/7*r**2. Factor l(q).
-2*(q - 2)**4/7
Let m(n) be the first derivative of -n**4/4 - n**3/3 + 16. Let o(v) = 19*v**3 + 24*v**2 - 13*v + 2. Let t(i) = -21*m(i) - 3*o(i). Suppose t(j) = 0. What is j?
-2, 1/4, 1/3
Let p(t) be the first derivative of 7*t**3/12 - 75*t**2/8 - 11*t/2 - 112. What is h in p(h) = 0?
-2/7, 11
Let u(n) be the second derivative of -n**4/12 + 2*n**3/3 + 21*n**2/2 - 43*n. Let u(z) = 0. What is z?
-3, 7
Suppose -5*z + 33 + 32 = 0. Determine w so that 5*w**5 - w**2 - 3*w**3 - 2*w + z*w**4 - 2 + 12*w**3 + 2 = 0.
-1, 0, 2/5
Let z(x) = -x**2 - 2*x + 2. Let k(n) = 4*n**3 - 123*n**2 - 134*n + 14. Let r(a) = k(a) - 7*z(a). Determine d so that r(d) = 0.
-1, 0, 30
Factor 5*g**2 - 13*g**3 - 25*g**2 + 8*g**3 - 113 + 55*g + 83.
-5*(g - 1)**2*(g + 6)
Let w(d) be the first derivative of 2/15*d**3 + 0*d**2 - 1/20*d**4 - 33 + 0*d. Solve w(k) = 0.
0, 2
Factor 36*x + 0*x**5 + 8 + 6*x**5 - 2*x**5 + 64*x**2 + 24*x**4 + 56*x**3.
4*(x + 1)**4*(x + 2)
Let r(x) = -20*x**2 + x - 1. Let m(t) = t**3 - 2*t**2 - t + 1. Let j(z) = m(z) + r(z). Factor j(c).
c**2*(c - 22)
Let r(y) = -y**4 - 7*y**3 - 12*y**2 - 8*y - 2. Let s(j) = -j**3 - 2. Let d(n) = -3*r(n) + 3*s(n). Find a such that d(a) = 0.
-2, 0
Let g(i) be the second derivative of -i**4/12 - 21*i**3/2 + 32*i**2 + 250*i. Solve g(h) = 0.
-64, 1
Let 0*v + 0 + 169/7*v**2 + 27/7*v**4 - 1/7*v**5 - 195/7*v**3 = 0. What is v?
0, 1, 13
Let w(q) be the first derivative of -9/4*q**4 + 3*q**2 + 18*q - 3/10*q**5 - 6 - 9/2*q**3. What is m in w(m) = 0?
-3, -2, 1
Factor 261*w - 2916 + 236*w + 99*w**2 + 3*w**3 + 151*w.
3*(w - 3)*(w + 18)**2
Let l(g) = -g**3 - 9*g**2 + 10*g + 2. Let s be l(-10). Suppose 0 = s*o - 4. Factor -2*j + 2*j**o - 2*j - 7 + 9.
2*(j - 1)**2
Let h(w) be the third derivative of -1/420*w**6 + 31*w**2 + 0*w - 25/7*w**4 + 1000/21*w**3 + 1/7*w**5 + 0. Factor h(l).
-2*(l - 10)**3/7
Let q(r) = -44*r**2 - 468*r - 3016. Let j(z) = 5*z**2 + 52*z + 335. Let o(c) = -52*j(c) - 6*q(c). Determine d so that o(d) = 0.
-13
Factor -10*v**2 - 60*v - 12*v**2 - 450 - 13*v**2 + 33*v**2.
-2*(v + 15)**2
Let y(z) be the third derivative of -z**5/105 - 9*z**4/56 - 3*z**3/7 - z**2 - 181. Solve y(k) = 0 for k.
-6, -3/4
Factor 29*p**3 - 19*p**3 - 6*p**2 + 5*p**4 - 13*p + 3*p + 15 - 14*p**2.
5*(p - 1)**2*(p + 1)*(p + 3)
Let c(b) be the third derivative of b**8/1008 - 7*b**6/360 - b**5/90 + b**4/6 + 4*b**3/9 - 34*b**2. Find x, given that c(x) = 0.
-2, -1, 2
Let h(q) be the first derivative of -q**3/3 + 5*q**2 - 3*q - 16. Let b(f) = f**3 - f**2 + 21*f - 6. Let y(z) = -2*b(z) + 5*h(z). Let y(k) = 0. Calculate k.
-3, 1/2, 1
Let y(k) = -3*k - 10. Let i be y(-4). Factor -15*m**3 + 8*m**3 - 2*m**i + 16*m**3.
m**2*(9*m - 2)
Let z(a) be the second derivative of -7*a**6/12 - 163*a**5/8 + 495*a**4/8 - 385*a**3/12 - 125*a**2/2 - 2*a - 282. What is u in z(u) = 0?
-25, -2/7, 1
Let h(z) be the first derivative of -z**3/7 - 3*z**2/14 + 36*z/7 + 241. Factor h(j).
-3*(j - 3)*(j + 4)/7
Suppose 2*j - 2*w = -10, -16*w + 25 = 2*j - 11*w. Factor -1/2*l**2 - 1/4*l**3 - 1/4*l + j.
-l*(l + 1)**2/4
Let a(x) be the third derivative of -x**7/210 + 11*x**6/240 - 7*x**5/40 + x**4/3 - x**3/3 - 2*x**2 - 81. Suppose a(g) = 0. Calculate g.
1/2, 1, 2
Let c(k) be the third derivative of -k**6/360 - k**5/36 - k**4/24 - 9*k**3/2 + 11*k**2. Let b(y) be the first derivative of c(y). What is l in b(l) = 0?
-3, -1/3
Let v(h) = -2*h**2 + 13*h + 136. Let p be v(12). Factor -x**3 + 7/9*x**2 + 0 - 2/9*x + 5/9*x**p - 1/9*x**5.
-x*(x - 2)*(x - 1)**3/9
Let u(r) = 12*r**2 + 10*r**5 - 6*r**3 - 2*r**4 - 6 - 6*r - 12*r**2. Let l(t) = -t**5 + t**4 + t**3 + t + 1. Let w(s) = -6*l(s) - u(s). Factor w(q).
-4*q**4*(q + 1)
Let w be 10*27/(-243)*12/(-10). Factor w - 2/3*d**2 + 2/3*d.
-2*(d - 2)*(d + 1)/3
Let b(v) be the third derivative of 0*v**3 + 1/150*v**5 + 0 + 23*v**2 + 0*v - 1/20*v**4. Find z such that b(z) = 0.
0, 3
Let 3*c**2 + 4 - 1 - 142*c + 136*c = 0. Calculate c.
1
Let l(a) be the first derivative of -4*a**3/3 + 14*a**2 + 72*a - 55. Factor l(o).
-4*(o - 9)*(o + 2)
Let f(n) be the second derivative of -n**8/10080 + n**7/840 - n**6/432 - 7*n**3/3 - 17*n. Let w(t) be the second derivative of f(t). Factor w(h).
-h**2*(h - 5)*(h - 1)/6
Let x(b) be the second derivative of -13*b**4/21 - 4*b**3/21 + b + 26. Solve x(w) = 0 for w.
-2/13, 0
Let m(y) be the third derivative of y**5/20 - y**4/2 + 2*y**3 + 8*y**2. Factor m(l).
3*(l - 2)**2
Solve 2/17*d**4 - 4/17*d**3 + 2/17*d**5 + 0 + 0*d + 0*d**2 = 0 for d.
-2, 0, 1
Let p(g) = -g**2 - 2*g - 12. Let z be p(-8). Let s be 2*3/z*-5. Solve o**4 + 0*o**3 - o**2 - s*o**5 + 1/2*o + 0 = 0 for o.
-1, 0, 1
Suppose 2*w = v - 3*w - 21, 9 = 4*v - 5*w. Let n = v + 8. What is x in -11*x**4 + 7*x**3 - 1 + 5*x - 9*x**2 + n*x**4 + 5*x**4 = 0?
1/2, 1
Let g = -639 + 642. Factor 2/9*n**2 - 1/9*n**4 - 1 + 4/3*n - 4/9*n**g.
-(n - 1)**2*(n + 3)**2/9
Let i(y) = -11*y**3 + 58*y**2 + 4*y + 4. Let d(q) = 75*q**3 - 405*q**2 - 27*q - 27. Let c(o) = -4*d(o) - 27*i(o). Solve c(r) = 0.
0, 18
Let l(k) be the second derivative of -k**5/80 - 3*k**4/16 + k + 9. Determine q, given that l(q) = 0.
-9, 0
Let r(a) be the first derivative of -20/39*a**3 - 2/13*a**5 + 1/39*a**6 + 5/13*a**4 - 21 - 2/13*a + 5/13*a**2. Let r(b) = 0. What is b?
1
Let j(g) = -3*g**2 + 7*g. Let w be j(2). Let q(t) be the second derivative of -6*t**w + 5*t - 8*t**3 - 9/20*t**5 - 13/4*t**4 + 0. Suppose q(p) = 0. What is p?
-2, -1/3
Let x(f) be the first derivative of f**6/240 + f**5/120 - f**4/6 - f**3 + 25*f**2/2 - 6. Let v(z) be the second derivative of x(z). Solve v(j) = 0 for j.
-2, 3
Let n(d) be the first derivative of -d**4/4 - 3*d**3 - 3*d**2 + 16*d - 44. Let w be n(-8). Factor w - 1/6*h**2 + 0*h.
-h**2/6
Suppose 41*z = 52*z - 55. Let p(u) be the second derivative of -1/100*u**z - 1/10*u**2 + 0 + 1/60*u**4 - u + 1/30*u**3. Find l, given that p(l) = 0.
-1, 1
Let c(p) = 11*p**2 + 2*p + 1. Let l be c(-1). Suppose -2