+ l**2/6 - 2*l/3 - 5. Factor k(j).
-(j - 2)*(j - 1)*(j + 1)/3
Let a(v) = 2*v**2 + 22*v - 24. Let g be a(-12). Let l(m) be the second derivative of 1/9*m**2 + 0*m**3 + g + 4*m - 1/54*m**4. Determine r, given that l(r) = 0.
-1, 1
Factor 1/3*r**3 + 0 + 0*r**2 + 0*r + 1/6*r**4.
r**3*(r + 2)/6
Let f(x) be the second derivative of x**5/30 - 6*x. Factor f(y).
2*y**3/3
Let h = -9908/3 - -3273. Let y = 31 + h. Factor 2/3*g**3 - 2/3*g + y*g**2 - 4/3.
2*(g - 1)*(g + 1)*(g + 2)/3
Let d(g) = -2*g**3 - 5*g - 1 - 2*g**3 + 3*g**3 - 5*g**2. Let a be d(-4). Let a*n**2 + n - 3*n + 4*n = 0. Calculate n.
-2/3, 0
Let b(z) be the third derivative of 1/24*z**3 + 0 + 1/120*z**6 + 1/840*z**7 + 0*z + 1/40*z**5 + z**2 + 1/24*z**4. Factor b(g).
(g + 1)**4/4
Suppose -a**4 + 3*a**3 + a**4 + 0*a**3 + 3*a**4 = 0. What is a?
-1, 0
Let f(p) = 5*p**2 - 5*p - 3. Let i = -17 - -25. Let g(j) = 14*j**2 - 14*j - 8. Let r(u) = i*f(u) - 3*g(u). Determine t so that r(t) = 0.
0, 1
Let k(g) be the third derivative of -g**8/168 - 2*g**7/105 + g**6/10 + 2*g**5/3 + 19*g**4/12 + 2*g**3 + 35*g**2 - 2*g. Suppose k(w) = 0. What is w?
-2, -1, 3
Suppose -2*b - 3*b = -20. Suppose c - 2 = -4*d, 3*c - 9 + 3 = -3*d. Solve d - 2/3*z**2 + 2/3*z**b + 2/3*z**3 - 2/3*z = 0 for z.
-1, 0, 1
Let b(h) be the second derivative of h**5/10 - 2*h**4/3 + h**3 + 3*h. Factor b(w).
2*w*(w - 3)*(w - 1)
Let n(p) = -p**3 + 5*p**2 - p + 3. Let d be n(4). Let l be (-1)/(d/9 - 2). Factor -6*c**2 + 6*c**3 + l - 2*c**4 - 3 + 2*c.
-2*c*(c - 1)**3
Let u(n) be the second derivative of -n**5/4 + n**4/4 + n**3/3 - 10*n. Let u(p) = 0. What is p?
-2/5, 0, 1
Let k(p) be the third derivative of 3*p**6/80 + 2*p**5/15 + 5*p**4/48 - p**3/6 + 3*p**2. Find j, given that k(j) = 0.
-1, 2/9
Let 5*i**3 - 2 + 3*i**3 + 0*i - 7*i**3 + 2*i**2 - i = 0. What is i?
-2, -1, 1
Let s(w) be the third derivative of 1/105*w**6 + 0*w**4 + 0 + 0*w**5 + 16/735*w**7 + 1/168*w**8 + 0*w**3 + 0*w + 7*w**2. Factor s(y).
2*y**3*(y + 2)*(7*y + 2)/7
Let x(o) = -2*o - 29. Let q be x(-16). Suppose -27 = -4*u - q*p, 25 = 2*u + 3*u + 2*p. Factor -3/2*w**5 + 1/2*w - 7*w**3 - u*w**2 - 11/2*w**4 + 1/2.
-(w + 1)**4*(3*w - 1)/2
Let l(c) be the third derivative of -c**8/33600 + c**7/1050 - c**6/75 - c**5/60 - 9*c**2. Let n(s) be the third derivative of l(s). Factor n(d).
-3*(d - 4)**2/5
Let t(z) be the first derivative of -z**6/3 + 6*z**5/5 + 3*z**4 - 20*z**3/3 - 21*z**2 - 18*z + 16. Determine l, given that t(l) = 0.
-1, 3
Let y be (4 + -2)/(96/40). Let j(m) be the first derivative of 7/8*m**4 + 0*m - 4 - 1/2*m**2 + y*m**3. Factor j(z).
z*(z + 1)*(7*z - 2)/2
Let f be (-1)/(-12) + 0/(-2). Let s(u) be the second derivative of 0*u**2 - f*u**4 - 2*u + 0 - 1/12*u**3 - 1/40*u**5. Factor s(m).
-m*(m + 1)**2/2
Let b(f) = -f**3 - 4*f**2 + 2. Let o be b(-4). Solve -43*c + 3*c**2 - 39*c**o - 60 - 48 - 4*c**3 - 65*c = 0.
-3
Let f(o) = o**2 - o - 2. Let n be f(2). Suppose 4*m = -n*m. Factor 0*u - 3/5 + m*u**3 + 6/5*u**2 - 3/5*u**4.
-3*(u - 1)**2*(u + 1)**2/5
Let h = 6 + -6. Let k(r) be the second derivative of -1/80*r**5 + 0*r**3 + 0 + h*r**2 - r + 1/48*r**4. Let k(y) = 0. What is y?
0, 1
Let y(k) be the third derivative of k**6/30 + 2*k**5/5 + 3*k**4/2 + 8*k**3/3 - 3*k**2. Factor y(i).
4*(i + 1)**2*(i + 4)
Let g(v) be the second derivative of -7*v**5/180 + v**4/6 + 2*v**3/9 + 7*v**2/2 + 8*v. Let p(o) be the first derivative of g(o). Suppose p(a) = 0. Calculate a.
-2/7, 2
Let d = -420 - -2944/7. Determine k so that 8/7*k + 0 + d*k**2 = 0.
-2, 0
Let t be -11 + 10 + 17/7. Solve 20/7*w**2 + 10/7*w**4 - t*w - 20/7*w**3 - 2/7*w**5 + 2/7 = 0.
1
Let n(w) = -w**2 + 9*w - 6. Let z be n(8). Let y(r) = -r**2 - 8*r - 5. Let o be y(-7). Find h, given that 2*h**2 + h**z - o*h**2 = 0.
0
Let i(r) be the first derivative of -3*r**5/10 + 3*r**4/2 - 2*r**3 + 1. Factor i(l).
-3*l**2*(l - 2)**2/2
Let x(c) = 18*c**2 - 3*c + 2. Let b be x(1). Suppose 5*a + 2 - b = 0, -4*k - 9 = -3*a. Let k*o + 0 - 2/5*o**2 = 0. What is o?
0
Let g = -6886/7 - -989. Let a = g - 5. Factor a*d**2 + 8/7 - 8/7*d.
2*(d - 2)**2/7
Let j(x) be the first derivative of 5 - 1/8*x**2 + 1/16*x**4 + 1/4*x - 1/12*x**3. Factor j(m).
(m - 1)**2*(m + 1)/4
Let h(u) be the first derivative of -u**6/9 - 2*u**5/15 + u**4/6 + 2*u**3/9 - 2. Suppose h(n) = 0. Calculate n.
-1, 0, 1
Let s(x) be the second derivative of -x**5/240 - x**4/24 - x**3/6 - x**2 - 2*x. Let a(f) be the first derivative of s(f). Suppose a(y) = 0. What is y?
-2
Let g(s) be the second derivative of -s**5/190 + s**3/19 - 2*s**2/19 - 9*s. Factor g(r).
-2*(r - 1)**2*(r + 2)/19
Factor -10/7*o**2 - 6/7 + 2*o + 2/7*o**3.
2*(o - 3)*(o - 1)**2/7
Let b = 991/9 + -110. Let u(a) be the second derivative of 0 + b*a**3 + 1/36*a**4 + 1/6*a**2 + 3*a. Let u(y) = 0. Calculate y.
-1
Let p(u) be the second derivative of u**6/165 + 3*u**5/110 + u**4/22 + u**3/33 - 4*u. Factor p(d).
2*d*(d + 1)**3/11
Let m(n) be the third derivative of -n**7/630 - n**6/180 - n**5/120 - n**4/8 + n**2. Let w(h) be the second derivative of m(h). Factor w(y).
-(2*y + 1)**2
Let s(i) be the first derivative of -2*i**3/45 + 8*i**2/15 + 6*i/5 + 40. Solve s(a) = 0.
-1, 9
Let f(u) = 12*u**2 + 2*u - 24. Let w(c) = -4*c**2 - c + 8. Let p(t) = -3*f(t) - 10*w(t). Solve p(x) = 0 for x.
-2, 1
Suppose 5*y - 2*m - 25 = 0, -4*m - 12 + 37 = 5*y. Let x = -2 + y. Factor x*n**2 - n**2 - 3*n**2.
-n**2
Let w be 1*(-4)/12*-9. Let n(i) be the second derivative of 1/4*i**4 + 0 + 1/10*i**6 + i - 7/20*i**5 - i**2 + 1/2*i**w. Factor n(a).
(a - 1)**3*(3*a + 2)
Let i(c) be the third derivative of -1/12*c**4 + 0 + c**2 - 1/30*c**5 + 0*c + 0*c**3. Suppose i(v) = 0. What is v?
-1, 0
Let h(k) be the second derivative of 0*k**4 + 2/15*k**6 + 0*k**3 + 0 + 0*k**2 - 1/7*k**7 - 7*k + 1/10*k**5. Factor h(n).
-2*n**3*(n - 1)*(3*n + 1)
Determine j so that -16/5*j**5 + 68/5*j**4 - 8/5*j - 96/5*j**3 + 52/5*j**2 + 0 = 0.
0, 1/4, 1, 2
Let f(n) be the third derivative of 1/24*n**4 - 1/720*n**6 + 0*n + 1/3*n**3 - 1/240*n**5 + 0 - 2*n**2. Let r(k) be the first derivative of f(k). Factor r(x).
-(x - 1)*(x + 2)/2
Let r(a) be the second derivative of -a**4/12 + a**3/2 + 3*a**2/2 - 3*a. Let h(l) = -l**2 + 3*l + 4. Let q(s) = -5*h(s) + 6*r(s). Determine b so that q(b) = 0.
1, 2
Let t(v) be the first derivative of -1/6*v**3 + 4 + 0*v + 0*v**2 + 1/8*v**4. Factor t(z).
z**2*(z - 1)/2
Suppose 5*c - 17 = 3*p, 4*c - p - 3 = 3*c. What is k in -14/5*k**c - 4/5*k**3 + 0 + 0*k - 6/5*k**5 + 0*k**2 = 0?
-2, -1/3, 0
Suppose -3*x + 4*f + 4 = 0, 0*x + 5*f = 2*x + 2. Factor -3*n**4 + 6*n - 2*n**2 + 6*n**2 - 2*n**5 - x*n**3 - 3*n**4 + 2.
-2*(n - 1)*(n + 1)**4
Let j(n) be the first derivative of -n**3 + n**2 + 2. Let b(v) = 2*v**2 - 2*v. Let x(q) = q + 7. Let f be x(-11). Let y(u) = f*b(u) - 3*j(u). Factor y(i).
i*(i + 2)
Find t, given that 9/4*t - 3/2*t**3 - 3/2*t**2 - 3/4*t**5 + 9/4*t**4 - 3/4 = 0.
-1, 1
Let u(y) be the third derivative of -7*y**6/12 + 11*y**5/12 - 5*y**4/12 + 17*y**2. Let u(z) = 0. What is z?
0, 2/7, 1/2
Let d(f) = -f**2 - 3*f + 6. Let k be d(1). Determine l so that 0 + 2/13*l**4 + 0*l - 2/13*l**k + 0*l**3 = 0.
-1, 0, 1
Suppose -s - 2*r = -3*s + 4, 1 = 2*s - 5*r. Let h be -2 - (-6 - -1) - 0. Suppose -4*f**3 - 2*f**2 - f**h - f**s - 6*f**4 - 2*f**5 = 0. Calculate f.
-1, 0
Determine k, given that -9*k - 4*k**2 + 23*k + 10*k - 22 - 14 = 0.
3
Let m = -45 - -676/15. Let q(w) be the second derivative of 0 + m*w**3 + 2*w - 1/50*w**5 + 1/5*w**2 - 1/30*w**4. Find z, given that q(z) = 0.
-1, 1
Suppose 3*m - 13 = -4*x, -5*m + 3*x + 4 = -8. Find v, given that -3/5*v**4 - 2/5*v**2 + 0 - 7/5*v**m + 0*v = 0.
-2, -1/3, 0
Let y(x) be the third derivative of -x**5/210 + x**4/28 - 2*x**3/21 - x**2. What is v in y(v) = 0?
1, 2
Let u = 1073/4 - 266. Determine w, given that 0 + 3/4*w**4 + 9/4*w**2 + 3/4*w + u*w**3 = 0.
-1, 0
Let v(f) = 2*f**3 - 4*f**2 + f + 2. Let q be v(2). Let -2*z**q + z**4 + 2*z**3 + 0*z**3 = 0. What is z?
0, 2
Suppose d - 27 = -2*d. Factor 9*w**2 - d*w + 1 + 6*w**3 + 2 - 9*w**3.
-3*(w - 1)**3
Let x = 47 + -45. Suppose -1 + 1/2*s**x + 1/2*s = 0. Calculate s.
-2, 1
Solve -208*v**2 - 11*v + 168*v**3 + 52*v**4 - 26*v**5 + 5*v**5 + 43*v - 23*v**5 = 0.
-2, 0, 2/11, 1, 2
Let b(w) be the second derivative of -w**6/45 + w**5/90 + w**4/18 - w**3/27 + 10*w. Let b(d) = 0. What is d?
