b**5 - 40*b**4/3 + 10*b**3 - 4*b**2 - 9*b. Find k, given that d(k) = 0.
2/7, 1
Let q(n) be the first derivative of -2/3*n**3 - 1 + n + 1/2*n**2. Suppose q(z) = 0. Calculate z.
-1/2, 1
Let h(t) = -t**2 + 4*t + 1. Let z(j) = 8*j**2 - 14*j + 3. Let u(r) = 9*r**2 - 15*r + 4. Let a(s) = 5*u(s) - 6*z(s). Let c(l) = 4*a(l) - 10*h(l). Factor c(b).
-2*(b + 1)**2
Let l(n) be the first derivative of 3*n**5/5 - 9*n**4/4 - 4*n**3 + 18*n**2 - 45. Solve l(h) = 0 for h.
-2, 0, 2, 3
Let y(s) be the second derivative of -s**4/78 + 4*s**3/39 + 5*s**2/13 + 11*s. Find m, given that y(m) = 0.
-1, 5
Suppose 3*m - 18 = -3*m. Let z(s) be the third derivative of -1/300*s**6 + 0 + 1/60*s**4 + 2*s**2 + 1/525*s**7 - 1/150*s**5 + 0*s**m + 0*s. Factor z(h).
2*h*(h - 1)**2*(h + 1)/5
Suppose -122 = -3*k - 4*i, -33 = -k - 3*i + 6. Factor 17*u - 12 + 2*u**2 - k*u - 29*u**2 - 6*u**3 - 11*u.
-3*(u + 2)**2*(2*u + 1)
Let q = -119 + 77. Let a be ((-9)/(-5))/(q/(-20)). Let -2/7*y**3 - a*y - 2/7 - 6/7*y**2 = 0. Calculate y.
-1
Let z(c) be the first derivative of -21*c**4/4 + 11*c**3/2 - 3*c**2/2 - 20. Determine d, given that z(d) = 0.
0, 2/7, 1/2
Factor 4/7*a**3 + 6/7*a**2 + 0 + 2/7*a.
2*a*(a + 1)*(2*a + 1)/7
Let l = -55 + 57. Factor -6/11*h + 2/11*h**l + 4/11.
2*(h - 2)*(h - 1)/11
Let w be (-30)/(-9) + 2/(-6). Factor -24*r**2 - 12*r + 0*r**3 + 11*r**w + r**3 + 3*r**3.
3*r*(r - 2)*(5*r + 2)
Let q be 4 - (4 + (-4)/12). Let n(g) be the first derivative of q*g**3 - 2 - 1/2*g**2 + 0*g. Factor n(v).
v*(v - 1)
Let b = -15 - -17. Let u(w) be the second derivative of -b*w - 1/105*w**6 + 0*w**4 + 0 + 0*w**3 + 1/70*w**5 + 0*w**2. Suppose u(h) = 0. Calculate h.
0, 1
Find c, given that 13 + 3 - 2*c**2 - 1 + 10*c - 3*c**2 = 0.
-1, 3
Factor -3/8*x**3 - 3/8*x**4 + 3/8*x**2 + 0 + 3/8*x.
-3*x*(x - 1)*(x + 1)**2/8
Let q(r) = -2*r**3 + 4*r**2 + 4*r. Let h(i) = -4*i**3 + 9*i**2 + 8*i. Let l(m) = -6*h(m) + 13*q(m). Let l(k) = 0. What is k?
-2, 0, 1
Let m(z) = z - 8. Let p be m(11). Let n(u) be the third derivative of 0 + 0*u**4 + 0*u**3 + 0*u**5 + 1/480*u**6 + p*u**2 + 0*u. Suppose n(j) = 0. What is j?
0
Suppose 0 = -0*d - d. Let u(p) be the third derivative of -1/672*p**8 + 0*p + d*p**4 + 0*p**3 - 1/84*p**7 - 1/30*p**5 - 1/30*p**6 + 0 - 2*p**2. Factor u(b).
-b**2*(b + 1)*(b + 2)**2/2
Let h be ((-31)/(-35) - 1)/(2/(-10)). Let 22/7*t - 10/7*t**4 - 6*t**2 + 34/7*t**3 - h = 0. Calculate t.
2/5, 1
Factor 2/3*d**3 + 2/3 - 2/3*d - 2/3*d**2.
2*(d - 1)**2*(d + 1)/3
Factor 0*f + 5/2*f**2 - 5/2.
5*(f - 1)*(f + 1)/2
Let u be (3 + 0)*6/27. Let p(v) be the first derivative of 1 - 2/3*v - u*v**3 - 1/6*v**4 - v**2. What is c in p(c) = 0?
-1
Let r be 2 + 65/30 - 4. Let c(p) be the second derivative of 0*p**2 + 2*p + r*p**4 - 3/20*p**5 + 0*p**3 + 0. Suppose c(z) = 0. Calculate z.
0, 2/3
Let b(c) be the first derivative of -c**5/330 + c**4/33 - 4*c**3/33 - 4*c**2 - 6. Let r(j) be the second derivative of b(j). Factor r(g).
-2*(g - 2)**2/11
Suppose 2*h + 66 = -2*n - 0*n, -h - 68 = 2*n. Let g = -32 - n. Factor 0 + 4/5*x**g + 2/5*x**2 - 2/5*x.
2*x*(x + 1)*(2*x - 1)/5
Let l(d) be the second derivative of d**5/120 - d**4/48 - d**3/6 - d**2 + 2*d. Let a(o) be the first derivative of l(o). Let a(y) = 0. What is y?
-1, 2
Let v(a) be the second derivative of 8/7*a**2 - 6*a + 1/21*a**4 - 8/21*a**3 + 0. Factor v(l).
4*(l - 2)**2/7
Let k(y) = 6*y**3 - 21*y**2 + 32*y - 8. Let n(m) = 3*m**3 - 11*m**2 + 16*m - 4. Let x be 3*(16/(-6))/(-4). Let p(b) = x*k(b) - 5*n(b). Let p(f) = 0. What is f?
1/3, 2
Let d be (-4 + (-8)/(-2))*1/(-3). Let a(j) be the second derivative of 2*j + 0 + 2/9*j**2 + 1/9*j**3 - 1/90*j**5 + d*j**4. Let a(y) = 0. Calculate y.
-1, 2
Suppose -16/5*t**4 + 0*t + 0*t**2 + 0 - 12/5*t**3 - 4/5*t**5 = 0. What is t?
-3, -1, 0
Suppose -s + 2 = -1. Suppose -2 = -s*p + 4*t, 0*p + 2*p + 1 = 5*t. Find g such that -14*g**p + 9*g + g - 6*g = 0.
0, 2/7
Let d be (-3 - -8) + -2*1. Suppose b - 7 - d = 3*q, -2*b + 2*q = -12. Find l, given that 1 - 1 + 2*l**2 + b*l = 0.
-2, 0
Let t = -2 + 6. Suppose -t*b = 5 - 21. Factor -178*k**3 - 61*k**4 + 192*k**2 + 493*k**b - 162*k**5 - 32*k - 254*k**3.
-2*k*(3*k - 2)**4
Let n(x) = -8*x**2 + 6*x - 4. Let g(a) = -23*a**2 + 18*a - 12. Let o(c) = -6*g(c) + 17*n(c). Factor o(u).
2*(u - 2)*(u - 1)
Suppose -4*l = -l + 2*l. Factor -1/4*v**2 - 1/4*v**3 + l + 1/2*v.
-v*(v - 1)*(v + 2)/4
Let y(h) be the second derivative of -2*h**8/105 - 2*h**7/105 - h**6/180 - h**3/3 - 3*h. Let a(r) be the second derivative of y(r). Find x, given that a(x) = 0.
-1/4, 0
Let b(k) be the first derivative of k**5/4 + 5*k**4/8 - 5*k**3/12 - 5*k**2/4 + 6. Factor b(d).
5*d*(d - 1)*(d + 1)*(d + 2)/4
Let j be 222/42 + 2/(-7). Suppose -k + j*k = 0. Suppose k*h**4 + 0 - 2/7*h**5 - 4/7*h**2 + 0*h + 6/7*h**3 = 0. Calculate h.
-2, 0, 1
Let k be 1 + 1 + -1 - -1. Factor 0*g**4 - 5*g**4 + 2*g**4 + 0*g**4 + k*g**3.
-g**3*(3*g - 2)
Let g(z) be the second derivative of z**7/210 + z**6/80 + z**5/120 + z**2 - 4*z. Let c(r) be the first derivative of g(r). Determine x, given that c(x) = 0.
-1, -1/2, 0
Let k = 5 - 9. Let g be 0*(k - 28/(-8)). Factor 0*j - 1/4*j**2 + g.
-j**2/4
Suppose 3/4*i - 1/4*i**2 + 0 = 0. What is i?
0, 3
Suppose r - 1 - 2 = 0. Let x(l) = 3*l + r*l**3 - l - 3*l - 2. Let p(f) = 12*f**3 - 3*f - 9. Let i(j) = -2*p(j) + 9*x(j). Suppose i(v) = 0. Calculate v.
-1, 0, 1
Let t = 12/11 - 277/264. Let d(g) be the second derivative of t*g**4 + 0*g**2 + g - 1/12*g**3 + 0. Determine a so that d(a) = 0.
0, 1
Let a(u) be the first derivative of 8*u**5/25 + 3*u**4 + 32*u**3/5 - 32*u**2/5 - 9. Factor a(j).
4*j*(j + 4)**2*(2*j - 1)/5
Let o = 79/210 - 3/70. Factor 2/3*a**2 - 1/3*a**4 + 0*a + 0*a**3 - o.
-(a - 1)**2*(a + 1)**2/3
Let z(n) be the third derivative of -n**8/5040 - n**7/1260 + n**6/90 + n**5/20 - 7*n**2. Let q(w) be the third derivative of z(w). Factor q(s).
-4*(s - 1)*(s + 2)
Let d(l) be the third derivative of l**6/600 - l**5/300 - 2*l**2. Determine z so that d(z) = 0.
0, 1
Let 4/5*d + 0 - 6/5*d**2 + 2/5*d**3 = 0. Calculate d.
0, 1, 2
Let y(f) be the second derivative of -f**4/30 - 2*f**3/15 + 3*f**2/5 - 21*f. Determine v so that y(v) = 0.
-3, 1
Let p be (-4)/14 + 8/28. Factor -6*i**2 - 5*i**4 + 5*i**2 + p*i**5 + 3*i**3 + 2*i**4 + i**5.
i**2*(i - 1)**3
Factor 6/11*z**2 + 6/11*z**3 + 0 + 0*z.
6*z**2*(z + 1)/11
Determine b, given that -54/7 - 18/7*b**2 - 2/7*b**3 - 54/7*b = 0.
-3
Let r(g) be the third derivative of -g**5/20 - 3*g**4/8 + 5*g**3 - 13*g**2. Factor r(q).
-3*(q - 2)*(q + 5)
Factor -6*i**3 + 15*i**2 + i + 16*i + 3*i**3 - 144 + 7*i.
-3*(i - 4)**2*(i + 3)
Let k(t) be the first derivative of 0*t**3 + 1/10*t**2 + 0*t - 3 - 1/10*t**4 + 1/30*t**6 + 0*t**5. Factor k(d).
d*(d - 1)**2*(d + 1)**2/5
Let y(q) = -q**2 - 9*q + 5. Let s be y(-10). Let h = 5 + s. Determine m so that h*m**4 - 2*m**4 - 3*m**2 - m + m**5 + 5*m**2 = 0.
-1, 0, 1
Let v be (-1 - -7) + 35/(-14). Determine z, given that 1/2*z - 3/2*z**4 + 0 + v*z**3 - 5/2*z**2 = 0.
0, 1/3, 1
Suppose 4*f + 0*m + 2*m = 14, -3*m + 1 = -4*f. Factor 1 + f*w**4 - 2*w**3 + 2*w**5 - 1 + 0*w**5 - 2*w**2.
2*w**2*(w - 1)*(w + 1)**2
Let i(s) = s**2 + s. Let v(t) = -2*t. Let a(p) = -2*i(p) - 2*v(p). Determine d, given that a(d) = 0.
0, 1
Let l(t) = -29 + 14 + 2*t + 14*t**2 + 11. Let q(n) = -n**2. Let f(j) = -l(j) - 12*q(j). Factor f(o).
-2*(o - 1)*(o + 2)
Let y = 9 - 5. Solve 8/3*d**y + 0 + 8/3*d**2 - 2/3*d**5 - 2/3*d - 4*d**3 = 0 for d.
0, 1
Let q(u) be the third derivative of u**5/240 + u**4/48 + u**3/24 - 41*u**2. Determine l, given that q(l) = 0.
-1
Let y(b) be the first derivative of b**9/10584 + b**8/5880 - b**7/2940 - b**6/1260 + b**3 + 2. Let k(q) be the third derivative of y(q). Factor k(w).
2*w**2*(w - 1)*(w + 1)**2/7
Let j(t) be the third derivative of t**6/120 + 5*t**2. Solve j(k) = 0 for k.
0
Let u(i) = -2*i**4 + i**3 + 2*i**2 + 5*i. Let d(p) = -p**4 + p**2 + 4*p. Let n(v) = -3*d(v) + 2*u(v). Factor n(r).
-r*(r - 2)*(r - 1)*(r + 1)
Let h(d) be the third derivative of -1/96*d**4 - 1/840*d**7 + 0*d**3 + 0 + 0*d + 1/480*d**6 + 2*d**2 + 1/240*d**5. Factor h(w).
-w*(w - 1)**2*(w + 1)/4
Let g(f) be the second derivative of f**5/80 + 5*f**4/48 - 13*f**3/24 + 7*f**2/8 - 11*f + 1. Find q, given that g(q) = 0.
-7, 1
Let p(l) be the first derivative of -4*l - 16/3*l**3 - 1/3*l**6 + 7*l**2 +