7 - 5. Determine r, given that 3*r**5 - 2*r**4 - r**4 + 3*r**s - 3*r**3 + 0*r**4 = 0.
-1, 0, 1
Let d(p) be the first derivative of -p**3/4 + 3*p**2/8 + 73. Factor d(j).
-3*j*(j - 1)/4
Let u(f) be the first derivative of f**3/7 + 33*f**2/14 + 30*f/7 + 46. Factor u(q).
3*(q + 1)*(q + 10)/7
Let m be (-2 - 1)/1 - -3. Let a(f) be the third derivative of m*f - 1/60*f**5 + 0 + f**2 - 1/210*f**7 - 1/60*f**6 + 0*f**3 + 0*f**4. Factor a(v).
-v**2*(v + 1)**2
Let f(q) be the second derivative of -9*q**5/20 + q**4/2 + 3*q**3/2 - 3*q**2 - q. Factor f(m).
-3*(m - 1)*(m + 1)*(3*m - 2)
Let u be (-45)/(-18)*(1 + 1/(-5)). Let -1/2*k**u + 2 + 0*k = 0. Calculate k.
-2, 2
Solve -16*j**3 - 2*j**2 - 2*j**2 + 28*j**3 + 4*j**5 - 12*j**4 = 0 for j.
0, 1
Let x(y) = 2*y**2 - y + 6. Let q(f) = -5*f**2 + 4*f - 16. Let l(g) = -3*q(g) - 8*x(g). Find c such that l(c) = 0.
-4, 0
Factor 2/3 - 4/3*d + 2/3*d**2.
2*(d - 1)**2/3
Let a be 21/12*(4 - 0). Suppose -5*d + a + 8 = 0. Factor -2*z**2 + 2*z + 3 + 4 - d.
-2*(z - 2)*(z + 1)
Let a(w) be the first derivative of -4*w**5/5 + w**4 + 4*w**3/3 - 2*w**2 - 8. Suppose a(u) = 0. Calculate u.
-1, 0, 1
Let b(a) = -4*a**2 - 6*a - 4. Let n(r) = -5*r**2 - 5*r - 3. Let t(j) = 6*b(j) - 4*n(j). Factor t(v).
-4*(v + 1)*(v + 3)
Suppose -h = -6*o + 5*o - 2, -h - o + 2 = 0. Factor -4/5*y**h - 14/5*y**3 + 14/5*y + 4/5.
-2*(y - 1)*(y + 1)*(7*y + 2)/5
Let h(t) = 6*t**2 - 3*t + 3. Let i(m) = m**3 + 11*m**2 - 7*m + 5. Let l(n) = 5*h(n) - 3*i(n). Factor l(q).
-3*q*(q - 1)*(q + 2)
Let v(a) = 12*a**5 - 5*a**4 - 4*a**3 + 7*a + 5. Let p(u) = 13*u**5 - 5*u**4 - 3*u**3 - u**2 + 8*u + 6. Let k(s) = 5*p(s) - 6*v(s). Determine f so that k(f) = 0.
-1, -2/7, 0, 1
Solve -3*b**2 + 21*b - 9*b + b**2 - b**2 = 0.
0, 4
Let b(v) = -5*v**3 - v**2 + 1. Let l be b(1). Let h be (-2)/l*(0 - -5). Factor 2 + 8*u**2 - 2*u**2 - 2*u**3 - h - 8.
-2*(u - 2)**2*(u + 1)
Let 2/5*h**4 + 0*h - 2/5*h**5 + 0*h**2 + 0*h**3 + 0 = 0. Calculate h.
0, 1
Suppose 0*f**3 - 1/3*f**5 + 0 + 0*f**2 + 2/3*f**4 + 0*f = 0. What is f?
0, 2
Suppose 0*p = -4*p. Suppose -5*f + 20 = -p*f. Factor 2*d**4 - 3*d - 2*d**2 + d - 4*d**4 + f*d**4 + 2*d**3.
2*d*(d - 1)*(d + 1)**2
Let d be 1 + 3 - 159/40. Let i(a) be the third derivative of 2*a**2 - d*a**5 + 0*a + 1/8*a**4 + 1/480*a**6 + 0 - 1/3*a**3. Factor i(l).
(l - 2)**3/4
Factor -15/4*j**3 - 15/2*j**2 - 45/8*j - 3/2 + 0*j**4 + 3/8*j**5.
3*(j - 4)*(j + 1)**4/8
Factor -2*n**3 + 0 + 1/2*n**2 + 2*n - 1/2*n**4.
-n*(n - 1)*(n + 1)*(n + 4)/2
Let x(d) = 5*d**4 - 14*d**3 + 19*d**2 - 16*d + 6. Let h(p) = p**4 - p**3 - p + 1. Let j(k) = -3*h(k) + x(k). Determine l so that j(l) = 0.
1/2, 1, 3
Let f(o) be the third derivative of -5*o**2 + 0*o**3 + 1/30*o**6 + 0*o**5 + 0*o + 0 - 1/6*o**4. Solve f(s) = 0 for s.
-1, 0, 1
Let b be 12/2*3/300. Let k(c) be the second derivative of -c + 0*c**3 + 1/105*c**7 - 1/25*c**6 + 0 + b*c**5 + 0*c**2 - 1/30*c**4. Factor k(g).
2*g**2*(g - 1)**3/5
Let b = 1/55 - -163/110. Let 9/2*l**2 + b + 3/2*l**3 + 9/2*l = 0. Calculate l.
-1
Let m be 6*(-25)/(-30) + -3. Solve 2/3*c**m + 2 - 8/3*c = 0 for c.
1, 3
Let i(o) be the second derivative of -o - 1/2*o**2 + 0 - 4/3*o**4 - 4/3*o**3. Solve i(s) = 0.
-1/4
Let a be (3 - 3)*(-3)/(-6). Suppose 2/5*b**3 + 0*b**2 + 0 + a*b = 0. What is b?
0
Let f be 10*(-3)/(-15) + 3/(-2). Let b(s) be the second derivative of 4*s**2 - 1/5*s**5 - f*s**4 + 4/3*s**3 + 2*s + 0 + 1/15*s**6. Solve b(t) = 0.
-1, 2
Let v(q) be the first derivative of -q**5/30 + q**4/4 - 2*q**3/3 + q**2 - 2. Let n(z) be the second derivative of v(z). Factor n(l).
-2*(l - 2)*(l - 1)
Let n be (-10)/4*(-4)/10. Find q, given that -q**3 - n + q + 10*q**2 - 13*q - 7 - 16*q**2 = 0.
-2
Let u(d) be the third derivative of -d**7/420 + d**6/24 - 11*d**5/40 + 5*d**4/6 - 4*d**3/3 - 5*d**2. Let u(p) = 0. Calculate p.
1, 4
Factor h**4 - 2*h**2 - 2 + 3 - 3*h**3 + 3*h**3.
(h - 1)**2*(h + 1)**2
Let p(l) be the first derivative of 39/4*l**4 + 9/5*l**5 - 24*l + 14*l**3 - 6*l**2 + 2. Solve p(o) = 0.
-2, -1, 2/3
Let h(g) = g**4 + 11*g**3 + 6*g**2 - 2*g - 2. Let w(b) = b**4 + 23*b**3 + 12*b**2 - 5*b - 5. Let o(d) = 5*h(d) - 2*w(d). Factor o(j).
3*j**2*(j + 1)*(j + 2)
Suppose -2*g - 60 = 3*g. Let m be 6/g + 5/2. Factor 3*z**2 - 2*z**m + 2*z**3 + z**2.
2*z**2*(z + 1)
Let z be ((-39)/91)/((-6)/8). Factor 6/7*a**3 + 2/7*a**4 - z - 6/7*a + 2/7*a**2.
2*(a - 1)*(a + 1)**2*(a + 2)/7
Suppose 25/4*i**3 + 9/4*i**5 - 5*i - 6 - 15*i**4 + 35/2*i**2 = 0. Calculate i.
-2/3, 1, 6
Let -2/9*l**3 - l**4 + 0 + l**2 + 2/9*l = 0. Calculate l.
-1, -2/9, 0, 1
Suppose -80*w = -75*w - 10. Factor 0 + 2/5*v**w - 3/5*v**4 + 0*v - v**3.
-v**2*(v + 2)*(3*v - 1)/5
Let r = 1427 - 15687/11. Factor 14/11*m - r*m**2 + 2/11*m**3 - 6/11.
2*(m - 3)*(m - 1)**2/11
Let z(g) be the second derivative of -g**6/450 - g**5/300 + g**4/60 + 2*g**3/3 + 6*g. Let q(p) be the second derivative of z(p). Find i, given that q(i) = 0.
-1, 1/2
Let t be -1 + -8 + -2 + 4. Let g = -5 - t. Solve -2*m**2 - 7*m**4 + 3*m**4 - 4*m**3 + g*m**4 = 0 for m.
-1, 0
Let v(p) be the first derivative of 2*p**3/9 + p**2/3 - 7. Factor v(u).
2*u*(u + 1)/3
Let y = 2321/8 - 290. Factor y*u + 1/8*u**5 + 0*u**2 + 0 + 0*u**4 - 1/4*u**3.
u*(u - 1)**2*(u + 1)**2/8
Let m(d) be the third derivative of -d**8/1512 - 2*d**7/945 + d**5/135 + d**4/108 - 6*d**2. Factor m(c).
-2*c*(c - 1)*(c + 1)**3/9
Suppose 3*k + 2*z = -1, 5*k - 2*k = -z + 4. Let 3 - g**2 - 6*g - 2*g**2 + 3*g**3 + k*g = 0. What is g?
-1, 1
Let v(x) = -x - 1. Let o(r) = 4*r**3 - 12*r**2 + 22*r + 6. Let a(z) = -o(z) - 10*v(z). Determine g, given that a(g) = 0.
1
Suppose 5*c - c = 0. Factor 3*n + 2*n**4 + 12*n**2 + c*n**4 + 3*n**3 + 5*n**3 + 2 + 5*n.
2*(n + 1)**4
Suppose 9*x = 7*x + 92. Let h = x - 124/3. Let 4/3*l**4 + 0 - h*l**5 + 0*l**2 + 0*l + 0*l**3 = 0. Calculate l.
0, 2/7
Factor o**3 + 3*o**3 + 15*o**2 - 32 - 16*o - 16*o**4 + 25*o**2 + 4*o**5.
4*(o - 2)**3*(o + 1)**2
Suppose 0 = -3*j - 8 - 1. Let y = -1 - j. What is n in -6*n + 2*n + 6*n - 6*n**4 - y*n**3 + 6*n**2 = 0?
-1, -1/3, 0, 1
Let q(b) = b**3 + 1. Let n(o) be the third derivative of -o**6/10 - o**5/20 - 7*o**3/6 + 4*o**2. Let k(f) = 2*n(f) + 22*q(f). Factor k(u).
-2*(u - 1)*(u + 2)**2
Let n = 15 - 10. Factor -21*s**4 + 6*s**5 + 2*s**3 + 2*s**n - 6*s**3 + 17*s**4.
4*s**3*(s - 1)*(2*s + 1)
Let v = 0 - -4. Let b(y) be the second derivative of y + 0*y**3 + 0*y**5 + 1/6*y**v + 0 - 1/15*y**6 + 0*y**2. Factor b(s).
-2*s**2*(s - 1)*(s + 1)
Suppose -15 = -5*r + 5. Let v be (r/6)/(8/3). Let v*l**4 + 1/4*l**3 - 1/4*l - 1/4*l**2 + 0 = 0. Calculate l.
-1, 0, 1
Let z(d) be the first derivative of -d**4/22 - 4*d**3/33 - 17. Factor z(f).
-2*f**2*(f + 2)/11
Let w(a) be the first derivative of 4*a**3/15 - 12*a**2/5 + 32*a/5 + 36. What is d in w(d) = 0?
2, 4
Let -1/2*f**2 - 1/4*f**3 + 2 + f = 0. What is f?
-2, 2
Let h be 3*(-2 - (-3 - 0)). Factor -3*b - 4*b**2 + 3*b**h + 2*b + 2*b**2.
b*(b - 1)*(3*b + 1)
Suppose -2*s + 6*s + 9*s - 48 - 3*s**2 + 11*s = 0. Calculate s.
4
Let o(w) = w**2 + 10*w - 7. Let z(y) = y + 1. Let a(l) = 3*l**2 + 9*l - 27. Let i(v) = a(v) + 12*z(v). Let f(k) = -4*i(k) + 9*o(k). Find p such that f(p) = 0.
1
Find b, given that 0*b**2 - 4*b**2 - 18*b**3 - 2*b - 11*b**4 + 2*b**4 - 7*b**2 = 0.
-1, -2/3, -1/3, 0
Let x be ((-12)/21)/(36/(-42)). Factor -2/3*k**2 - 4/3*k + x*k**3 + 0.
2*k*(k - 2)*(k + 1)/3
Let u be (24/15)/(32/40). Factor -1/2 + 1/2*a**u + 0*a.
(a - 1)*(a + 1)/2
Let y(c) be the third derivative of -c**8/1344 + c**7/840 + c**6/80 - c**5/60 - c**4/12 - 10*c**2. Suppose y(b) = 0. What is b?
-2, -1, 0, 2
Let n(c) = c**2 + 2*c - 4. Let p be n(2). Suppose 6/5*j**2 - 2*j + 4/5 - 2/5*j**p + 2/5*j**3 = 0. Calculate j.
-2, 1
Let w(j) be the third derivative of j**5/60 - j**4/18 + j**3/18 - 4*j**2. Factor w(d).
(d - 1)*(3*d - 1)/3
Let k(z) = -6*z**2 + z + 1. Let n be k(-1). Let a = -3 - n. Factor t**a + 1 - 2*t - t**2 - 3*t + 4*t.
(t - 1)**2*(t + 1)
Let z be 2/((-8)/12) + 7. Let w be 6/(1/2 + 1). What is g in 4*g**2 - g + g**3 - z*g**w + 0*g**3 + 0*g**4 = 0?
-1, 0, 1/4, 1
Let p = -304 + 7297/24. Let c(a) be the third derivative of 1/240*a**5 + 0 - a**2 + 0*a - 1/48*a**4 + p*a**3. Factor c(q).
(q - 1)**2/4
Let a(u) be the second derivative of -81*u**7/14 - 27*u**6/5 + 162*u**5/5 + 84*u**4 + 88*u**3 + 48*u**2 + 4*u. Let a(q) = 0. What is q