3). Find y such that -u*y**k + 9/4*y**2 - 3/4*y + 0 = 0.
0, 1/2, 1
Let y(i) = 2*i**2 + 8*i - 7. Let x(g) = -g**2 - 5*g + 3. Let d(f) = 14*x(f) + 6*y(f). Solve d(q) = 0 for q.
-11, 0
Let j(u) = -3*u**3 - 21*u**2 - 30*u - 12. Let f(a) = 14*a**3 + 104*a**2 + 149*a + 60. Let t(y) = 2*f(y) + 11*j(y). Factor t(w).
-(w + 2)**2*(5*w + 3)
Let w(a) be the second derivative of -1/78*a**4 + 1/195*a**6 + 0*a**2 + 0 - 9*a + 1/65*a**5 - 2/39*a**3. Determine b so that w(b) = 0.
-2, -1, 0, 1
Factor 16/3*n + 8/3*n**3 - 20/3*n**2 - 4/3.
4*(n - 1)**2*(2*n - 1)/3
Let g(c) be the third derivative of -c**7/2940 - c**6/1008 + c**5/840 + 3*c**4/8 + 2*c**2. Let y(o) be the second derivative of g(o). Let y(j) = 0. Calculate j.
-1, 1/6
Suppose k + 3 = 2*f, -4*f - f = k - 25. Suppose -f*y = -s - 1, 0 = -y - 4*y - 3*s + 14. Find b, given that -17*b + 13*b - y + 1 + 4*b**2 = 0.
0, 1
Let u be (-13 + 637/52)/((-15)/40). Factor -2/5*y**u - 4/5 + 6/5*y.
-2*(y - 2)*(y - 1)/5
Suppose -l - r = 0, -4*l - 2*r + 10 = -3*r. Factor 7*o + 4*o - l*o**2 - 4*o - o.
-2*o*(o - 3)
Let k(f) = -23*f**2 + 175*f + 45. Let j(i) = -24*i**2 + 175*i + 45. Let q(y) = -3*j(y) + 4*k(y). Factor q(l).
-5*(l - 9)*(4*l + 1)
Suppose 4*m = n + 5, m - 2*m = -n + 1. Factor -32*b - n*b**3 + 64*b + b**4 - 28*b.
b*(b - 2)**2*(b + 1)
Let i(s) = 3*s - 11*s - 20*s**2 - 12*s - 4 - 3. Let d(h) = 240*h**2 + 240*h + 85. Let z(f) = -2*d(f) - 25*i(f). Suppose z(c) = 0. What is c?
-1/2
Let m(l) = l**2 - l. Let y be m(2). Factor 0 + 2/13*g**y + 0*g - 2/13*g**3.
-2*g**2*(g - 1)/13
Let s be (-7)/((-3)/3) + -4. Suppose -1 + 5*n - 1 + n**2 + 5*n**2 - s*n**2 = 0. Calculate n.
-2, 1/3
Let n be (12 + 2)*(-2 - -3). Let w be n/(-4)*720/(-455). Factor -54/13 + 20/13*d**3 - w*d**2 - 2/13*d**4 + 108/13*d.
-2*(d - 3)**3*(d - 1)/13
Let l(o) = 6*o**4 - 33*o**2 + 99*o + 108. Let f(x) = -3*x**4 + x**3 + 17*x**2 - 49*x - 54. Let r(j) = -9*f(j) - 4*l(j). Suppose r(u) = 0. Calculate u.
-2, -1, 3
Let a be (3 - -9) + 2/(-1). Determine m so that 159*m**3 - 183*m**5 + 581*m**3 + 240*m**4 - 162*m**5 - 45*m + 145*m**2 + 25*m**5 - a = 0.
-1, -1/4, 1/4, 2
Let g(u) be the third derivative of -u**7/70 - u**6/2 - 9*u**5/10 + 5*u**4/2 + 19*u**3/2 + 4*u**2 - 13. What is m in g(m) = 0?
-19, -1, 1
Factor -1/2*p**2 + 3*p + 7/2.
-(p - 7)*(p + 1)/2
Let z(v) = -30*v**2 + 133*v - 459. Let f(t) = -16*t**2 + 66*t - 230. Let c(k) = -11*f(k) + 6*z(k). Determine j, given that c(j) = 0.
4, 14
Let x be -6 + (17 - (-15 - -11)). Let z(f) be the first derivative of -1/28*f**4 - 4/21*f**3 + x + 0*f - 2/7*f**2. Factor z(v).
-v*(v + 2)**2/7
Let p(u) = -4*u + 30. Let a be p(7). Suppose -a*t = -6*t + 8. Find i such that 0*i**t + 2/3*i**3 + 0 - 2/3*i = 0.
-1, 0, 1
Let n(c) be the first derivative of -5*c**8/336 + c**7/21 + c**6/24 - c**5/6 - 6*c**2 - 4. Let s(z) be the second derivative of n(z). What is p in s(p) = 0?
-1, 0, 1, 2
Let k be 12 + ((-48)/64)/((-3)/(-45)). Determine l, given that 0*l + k*l**4 + 0 + 0*l**3 - 3*l**2 = 0.
-2, 0, 2
Let i(r) be the second derivative of 3*r**7/14 - r**6/10 - 27*r**5/20 - 3*r**4/4 + r**3 + r + 1. Find d, given that i(d) = 0.
-1, 0, 1/3, 2
Let r = -82 + 86. Let -1 + 2*t + r*t**2 - 3*t**2 + 2*t**2 - 4*t**2 = 0. Calculate t.
1
Let r be (3/108)/((-69)/10 - -7). Let n(t) be the second derivative of 0 + 1/6*t**2 + 1/18*t**6 - 5*t + r*t**3 + 1/126*t**7 + 5/18*t**4 + 1/6*t**5. Factor n(l).
(l + 1)**5/3
Suppose 2*j - 30 = -3*j. Suppose -2*z + 3*z - j = 0. Factor 3*h**3 - z*h**3 + 4*h - h**3.
-4*h*(h - 1)*(h + 1)
Solve 0 + 198/7*i + 90/7*i**3 - 3/7*i**4 + 291/7*i**2 = 0.
-2, -1, 0, 33
Let j(g) be the third derivative of 0*g - 1/40*g**4 - 5/6*g**3 + 0 + 1/100*g**5 + 4*g**2 - 1/600*g**6. Let o(f) be the first derivative of j(f). Factor o(c).
-3*(c - 1)**2/5
Let g = 33273 - 166364/5. Let -g*h**2 - 2/5 + 3/5*h = 0. Calculate h.
1, 2
Let -6/5 + 6/5*m**2 - 3/5*m**3 + 3/5*m = 0. What is m?
-1, 1, 2
Factor 11*u + 5 - 35*u + 35 + 2*u + u**2.
(u - 20)*(u - 2)
Find m, given that 5 + 367*m**2 + 25*m - 15 - 387*m**2 + 5*m**3 = 0.
1, 2
Let x(t) be the first derivative of 1/5*t**5 - 6*t**2 - 3/2*t**4 + 4*t + 13/3*t**3 + 26. Determine q, given that x(q) = 0.
1, 2
Let i(j) be the first derivative of 32*j**3/33 + 3*j**2 + 4*j/11 + 208. Factor i(h).
2*(h + 2)*(16*h + 1)/11
Let y = -13365 - -13367. Factor -1/9*h**3 - 1/9 + 1/9*h + 1/9*h**y.
-(h - 1)**2*(h + 1)/9
Factor -16/11 + 2/11*w**2 + 4/11*w.
2*(w - 2)*(w + 4)/11
Suppose -17 - 13 = -10*d. Let 19 + 3*s**4 - 18*s + d*s**3 + 15 + 6*s - 18*s**2 - 10 = 0. Calculate s.
-2, 1, 2
Let z(l) = 19*l**2 - 111*l + 99. Let c(g) = -18*g**2 + 110*g - 98. Let f(r) = 7*c(r) + 6*z(r). Determine m so that f(m) = 0.
1, 23/3
Let m(i) be the first derivative of -i**5/10 + 23*i**4/8 + 103*i**3/6 + 133*i**2/4 + 27*i - 113. Factor m(r).
-(r - 27)*(r + 1)**2*(r + 2)/2
Let n(u) = 2*u**2 + 52*u - 74. Let y(z) = 2*z + 3. Let i(w) = -n(w) - 4*y(w). Let i(s) = 0. Calculate s.
-31, 1
Let c(u) be the first derivative of u**4/8 - 9*u**3/4 + 6*u**2 - 42*u - 46. Let g(x) be the first derivative of c(x). Factor g(d).
3*(d - 8)*(d - 1)/2
Let g be 48/68 + 2/(-3). Let t = 5/17 + g. Factor 0 + 1/3*s**4 - 2/3*s**2 - t*s**3 + 0*s.
s**2*(s - 2)*(s + 1)/3
Suppose 20/3*o + 2*o**2 - 4*o**3 + 0 + 2/3*o**4 = 0. What is o?
-1, 0, 2, 5
Let o(p) be the first derivative of -3*p**5/140 - p**4/28 + p**3/14 + 3*p**2/14 - 13*p + 12. Let s(t) be the first derivative of o(t). Factor s(h).
-3*(h - 1)*(h + 1)**2/7
Let t = -17 - -19. Factor 2*u - 6*u**t + 6*u - 14*u**2 + 18*u**2 - 8.
-2*(u - 2)**2
Let d(v) be the first derivative of -v**3/24 + 47*v**2/8 - 2209*v/8 - 58. Solve d(o) = 0.
47
Let g be 15/(-30) - (-306)/596. Let w = 145/298 + g. Find l such that -2*l**2 - 3/2*l**3 - w*l**5 + 2*l + 0 + 2*l**4 = 0.
-1, 0, 1, 2
Let d be (2/((-8)/142))/(-100). Let h = 12/25 - d. Factor 0*v**2 + 0 + 0*v + h*v**5 + 1/4*v**4 + 1/8*v**3.
v**3*(v + 1)**2/8
Let f(w) = -8*w**2 - 2111*w - 141495. Let x(v) = -v**2 - 264*v - 17687. Let p(t) = 6*f(t) - 51*x(t). Determine s so that p(s) = 0.
-133
Let d(c) = 2*c**4 - 7*c**3 - 81*c**2 - 20*c + 100. Let v(t) = -t**4 + t**3 - 2*t**2. Let o(l) = -d(l) + 3*v(l). Determine a, given that o(a) = 0.
-2, 1, 5
Let c = 1795 - 1784. Let v(o) be the first derivative of -1/2*o**2 + 4/3*o - 1/9*o**3 + c. Determine g, given that v(g) = 0.
-4, 1
Let f be 12/42 + (-174)/119. Let y = 134/85 + f. Factor 2/5*z**2 - y*z + 0.
2*z*(z - 1)/5
Let c(s) be the first derivative of -s**7/42 + 5*s**6/24 - 2*s**5/3 + 5*s**4/6 + 13*s**2/2 + 8. Let n(p) be the second derivative of c(p). Factor n(q).
-5*q*(q - 2)**2*(q - 1)
What is a in 2016*a**2 - 354/5*a**3 + 0 + 4320*a + 3/5*a**4 = 0?
-2, 0, 60
Let g(b) be the first derivative of b**6/960 + 11*b**5/480 - 25*b**4/192 + 13*b**3/48 - 45*b**2/2 + 48. Let o(y) be the second derivative of g(y). Factor o(s).
(s - 1)**2*(s + 13)/8
Let w be (-22)/(-5) - (-35)/(2100/(-24)). Suppose -1/4*f**w + 0 + 0*f + 0*f**3 + 0*f**2 = 0. Calculate f.
0
Let q(j) be the third derivative of -2*j**7/105 + j**6/30 - 2*j**2 + 23. Factor q(n).
-4*n**3*(n - 1)
Let v(i) be the second derivative of 1/10*i**5 + 6*i + 0*i**3 - 1/45*i**6 + 0*i**2 + 0 - 1/9*i**4. Factor v(a).
-2*a**2*(a - 2)*(a - 1)/3
Let i(o) be the second derivative of o**7/42 + o**6/30 - o**5/10 - o**4/6 + o**3/6 + o**2/2 - 2*o - 113. Factor i(y).
(y - 1)**2*(y + 1)**3
Let m be (-1 + 1)*(-2)/(-4). Let z = -12/17 - -41/34. Determine r, given that m*r + z*r**5 - 1/2*r**2 + 3/2*r**3 - 3/2*r**4 + 0 = 0.
0, 1
Let j = 349/4 - 86. Let c(p) be the first derivative of -7/8*p**4 - 1/2*p - 3/2*p**3 - 1/5*p**5 - j*p**2 + 4. What is q in c(q) = 0?
-1, -1/2
Factor b**2 - 5*b**4 + 23*b + 4*b**2 - 10*b**3 + 28*b - 41*b.
-5*b*(b - 1)*(b + 1)*(b + 2)
Let o be ((-9)/(-6))/((-2)/(-4)). Factor -34*z**2 - 9*z - 7*z - 5*z**2 - 8*z**4 - 9*z**2 - 36*z**o.
-4*z*(z + 2)**2*(2*z + 1)
Let o = 207 + -120. Let k = o + -84. Factor -1/2*d**k + 0 - 3*d**2 - 9/2*d.
-d*(d + 3)**2/2
Let x(f) = f + 21. Let a be x(-6). Let h be (-27)/(-15) - a/25. Determine l, given that -h*l + 3/5*l**4 + 0*l**2 + 6/5*l**3 - 3/5 = 0.
-1, 1
Let y(x) = 86*x - 17028. Let m be y(198). Solve -18/5*b**2 - 2/5*b + m = 0.
-1/9, 0
Let d(n) be the third derivative of n**8/53760 - n**6/1920 - n**5/480 + n**4/24 + n**2. Let p(x) be the second derivative of d(x).