. Determine k so that w(k) = 0.
-2, 1, 3
Let r(b) = -b**5 - b**4 + b**3 - 3*b**2 + b. Let g(x) = 3*x**5 + 11*x**4 + x**3 + x**2 - 17*x. Let h(j) = g(j) + 5*r(j). Let h(y) = 0. Calculate y.
-1, 0, 2, 3
Let o(b) = b - 13. Let k be o(13). Let l(s) = -s**3 + 8*s**2 - 14*s + 12. Let z be l(6). Factor -1/2*w**4 + 1/2*w**2 + 0 + z*w**3 + k*w.
-w**2*(w - 1)*(w + 1)/2
Factor 0 + 2420/3*x + 2090*x**2 + 185*x**3 + 25/6*x**4.
5*x*(x + 22)**2*(5*x + 2)/6
Let n(b) = -b**2 + 10*b + 7. Let l be n(10). Let m(h) = h**2 - 6*h + 6. Let y be m(l). Factor y + 3 + f + 11*f + 3*f**2 - 4.
3*(f + 2)**2
Let j(c) = c**3 + c**2 - 2*c. Let s be j(-2). Let a be 2/(-3)*9/(-15). Factor 2/5*w**2 + s*w - a.
2*(w - 1)*(w + 1)/5
Let r(h) = -21*h**2 - 162*h + 147. Let k(x) = -5*x**2 - 40*x + 37. Let j(n) = 9*k(n) - 2*r(n). What is c in j(c) = 0?
-13, 1
Let o(h) be the first derivative of -h**3/2 - 27*h**2/4 - 12*h + 79. Factor o(t).
-3*(t + 1)*(t + 8)/2
Suppose -436*l + 416*l + 60 = 0. Let v(m) be the first derivative of 2/3*m**l - m - 10 + 1/2*m**2. Suppose v(a) = 0. Calculate a.
-1, 1/2
Let b = 929 - 645. Let z = b - 282. Factor 0*l - 2/7 + 2/7*l**z.
2*(l - 1)*(l + 1)/7
Let y be (-3 - -4)/(1/2). Factor 1 - y*h**2 + 7 + 1132*h - 3*h**3 - 1120*h.
-(h - 2)*(h + 2)*(3*h + 2)
Determine w so that 1/4*w**2 + 45/4 - 9/2*w = 0.
3, 15
Let q(o) = 129*o**2 + 1101*o + 2175. Let w(u) = -16*u**2 - 137*u - 272. Let k(c) = -4*q(c) - 33*w(c). Factor k(m).
3*(m + 4)*(4*m + 23)
Suppose 2*d - 31 = 3*d. Let j = d + 31. Factor 0 + 1/6*z**4 + j*z - 1/6*z**2 + 0*z**3.
z**2*(z - 1)*(z + 1)/6
Let d(t) be the first derivative of t**6/2 + 42*t**5/5 + 183*t**4/4 + 84*t**3 + 54*t**2 + 110. Let d(s) = 0. What is s?
-6, -1, 0
Determine h, given that -8*h**5 + 5*h**5 + 21*h**3 - 92*h - 36*h + 64 + 64*h**2 - 20*h**4 + 7*h**5 - 5*h**3 = 0.
-2, 1, 2
Let v(j) = 2*j**2 + 180*j + 4414. Let p(z) = 4*z**2 + 358*z + 8827. Let b(y) = 4*p(y) - 9*v(y). Factor b(h).
-2*(h + 47)**2
Let z be 752/(-470)*55/(-7). Factor 32/7*a**2 - 20/7*a**5 - z*a**3 - 8/7 + 72/7*a**4 + 12/7*a.
-4*(a - 1)**4*(5*a + 2)/7
Let v = 2/12931 - -12927/25862. What is a in 1/4*a**3 - 1/2*a**2 - 1/4*a + v = 0?
-1, 1, 2
Suppose -2*z - 23 = -39, z = 3*t - 1. What is u in 441/4*u + 3/4*u**t + 1029/4 + 63/4*u**2 = 0?
-7
Let r be -5*3/5*-1. Let d = -2/35 - -76/105. Factor d*l**r - 2/3*l - 2/3*l**2 + 2/3.
2*(l - 1)**2*(l + 1)/3
Let s(n) = -79*n. Let r be s(1). Let u = r + 81. Factor -5/2*f**u + 0 + 1/2*f.
-f*(5*f - 1)/2
Suppose 4*l = 2*c + 48 + 22, 5*l = -2*c + 74. Factor 8 + 52*a - l*a**2 - 16*a**3 + 4*a**3 - 32.
-4*(a - 1)*(a + 3)*(3*a - 2)
Factor -4624/7 - 5172/7*f**2 + 40*f**3 - 4/7*f**4 + 1360*f.
-4*(f - 34)**2*(f - 1)**2/7
Let n(s) = 5*s - 1. Let k be n(1). Suppose -6*g - 4*g + 20 = 0. Factor 3*d + d**2 + k*d + 2*d**g - d.
3*d*(d + 2)
Let p(i) = 2*i + 81. Let m be p(-38). What is l in -10*l**2 + 9/2*l**m + 12*l**4 - 17/2*l**3 + 6*l + 0 = 0?
-3, -1, 0, 2/3
Let l(h) be the first derivative of -h**4/4 - h**3 - h**2 + 38. Let l(t) = 0. Calculate t.
-2, -1, 0
Suppose -33*h + 19 + 14 = 0. Factor u + h + 1/4*u**2.
(u + 2)**2/4
Factor 16*p - 84 - 75*p - 2*p**2 + 139*p + 6*p**2.
4*(p - 1)*(p + 21)
Let a(m) be the second derivative of -m**5/20 + m**4/6 + 5*m**3/2 + 79*m. Let a(c) = 0. Calculate c.
-3, 0, 5
Factor -1/3*m**3 - 14/3*m**2 + 14/3 + 1/3*m.
-(m - 1)*(m + 1)*(m + 14)/3
Let d(p) be the second derivative of -p**5/10 + 7*p**4/6 - 11*p**3/3 + 5*p**2 - 17*p - 4. Factor d(l).
-2*(l - 5)*(l - 1)**2
Let m(b) be the first derivative of -2/3*b**3 + 0*b - 4*b**2 + 9. Factor m(l).
-2*l*(l + 4)
Find r, given that -r**2 + 1/8*r**5 - 3/8*r**3 + 0 - 1/2*r + 1/4*r**4 = 0.
-2, -1, 0, 2
Let a(d) be the third derivative of -d**5/100 - d**4/5 - 7*d**3/10 + 95*d**2. Suppose a(m) = 0. Calculate m.
-7, -1
Let y(w) be the second derivative of 0 - 1/36*w**4 + 1/9*w**3 + 1/2*w**2 - 11*w. Factor y(m).
-(m - 3)*(m + 1)/3
Determine k so that -2/15*k**2 + 14/3 - 4/15*k = 0.
-7, 5
Let y = -865 + 869. Let x(q) be the first derivative of -5/3*q**3 - 4*q + 1/4*q**y + 9 + 4*q**2. Factor x(t).
(t - 2)**2*(t - 1)
Suppose 0 = -8*b + 28*b - 60. Let l(n) be the first derivative of -6*n + 9/2*n**2 - 1 + 3/5*n**5 + n**b - 9/4*n**4. Factor l(x).
3*(x - 2)*(x - 1)**2*(x + 1)
Let l(k) be the second derivative of k**6/15 + 7*k**5/10 - 3*k**4 - 56*k. Solve l(n) = 0 for n.
-9, 0, 2
Suppose -8*g - 14*g - 60 - 3*g**2 - 14*g = 0. What is g?
-10, -2
Let z(b) = b - 4. Let g be z(-9). Let f = 15 + g. Factor -22 - 5 + 32*w + f*w**4 - 5 - 8*w**3.
2*(w - 2)**3*(w + 2)
Let 7/3*h**2 + 1/3*h**3 + 14/3*h + 8/3 = 0. Calculate h.
-4, -2, -1
Let f = 32468 + -584273/18. Let g = f - 15/2. Solve -2/9*j**3 + 8/9*j + g - 2/9*j**2 = 0 for j.
-2, -1, 2
Let p = 29466/17 + -1734. Let v = p - -41/34. Factor 0 - v*f - 1/4*f**2.
-f*(f + 2)/4
Let h(q) be the first derivative of -q**6/6 + q**5 - 2*q**4 + 4*q**3/3 + 607. Determine n so that h(n) = 0.
0, 1, 2
Let s be 1*(180/(-228) - -1). Factor 6/19*b**3 + 0*b + 14/19*b**5 + 0 - s*b**2 + 24/19*b**4.
2*b**2*(b + 1)**2*(7*b - 2)/19
Let q(c) be the second derivative of -9*c + 0*c**2 + 1/21*c**4 + 0*c**3 + 0 + 9/70*c**5 + 4/105*c**6. Factor q(z).
2*z**2*(z + 2)*(4*z + 1)/7
Factor -6/11*k**3 + 0 + 6/11*k**4 - 2/11*k**5 + 2/11*k**2 + 0*k.
-2*k**2*(k - 1)**3/11
Let d = -39237/5 - -7849. Factor d*t**3 + 0 + 4/5*t**4 + 0*t + 4/5*t**2.
4*t**2*(t + 1)**2/5
Let a = -36 - -42. Suppose -1 = a*r - 1. Find h, given that r + 1/4*h**4 + 1/4*h**5 - 1/4*h**3 - 1/4*h**2 + 0*h = 0.
-1, 0, 1
Let m = -14 + 17. Suppose o + 82 = 3*z, -m*z + 0*o = o - 86. Factor 2*s**3 + z - 28.
2*s**3
Find a, given that 144/7 - 60/7*a**3 - 138/7*a**2 - 6/7*a**4 + 60/7*a = 0.
-6, -4, -1, 1
Let u(d) be the second derivative of 0*d**2 + 1/5*d**5 + 4/9*d**4 - 2/45*d**6 + 22*d + 0*d**3 + 0. Suppose u(q) = 0. What is q?
-1, 0, 4
Let h(s) = 3*s**3 + 2*s - 1. Let b be h(1). Solve -j**5 + 71 + 5*j**4 - b*j**5 - 71 = 0.
0, 1
Let m(v) be the first derivative of 0*v - 1/2*v**2 - 8/3*v**3 - 20. Determine g, given that m(g) = 0.
-1/8, 0
Let j(l) be the second derivative of -l**5/20 + l**4/4 + l**3/6 - 3*l**2/2 - 88*l. What is n in j(n) = 0?
-1, 1, 3
Let d(o) be the third derivative of o**5/330 - 73*o**4/132 + 24*o**3/11 - 11*o**2 + 16. Factor d(f).
2*(f - 72)*(f - 1)/11
Let p(z) be the first derivative of 7*z**5/5 - 5*z**4/3 - 4*z**3/3 + 31*z - 8. Let k(m) be the first derivative of p(m). Let k(i) = 0. What is i?
-2/7, 0, 1
Let z be (-54)/288 - (-18)/32. Factor z*b**3 - 1/4*b - 1/8*b**2 + 0.
b*(b - 1)*(3*b + 2)/8
Suppose -w = 2*s + 8 - 4, -3*w - 7*s - 16 = 0. Factor 0 - 1/6*n**2 + 0*n - 1/3*n**3 - 1/6*n**w.
-n**2*(n + 1)**2/6
Let d be (24/(-11) + 2)*-11. Suppose -3*j - 9 = d*i, -j - 2*j = -i + 18. Solve 1 + 3 - i + z**2 + 0*z + 2*z = 0 for z.
-1
Determine j so that -5/3 + 14/3*j + 1/3*j**4 + 2/3*j**3 - 4*j**2 = 0.
-5, 1
Let r(f) be the first derivative of -f**6/9 + 2*f**5/15 + 2*f**4/3 - 8*f**3/9 - 140. Let r(t) = 0. What is t?
-2, 0, 1, 2
Suppose 0 = -3*t + 3*x + 38 - 29, -4*x = 4. Factor 4*f**t + 40/9*f + 2/9*f**4 + 14/9*f**3 + 16/9.
2*(f + 1)*(f + 2)**3/9
Let b(g) = g**2 + 1. Let f = -12 + 14. Let t be b(f). Let r**3 + 17*r - t*r**3 - r = 0. Calculate r.
-2, 0, 2
Let y(n) be the second derivative of -n**7/168 - n**6/24 + 7*n**5/40 - n**4/24 - 13*n**3/24 + 7*n**2/8 - 161*n - 2. Determine g, given that y(g) = 0.
-7, -1, 1
Let j(r) = r**3 + 7*r**2 - 10*r - 13. Let i be j(-8). Factor 5 + i*y**4 - 5*y**4 + 3*y**4 - 2*y**2 - 4.
(y - 1)**2*(y + 1)**2
Let c(q) be the second derivative of -q**7/56 - q**6/40 + 9*q**5/40 + 211*q. Factor c(i).
-3*i**3*(i - 2)*(i + 3)/4
Let g(t) be the third derivative of t**9/756 - t**8/240 + t**7/315 + 3*t**4/8 + 13*t**2. Let n(w) be the second derivative of g(w). Factor n(p).
4*p**2*(p - 1)*(5*p - 2)
Solve 13/3*g - 4/3 + 7/3*g**3 - 1/3*g**4 - 5*g**2 = 0.
1, 4
Let l(c) be the third derivative of 2*c**7/735 + 2*c**6/105 + c**5/105 - c**4/7 + 2*c**2 - 115*c. Let l(z) = 0. Calculate z.
-3, -2, 0, 1
Let -28*x - 18 - 8/3*x**2 - 2/3*x**4 + 20/3*x**3 = 0. What is x?
-1, 3, 9
Let p(a) be the first derivative of 2/3*a**3 + 8*a**2 - 28 + 14*a. Factor p(n).
2*(n + 1)*(n + 7)
Let l(j) be the second derivative of 1/15*j**6 - 2*j - 2/3*j**3 + 1/21*j**7 - 3/10*j**5 + 0*j**2 + 0 - 5/6*j**4. Factor l(k).
2*k*(k - 2)*(k + 1)**3