c). Factor l(i).
-i**2*(i + 2)**2*(5*i - 1)
Solve 0 + 3/2*j + 1/4*j**3 - 5/4*j**2 = 0 for j.
0, 2, 3
Let x(j) be the third derivative of -j**6/40 - j**5/20 + 7*j**4/4 + 12*j**3 - 125*j**2. Find k such that x(k) = 0.
-3, -2, 4
Let f(j) = 62*j**2 - 26*j - 14. Let w(t) = -3*t**2 - 2. Let h be w(-2). Let r(q) = 21*q**2 - 9*q - 5. Let y(k) = h*r(k) + 5*f(k). Factor y(s).
4*s*(4*s - 1)
Let m = 344/7 + -1692/35. Factor m*d**2 - 4/5 + 0*d.
4*(d - 1)*(d + 1)/5
Let s be ((15/(-25))/(-3))/(4/8). Let y(w) be the first derivative of 0*w + 1/10*w**4 - 2/5*w**3 + s*w**2 - 9. Solve y(k) = 0 for k.
0, 1, 2
Let 0 + 0*o + 2/15*o**2 = 0. What is o?
0
Let y(s) be the second derivative of 0 + 0*s**2 + 1/36*s**4 - 1/18*s**3 - 13*s. Find a, given that y(a) = 0.
0, 1
Let n(z) be the first derivative of -5*z**6/3 + 23*z**5 - 55*z**4/4 + 278. Find g, given that n(g) = 0.
0, 1/2, 11
Let b = -15671 - -15673. Factor 3/2*f**b + 9*f + 0.
3*f*(f + 6)/2
Let f(h) be the first derivative of -8 - 1/36*h**4 + 1/18*h**2 + 1/45*h**5 + 2/3*h - 7/27*h**3. What is l in f(l) = 0?
-2, -1, 1, 3
Let n be (1 - -8)/(-1)*9/3. Let o be (-26)/(-117) - 3/n. Let -1/9*q**3 + 0 - 1/3*q**2 - 1/9*q**5 + 2/9*q + o*q**4 = 0. Calculate q.
-1, 0, 1, 2
Suppose 0 + 2/7*h**3 + 0*h - 24/7*h**2 = 0. What is h?
0, 12
Let s(i) be the second derivative of i**6/15 - 18*i**5/5 + i - 55. Solve s(t) = 0.
0, 36
Let v(k) = 9*k**3 - 78*k**2 + 123*k - 36. Let p(g) = -9*g**3 + 78*g**2 - 121*g + 37. Let i(h) = 6*p(h) + 5*v(h). What is s in i(s) = 0?
2/3, 1, 7
Factor -97*v**3 + 57*v**2 - 2700 + 720*v - 87*v**3 + 185*v**3.
(v - 3)*(v + 30)**2
Suppose 11*l - 9*l = -l - 40*l. Factor l - 3*h + 3/2*h**2.
3*h*(h - 2)/2
Let n(g) = 5*g**5 + 7*g**4 - 5*g**3 + g**2 + 4*g. Let d(q) = 6*q**5 + 8*q**4 - 6*q**3 + 3*q**2 + 5*q - 1. Let k(l) = 4*d(l) - 5*n(l). Factor k(h).
-(h - 1)**2*(h + 1)*(h + 2)**2
Let m be 45/135 - 22/(-6). Solve 2/5*p**5 + 0 - 8/5*p**m + 0*p + 8/5*p**3 + 0*p**2 = 0 for p.
0, 2
Let v(d) be the second derivative of -d**6/6 + 61*d**5/4 - 4495*d**4/12 - 4805*d**3/6 + 39*d. Factor v(f).
-5*f*(f - 31)**2*(f + 1)
Let x(u) be the first derivative of u**7/3360 + u**6/1440 - u**5/60 - u**4/8 - 3*u**3 + 18. Let s(h) be the third derivative of x(h). Factor s(r).
(r - 3)*(r + 2)**2/4
Let l(i) = -i**3 + 3*i**2 - 4. Let h(k) = 3*k**3 - 6*k**2 + 9. Let f(x) = -4*h(x) - 9*l(x). Suppose f(y) = 0. Calculate y.
-1, 0
Let m(r) be the first derivative of -r**7/280 - r**6/60 + 3*r**5/40 + 14*r**3 - 17. Let q(i) be the third derivative of m(i). Factor q(k).
-3*k*(k - 1)*(k + 3)
Let y(j) be the second derivative of 32 + 1/3*j**3 - 2/3*j**2 + 1/45*j**6 - 1/10*j**5 + 1/18*j**4 + j. Find h such that y(h) = 0.
-1, 1, 2
Let r(m) = m**3 + 7*m**2 + 3*m + 6. Let x be r(-4). Suppose 0*y = -3*y + x. Factor -y*l**2 - 1 - l**4 - 20*l**2 - 4*l + 28*l**2 - 4*l**3.
-(l + 1)**4
Let r be 6/69 - (-12)/(-138). Let u(p) be the third derivative of 0*p**5 + 0 + 0*p**3 + 1/336*p**8 + r*p + 1/210*p**7 - 7*p**2 + 0*p**4 + 0*p**6. Factor u(w).
w**4*(w + 1)
Suppose -20 = -13*u - 39*u + 240. What is p in -6 + 57/2*p**3 - 6*p**u - 12*p**2 - 45/2*p + 18*p**4 = 0?
-1, -1/2, 1, 4
Let g be ((-82)/(-10) - 7)/((-12)/(-40)). Factor -2/3*n**5 + 0*n**g + 0 + 0*n + 2*n**3 - 4/3*n**2.
-2*n**2*(n - 1)**2*(n + 2)/3
Factor -2/7*t**2 - 34/7 + 36/7*t.
-2*(t - 17)*(t - 1)/7
Suppose 2*k = 2*d - 2, 2*d + k - 3 = d. Suppose -l = -d*l + 4. Suppose -4*x**3 - 4*x**3 + 2*x**4 - l*x - 2*x**2 + 12*x**2 = 0. Calculate x.
0, 1, 2
Let i be 8*(-5)/(-10)*(-2)/(-8). Let b = -5 - -8. Factor 4 - b - 4*w**2 - i.
-4*w**2
Suppose 2*a + 3*s - 12 = 0, 5*a + 835*s - 840*s - 5 = 0. Find i, given that -84/5*i**a + 32/5*i**4 - 96/5 - 4/5*i**5 + 56/5*i**2 + 16*i = 0.
-1, 2, 3
Let t(n) = -1 - n**2 + 6*n - n - 4*n. Let w(s) = -3 - 6*s**2 + 6*s**2 - 6*s**2. Let q(z) = 3*t(z) - w(z). Factor q(d).
3*d*(d + 1)
Let c(g) be the third derivative of -25*g**7/84 - 155*g**6/48 + 47*g**5 - 628*g**4/3 + 1408*g**3/3 - 7*g**2 - 54*g. Factor c(a).
-(a + 11)*(5*a - 8)**3/2
Let m = 295 - 295. Let i(x) be the first derivative of m*x**4 + 0*x**2 - 1/5*x**6 - 9/25*x**5 + 1/5*x**3 - 2 + 0*x. Suppose i(a) = 0. Calculate a.
-1, 0, 1/2
Suppose 3*o + t + 12 = -0, -5*t - 15 = 0. Let c = o + 5. What is d in 0 - 3/7*d**3 - 6/7*d**c - 3/7*d = 0?
-1, 0
Let w(a) = -a**5 - a**4 + 2*a**3 - a**2 + a + 2. Let k(g) = -11*g**5 - 21*g**4 + 12*g**3 + 14*g**2 + 6*g + 12. Let t(u) = -k(u) + 6*w(u). Factor t(f).
5*f**2*(f - 1)*(f + 2)**2
Suppose -23 = -4*d - 7. Let j(p) = p**2 - 2*p + 4. Let a be j(0). Let -4*f**a + 3*f**2 + 13*f**2 + 8*f - d*f**2 = 0. What is f?
-1, 0, 2
Let c(t) be the second derivative of -10*t + 1/14*t**4 + 0*t**2 + 0 + 1/140*t**5 + 0*t**3 - 1/210*t**6. Let c(u) = 0. Calculate u.
-2, 0, 3
Let k(z) be the second derivative of -z**6/15 + 37*z**5/5 - 503*z**4/2 + 5180*z**3/3 - 4900*z**2 + 82*z - 2. Determine c, given that k(c) = 0.
2, 35
Let w = 8 + -6. Let u = 37081/8898 - 1/1483. Factor 5/3*l + 1/6*l**w + u.
(l + 5)**2/6
Let s = 4/8365 + 25079/33460. Factor 0 + s*g**3 - 9/2*g - 15/4*g**2.
3*g*(g - 6)*(g + 1)/4
Let g = -31675/4 + 7919. Suppose -3*z + 4*c + 26 = 0, 5*c - c = 2*z - 24. Factor g*a**z + 1/4*a - 1/2.
(a - 1)*(a + 2)/4
Suppose 0 = -3*c - 5*g + 82, -2*g - 52 = -2*c - 4*g. Solve 19*r**3 - 2*r**2 - c*r**4 - 51*r**3 - 16*r**5 + 20*r**3 = 0.
-1/2, 0
Let n(a) = -1471*a + 2. Let q be n(0). Let 2/11*x**5 + 16/11 + 8/11*x - 20/11*x**q - 10/11*x**3 + 4/11*x**4 = 0. What is x?
-2, -1, 1, 2
Let a(j) be the third derivative of -j**5/390 - 2*j**4/13 - 48*j**3/13 - 3*j**2 - 10*j. Factor a(b).
-2*(b + 12)**2/13
Let z(x) be the second derivative of -x**5/50 + 2*x**4/15 + x**3/3 + 94*x. Factor z(p).
-2*p*(p - 5)*(p + 1)/5
Let z be 5/(-6)*(-2)/15. Let u(x) be the second derivative of 0 + 1/15*x**5 + 5*x - 2/9*x**3 + 0*x**2 - 5/18*x**4 + z*x**6. Suppose u(s) = 0. Calculate s.
-1, -2/5, 0, 1
Let j(d) be the first derivative of d**4/5 - 26*d**3/5 + 216*d**2/5 - 486*d/5 + 393. Factor j(m).
2*(m - 9)**2*(2*m - 3)/5
What is u in 2*u**4 - 11*u**2 + 3*u**2 + 3*u**3 - 5*u**3 - 22*u**3 - 17*u + 113*u = 0?
-2, 0, 2, 12
Let d(x) be the third derivative of x**8/2240 + x**7/420 + x**6/240 - x**4/8 + 17*x**3/6 - 47*x**2. Let m(j) be the second derivative of d(j). Solve m(k) = 0.
-1, 0
Let y be 8 + 0 + 40/(-10). Find p such that -28*p**5 + 8*p**3 - 7*p + 7*p + 8*p**3 - 48*p**y = 0.
-2, 0, 2/7
Factor 16/5*w + 4/5*w**2 - 48.
4*(w - 6)*(w + 10)/5
Let r be ((-280)/(-42))/((-8)/(-6)). Let j = -7 - -11. Determine y, given that 36*y - r*y**j + y**4 + 12*y**2 - 4*y**3 + 8 - 16*y = 0.
-1, 2
Let v be -8 - 405/(-60)*2. Factor -6 + 5/2*z**2 + v*z.
(z + 3)*(5*z - 4)/2
Factor -34*u - 28*u**2 - 21 + 4*u - 2*u + 37 + 20*u**3.
4*(u - 2)*(u + 1)*(5*u - 2)
Let s be -23*8 + 5/(5/(-3)). Let w = s - -936/5. Factor -3/10*l + 1/10*l**4 - w + 3/10*l**3 + 1/10*l**2.
(l - 1)*(l + 1)**2*(l + 2)/10
Let g be (1 - 1) + 6/12*(1 - -3). Factor 0*m + 0*m**g + 0*m**3 + 0*m**4 + 0 - 1/8*m**5.
-m**5/8
Suppose -22*j**2 + 105/4*j**3 + 0 + 4*j - 37/4*j**4 + j**5 = 0. Calculate j.
0, 1/4, 1, 4
Let z(f) be the first derivative of -f**6/42 + 9*f**5/35 - 25*f**4/28 + 9*f**3/7 - 5*f**2/7 - 74. Determine n so that z(n) = 0.
0, 1, 2, 5
Let p be (-18 + -2)*(-4)/20. Let q(d) be the second derivative of 0 - 1/60*d**5 - 1/9*d**3 + 1/12*d**4 + 0*d**2 + p*d. Factor q(c).
-c*(c - 2)*(c - 1)/3
Suppose -3*g - 12 = 0, 3*g - 87 = -q - 97. Let s(n) be the first derivative of 3/4*n**4 + 9 + 3/2*n**q + 0*n - 2*n**3. Let s(d) = 0. What is d?
0, 1
Let t(k) be the first derivative of k**3/18 - 31*k**2/6 + 7. Factor t(s).
s*(s - 62)/6
Let d be -1 + (-21)/(-27) - ((-628)/(-252) - 5). Let d*n**3 + 4/7*n**2 - 4/7 - 16/7*n = 0. What is n?
-1, -1/4, 1
Suppose 52*x - 106*x = -162. Let 0 + 1/6*r**x + 1/3*r**2 + 1/6*r = 0. What is r?
-1, 0
Let k(t) = -3*t**2 - 7*t + 8. Let a(p) = 2*p**2 + p - 1. Let u(n) = -4*a(n) - 4*k(n). Determine g so that u(g) = 0.
-7, 1
Let t be (1/(-1) - -2) + -6 + 7. Solve -1/2*l**t + 0 + 1/2*l**5 + 1/2*l**4 + 0*l - 1/2*l**3 = 0.
-1, 0, 1
Let r(a) = -5*a**4 - 3*a**3 - 15*a**2 - 23*a + 6. Let t(v) = 11*v**4 + 6*v**3 + 30*v**2 + 47*v - 14. Let n(x) = 13*r(x) + 6*t(x). Let n(u) = 0. Calculate u.
-1, 6
Let c be 100/20 - (-42)/(-10). Let g be 2/(-10)*-4 + 0. Let 8/5*a**2 - 14/5*a - c - 14/5*a**5 - g*a**4 + 