 45. Let q be g/(-4) + 2/4. Factor 0 - 4/7*m**2 + 2/7*m - 8/7*m**4 - 2*m**q.
-2*m*(m + 1)**2*(4*m - 1)/7
Let y(n) = -3*n - 2. Let r(s) = -s**2 + s + 1. Suppose 0 = 5*v - 5 - 0. Let a(w) = v*y(w) + r(w). Find i such that a(i) = 0.
-1
Let t(n) be the second derivative of n**6/60 + 8*n**5/105 + n**4/21 - n**2 - 7*n. Let g(p) be the first derivative of t(p). Factor g(d).
2*d*(d + 2)*(7*d + 2)/7
Suppose 3/4*i**4 - 3 + 9/4*i**2 + 3*i - 3*i**3 = 0. Calculate i.
-1, 1, 2
Let k(x) = -15*x - 75. Let t be k(-5). Let 24/7*q**4 + t - 2/7*q**2 - 2/7*q**3 + 0*q = 0. Calculate q.
-1/4, 0, 1/3
Let o(u) = u**3 + u + 3. Let c be o(0). Let -4*k - 12*k**2 + 0*k**c + 6*k**4 + 12*k + 8 - 2*k**2 - 8*k**3 = 0. Calculate k.
-1, -2/3, 1, 2
Factor 87*z**4 - 45*z**4 - 43*z**4 + z**2 - 2*z**3 - 2*z**2.
-z**2*(z + 1)**2
Let q(c) be the first derivative of -1/6*c**4 - 2*c - 4 + 0*c**2 + 0*c**3. Let y(d) be the first derivative of q(d). Find p, given that y(p) = 0.
0
Let y = -146 + 58. Let q be y/(-110)*(-5)/(-2). Let 1/3*f**3 + 1/3 - 1/3*f**q - 1/3*f = 0. Calculate f.
-1, 1
Let r(s) be the first derivative of -s**4/20 - s**3/15 + 28. Factor r(n).
-n**2*(n + 1)/5
Let t(m) be the third derivative of 0*m**3 + 0*m + 7*m**2 + 0 + 1/60*m**6 + 1/10*m**5 + 1/6*m**4. Find l such that t(l) = 0.
-2, -1, 0
Let z = -362 - -10861/30. Let f(g) be the third derivative of 1/15*g**3 + 0*g + 2*g**2 + z*g**4 + 0 + 1/150*g**5. Determine p, given that f(p) = 0.
-1
Factor 3*i - 24*i + 12 - i**3 + 4*i**3 + 6*i**2.
3*(i - 1)**2*(i + 4)
Let a be (-2)/516*1162/(-21). Let c = 1/129 + a. Let 2/9*h**5 + 4/9*h**4 + 0 - 4/9*h**2 - c*h + 0*h**3 = 0. What is h?
-1, 0, 1
Suppose -5*l = -2*a + 3*a, 0 = -l + a. Let z(h) be the third derivative of 0*h**6 - 1/735*h**7 + l + 2*h**2 + 0*h**3 + 0*h**4 + 1/210*h**5 + 0*h. Factor z(r).
-2*r**2*(r - 1)*(r + 1)/7
Factor -2/5*v**4 + 16/5*v - 2*v**3 + 8/5 + 2/5*v**5 + 2/5*v**2.
2*(v - 2)**2*(v + 1)**3/5
Let o(j) be the first derivative of -3*j**5/25 + 3*j**4/4 - 9*j**3/5 + 21*j**2/10 - 6*j/5 - 16. Factor o(c).
-3*(c - 2)*(c - 1)**3/5
Let w(k) be the second derivative of -k**5/50 + k**3/5 + 2*k**2/5 - 4*k + 11. Find s such that w(s) = 0.
-1, 2
Let j(v) = -v**2 + 13*v - 16. Let s be j(10). Let t be (6/5)/(4/s). Find r, given that -6/5 - 3*r + t*r**2 = 0.
-2/7, 1
Let u = 4 - 12. Let n be (-3)/14 + (-4)/u. Factor -2/7*h**2 + 4/7*h - n.
-2*(h - 1)**2/7
Let o(j) be the first derivative of -j**5/10 - j**4/2 - j**3/2 + j**2 + 2*j + 7. Solve o(x) = 0.
-2, -1, 1
Let r = -279 + 1117/4. Suppose 3*q + 2 = -g - 2, -q + 4 = -g. Factor q + r*u**2 + 3/4*u.
u*(u + 3)/4
Let t(z) = -19*z**3 - z**2 - z - 1. Let o be t(-1). Let r = -16 + o. Determine c, given that 0 - 1/2*c**r - c + 4*c**3 - 5/2*c**4 = 0.
-2/5, 0, 1
Let m(v) = -v**2 - 5*v - 4. Let o be m(-4). Let d(y) = -y**3 + 2*y**2 + 4*y + 1. Let u be d(3). Solve -w**u + o*w - 2*w**3 - w**2 + 4*w + 4*w**2 - 4 = 0 for w.
-2, 1
Let o(y) = 6*y**2 - 5*y. Suppose 5*k + 25 = -0*k. Let h(v) = 7*v**2 - 6*v. Let n(c) = k*h(c) + 6*o(c). Factor n(w).
w**2
Let h(v) = -v**3 + 7*v**2 + 4. Let o be h(7). Suppose j = 2*j - o*w, 16 = 3*j + 4*w. Let -a**2 + 4 + a - j - 2*a = 0. What is a?
-1, 0
Let r(u) be the third derivative of -u**7/70 + 7*u**5/20 + 3*u**4/4 - 52*u**2. Factor r(i).
-3*i*(i - 3)*(i + 1)*(i + 2)
Let u(i) = -i**3 + 41*i**2 - 9*i - 9. Let k(x) = -10*x**2 + 2*x + 2. Let j(l) = 18*k(l) + 4*u(l). Let j(v) = 0. Calculate v.
-4, 0
Let j(h) = h**2 - h + 1. Let v(a) be the third derivative of -2*a**5/15 - a**4/12 - a**3/3 + 3*a**2. Let p(m) = -2*j(m) - v(m). Factor p(d).
2*d*(3*d + 2)
Let d(c) be the third derivative of -5*c**7/126 - 13*c**6/72 - c**5/4 + 5*c**4/72 + 5*c**3/9 - 22*c**2. Find k, given that d(k) = 0.
-1, 2/5
Let d(t) be the third derivative of t**7/126 - t**6/72 - t**5/18 - 8*t**2. Solve d(a) = 0 for a.
-1, 0, 2
Let l be (6/(-2))/((-75)/10). Factor 0*m**3 + 2/5*m**4 + 0 - l*m**2 + 0*m.
2*m**2*(m - 1)*(m + 1)/5
Find c such that c - 4/7*c**2 - 1/7*c**3 + 10/7 = 0.
-5, -1, 2
Let q be 103/(-4) - 3/(-12). Let c = q + 26. Factor 0 - c*s - 1/2*s**3 - s**2.
-s*(s + 1)**2/2
Let y be 39/27 + (-1 - 0). Let w be (2 + (-36)/8)*(-1 - 1). Factor 2/3*m**4 - 4/9*m**2 - 2/9 + 2/3*m - y*m**3 - 2/9*m**w.
-2*(m - 1)**4*(m + 1)/9
Let g = 35 - 31. Let n(j) be the second derivative of 1/12*j**3 + 0*j**2 - 2*j + 1/24*j**g + 0. Find u such that n(u) = 0.
-1, 0
Let m be 40/3*(-12)/(-10). Let c(l) = -7*l**2 + 8*l. Let s(k) = -36*k**2 + 40*k. Let b(t) = m*c(t) - 3*s(t). Factor b(d).
-4*d*(d - 2)
Suppose -2*p + 3*p - 28 = 3*b, 3*b = 3*p - 18. Let y = b + 45/4. Find d such that -1/4*d**5 + 0 + 1/4*d**3 + y*d**4 - 1/4*d**2 + 0*d = 0.
-1, 0, 1
Let o be 5/970*(-1 + 907). Let u = o - 1/291. Factor -u*j**2 + 14/3*j - 4/3 + 4/3*j**3.
2*(j - 2)*(j - 1)*(2*j - 1)/3
Let k(c) = -c**2 + c + 2. Let y be k(0). Suppose -2*q - 2 = -3*v, 1 + 1 = -q + y*v. Factor -3/4*g + 1/4 + 1/2*g**q.
(g - 1)*(2*g - 1)/4
Suppose -5*u + 0 + 10 = 0. Factor -2*n**4 - 3*n + 3*n**2 + n**3 + 4*n - u*n - 5 + 4.
-(n - 1)**2*(n + 1)*(2*n + 1)
Let v be -6 + ((-13)/(-3))/(56/84). What is l in v*l**2 + 0*l + 0 = 0?
0
Let n(d) = 0*d**2 + 4 - d - 4*d + d**2. Let y be n(5). Solve 4*j**2 - 3*j**2 - j**4 - 2*j**3 + 2*j**y = 0 for j.
0, 1
Let w(h) be the third derivative of 0*h - h**2 - 1/240*h**6 + 1/120*h**5 + 0 + 0*h**3 + 1/24*h**4. Solve w(r) = 0.
-1, 0, 2
Let j(k) be the second derivative of -k**7/147 + k**6/15 - 9*k**5/35 + 10*k**4/21 - 8*k**3/21 + 36*k. Factor j(p).
-2*p*(p - 2)**3*(p - 1)/7
Let n(a) be the second derivative of a**9/60480 - a**8/13440 - a**4/3 + a. Let s(g) be the third derivative of n(g). Find v, given that s(v) = 0.
0, 2
Let w(t) be the third derivative of t**7/1050 + t**6/150 + t**5/300 - t**4/20 + 32*t**2. Find p, given that w(p) = 0.
-3, -2, 0, 1
Let p(z) = -8*z**5 - 4*z**4 + 4*z**3 + 8*z**2 - 4. Let a(y) = 7*y**5 + 4*y**4 - 4*y**3 - 7*y**2 + 3. Let o(k) = -4*a(k) - 3*p(k). Factor o(v).
-4*v**2*(v - 1)*(v + 1)**2
Let i(c) be the third derivative of -c**8/120960 + c**7/15120 - c**5/20 + c**2. Let y(j) be the third derivative of i(j). Solve y(n) = 0 for n.
0, 2
Let w(b) be the third derivative of b**8/448 - b**6/40 + b**5/40 + 3*b**4/32 - b**3/4 + 13*b**2. Factor w(x).
3*(x - 1)**3*(x + 1)*(x + 2)/4
Let k(a) be the third derivative of -a**7/945 + a**6/270 + a**5/90 - a**4/27 - 4*a**3/27 - 12*a**2. What is c in k(c) = 0?
-1, 2
Determine n so that 2/9*n + 4/3 - 2/9*n**2 = 0.
-2, 3
Let c be 6/(-4) - (0 - (-1 + 3)). Suppose -c*d - 1/6*d**4 + 1/3 - 1/6*d**2 + 1/2*d**3 = 0. Calculate d.
-1, 1, 2
Let h(k) = 8*k**2 + 0*k**3 - 6*k - k**3 - 3*k**3. Let y(t) = 3*t**3 - 7*t**2 + 5*t. Let c(i) = 5*h(i) + 6*y(i). Factor c(n).
-2*n**2*(n + 1)
Let v(d) be the third derivative of -d**8/42 - 17*d**7/105 - 7*d**6/15 - 11*d**5/15 - 2*d**4/3 - d**3/3 + 5*d**2. Factor v(n).
-2*(n + 1)**4*(4*n + 1)
Suppose 0 = h + 2*h. Let k(p) be the third derivative of -1/160*p**6 + 0*p**3 + 0*p - 1/280*p**7 + 0 - 1/1344*p**8 + p**2 + h*p**4 - 1/240*p**5. Factor k(f).
-f**2*(f + 1)**3/4
Suppose -8/3*m**2 + 0 + 2/3*m**3 + 2*m = 0. What is m?
0, 1, 3
Let n(q) be the second derivative of 0 + 2*q + 0*q**3 + 1/20*q**5 + 0*q**4 + 0*q**2 + 1/10*q**6. Solve n(j) = 0 for j.
-1/3, 0
Let k = 0 - -2. Factor 4*r**2 - 6*r**2 + k*r + 3*r**2 - r**3.
-r*(r - 2)*(r + 1)
Determine k so that 8*k**3 - 11*k**2 + 42*k**2 - 6*k**2 + 12*k - 7*k**2 + 2 = 0.
-1, -1/4
Let j(g) be the first derivative of 3*g**4/4 - 3*g**2/2 - 7. Factor j(v).
3*v*(v - 1)*(v + 1)
Let c be (-166)/(-8) - (-5)/20. Suppose -4*t - 3*x + c = 1, -x = -4. What is k in 1/5*k**3 - 1/5*k - 2/5 - 3/5*k**4 + k**t = 0?
-1, -2/3, 1
Let d(x) = -x**3 - 14*x**2 + 32*x - 28. Let k(t) = t**3 - t**2 + t + 1. Let a(p) = d(p) + 4*k(p). Determine f, given that a(f) = 0.
2
Let z(l) be the first derivative of -l**4/6 + 4*l**3/9 + 9. Determine w so that z(w) = 0.
0, 2
Let t(n) be the third derivative of -n**8/13440 + n**7/1260 - n**6/360 + 5*n**4/24 + 2*n**2. Let m(p) be the second derivative of t(p). Factor m(h).
-h*(h - 2)**2/2
Find n such that 0*n**2 + 0 - 4/3*n - 1/3*n**4 + n**3 = 0.
-1, 0, 2
Let z(l) be the first derivative of 3/4*l**2 + 3 - 1/2*l**3 - 3/8*l**4 + 0*l + 3/10*l**5. Determine t, given that z(t) = 0.
-1, 0, 1
Let n(o) = -o**2 + 6*o + 2. Let k be n(6). Let 147*i**3 - 148*i**3