1)
Suppose -2*t = 5*t - 2*t. Determine y, given that -y**2 - 1/2*y**3 - 1/2*y + t = 0.
-1, 0
Let s(n) be the third derivative of -n**7/70 - n**6/10 - n**5/4 - n**4/4 - n**2. Determine b so that s(b) = 0.
-2, -1, 0
Solve -1/2*k**4 - 1/4*k**3 - 1/2*k + 5/4*k**2 + 0 = 0.
-2, 0, 1/2, 1
Let m(a) be the second derivative of -a**4/4 + 3*a**3/2 - 3*a**2 - 17*a. Factor m(i).
-3*(i - 2)*(i - 1)
Let w(q) = -13*q**4 + 17*q**3 - 37*q**2 + 19*q. Let n(f) = -4*f**4 + 6*f**3 - 12*f**2 + 6*f. Let m(l) = 14*n(l) - 4*w(l). Determine j, given that m(j) = 0.
0, 1, 2
Let s(d) be the third derivative of d**6/120 - d**5/12 + d**3/3 + d**2. Let c be s(5). Let -4 + m - 5*m - 3*m**c + 2*m**2 = 0. Calculate m.
-2
Let c be 2/(4/14) + -1. Suppose c = -2*p + 5*p. Factor 2*g**p + 5*g - g + g**3 - 3*g.
g*(g + 1)**2
Factor 2/3 - 4/3*j + 2/3*j**2.
2*(j - 1)**2/3
Let y(f) be the first derivative of 0*f**4 + 1/5*f**5 + f - 2/3*f**3 + 0*f**2 - 2. Factor y(l).
(l - 1)**2*(l + 1)**2
Let r(s) be the third derivative of 4*s**7/105 + 7*s**6/30 + 7*s**5/15 + s**4/3 - 7*s**2. Suppose r(l) = 0. What is l?
-2, -1, -1/2, 0
Let c be (-1*4/7)/(4/(-14)). Factor 1/4*y**3 + 0*y - 1/4*y**c + 0.
y**2*(y - 1)/4
Suppose 0 = -2*v - 3*v + 455. Let i be 40/v + (-2)/13. Suppose 4/7*t**3 - 4/7*t**2 - 2/7*t - i*t**5 + 2/7*t**4 + 2/7 = 0. What is t?
-1, 1
Let r(j) be the first derivative of -2*j**5 - 5*j**4/4 + 25*j**3/3 - 5*j**2 + 22. Let r(d) = 0. Calculate d.
-2, 0, 1/2, 1
Let p(k) be the third derivative of 1/120*k**4 + 0*k**3 - 1/100*k**5 + 0*k + 1/200*k**6 + 5*k**2 - 1/1050*k**7 + 0. Factor p(v).
-v*(v - 1)**3/5
Suppose 23*b + 180 = 83*b. Determine l, given that -5/4*l**2 - 1 + b*l = 0.
2/5, 2
Let b(f) be the first derivative of f**6/4 + f**5/10 - f**4/4 + 3. Factor b(n).
n**3*(n + 1)*(3*n - 2)/2
Let b(z) be the second derivative of 1/240*z**6 + 0*z**4 + 0*z**3 - z**2 + 0 - 4*z + 1/120*z**5. Let l(w) be the first derivative of b(w). Factor l(j).
j**2*(j + 1)/2
Let 0*h + 0 - 2*h**3 - 2 + 2*h + 2*h**2 = 0. What is h?
-1, 1
Let 10/11*w - 4/11 + 2/11*w**3 - 8/11*w**2 = 0. Calculate w.
1, 2
Determine z so that -1/5*z**2 + 4/5*z - 4/5 = 0.
2
Let d(m) be the second derivative of 0*m**2 - 1/80*m**5 + 1/168*m**7 - 1/120*m**6 - 2*m + 0 + 1/48*m**4 + 0*m**3. What is s in d(s) = 0?
-1, 0, 1
Let k(b) be the first derivative of -14*b**3/3 + 20*b**2 - 200*b/7 - 42. Suppose k(w) = 0. What is w?
10/7
Let j = 1 + -6. Let w = 7 + j. Determine i so that -i**w - i**2 - 6 + 6 = 0.
0
Let l be (1/(-3))/((-3)/(-9)). Let d be (8/(-80))/(l/8). Solve 0*b**2 + 0 + 0*b - 6/5*b**4 - 2/5*b**3 - d*b**5 = 0.
-1, -1/2, 0
Let 32/9 + 2/9*c**2 - 16/9*c = 0. Calculate c.
4
Let q be ((-3)/(-6))/((-6)/(-36)). Let o(y) be the first derivative of -1/6*y**q + 0*y**2 - 1 + 1/2*y. Factor o(s).
-(s - 1)*(s + 1)/2
Let b(q) be the second derivative of 5*q**7/273 - q**6/15 + 9*q**5/130 + q**4/78 - 2*q**3/39 + 8*q. Factor b(r).
2*r*(r - 1)**3*(5*r + 2)/13
Let z = -2 - 8. Let w = z - -12. Factor -1/2 - 2*q - 2*q**3 - 3*q**w - 1/2*q**4.
-(q + 1)**4/2
Let u(z) be the first derivative of 4*z**5/5 - z**4/8 - 4*z**3 + 19*z**2/4 - z - 56. Determine n so that u(n) = 0.
-2, 1/8, 1
Suppose 0 = -3*y - y. Suppose -5*g + y*g + 30 = 5*f, -2*f = -g. Determine r, given that 196*r**3 - 4 + 34*r - 8*r - 161*r**f + 18*r = 0.
1/4, 2/7
Suppose 3*r = 2*r. Let h(l) be the third derivative of 0*l - l**2 + 0 + 0*l**5 - 1/84*l**4 + r*l**3 + 1/420*l**6. Let h(w) = 0. Calculate w.
-1, 0, 1
Factor 42*s**3 - 12*s**2 + 2*s - 39*s**3 - 2*s.
3*s**2*(s - 4)
Suppose 2*f - 3 = -1, f = 3*l - 11. Let r be ((3/4)/3)/1. Suppose 1/4*x**2 + 1/4*x**3 - r*x**l + 0 - 1/4*x = 0. What is x?
-1, 0, 1
Let w = -3 - -8. Let r be ((-12)/(-15))/(2/w). Solve y - 2*y - 22*y**3 - 6*y**r - 9*y**5 + 24*y**4 + 14*y**2 = 0.
0, 1/3, 1
Suppose 0 = a - 5*g - 17, 0 = -2*a + 5*g + 19. Suppose 2*y**4 - 8*y**2 + 0*y**4 - 8*y**3 - 2*y**4 - a*y**4 = 0. What is y?
-2, 0
Suppose 2*w - 6 = 8. Let o = w - 3. Factor -3*m**2 + 3*m + 0*m - m + m + 3*m**o - 3*m**3.
3*m*(m - 1)**2*(m + 1)
Factor 0*h + 0 + 3/8*h**3 + 9/4*h**2.
3*h**2*(h + 6)/8
Let u(k) = -5*k**3 + 3*k**2 + 5*k + 3. Let g(y) = -10*y**3 + 5*y**2 + 10*y + 5. Let c(p) = -3*g(p) + 5*u(p). Solve c(b) = 0.
-1, 0, 1
Suppose 1/2 - 1/2*p**2 + 0*p = 0. What is p?
-1, 1
Let x(z) = z**2 - z**2 + z**3 + 3*z**2 + 2. Let n be x(-3). Factor 2*a - 5*a**2 - n*a**3 + a**2 - 4*a.
-2*a*(a + 1)**2
Let r(j) be the first derivative of -3/4*j**4 - 1/6*j**6 + 3/5*j**5 + 1/3*j**3 + 0*j**2 - 3 + 0*j. Factor r(f).
-f**2*(f - 1)**3
Suppose -4*m = m - j + 2, 0 = 4*j - 8. Factor -3*x**3 + x**3 + m*x + x - x**3 - 2*x**2.
-x*(x + 1)*(3*x - 1)
Let r be 12/3 - (3 + -3). Suppose 0 = q + q - r. Determine d, given that 1/3*d - 2/3*d**4 + 0 + 2/3*d**q - 1/3*d**5 + 0*d**3 = 0.
-1, 0, 1
Determine d, given that 3*d**2 + 4*d**2 - 4 - 3*d**2 = 0.
-1, 1
Find h such that -8*h**5 - 21*h**4 + 3 - 6*h**2 - 24*h**3 + 59*h + 2*h**5 - 53*h = 0.
-1, 1/2
Let f = 25 + -24. Let o be f - (0 - (0 + -1)). Factor -1/3*y**5 + o*y**2 + 0 + 0*y - 1/3*y**3 + 2/3*y**4.
-y**3*(y - 1)**2/3
Suppose 0 = 2*l + 3 - 7. Let n(v) be the first derivative of 0*v**l + 1 - 1/18*v**6 + 0*v + 1/12*v**4 - 1/9*v**3 + 1/15*v**5. Suppose n(p) = 0. Calculate p.
-1, 0, 1
Let r(y) be the second derivative of 3*y + 0 - 25/78*y**4 + 10/39*y**3 - 1/13*y**2. Factor r(p).
-2*(5*p - 1)**2/13
Let k(c) be the first derivative of -2*c**3/27 + 2*c**2/9 + 2. Factor k(w).
-2*w*(w - 2)/9
Let f(b) be the third derivative of b**11/1663200 - b**10/378000 + b**9/302400 - b**5/30 + 3*b**2. Let g(i) be the third derivative of f(i). Factor g(n).
n**3*(n - 1)**2/5
Let r(s) = 6*s**3 + 16*s**2 - 11*s - 11. Let n(o) = 4*o + 3*o**2 + 3*o**3 - 2 - 2*o**3 - 4*o - 2*o. Let u(j) = 11*n(j) - 2*r(j). Factor u(i).
-i**2*(i - 1)
Let q(j) be the first derivative of j**4/10 - 4*j**3/15 + j**2/5 + 11. Factor q(v).
2*v*(v - 1)**2/5
Let g be 8/(-116) + (-480)/(-232). Let x = 1969/2289 + -1/327. Solve -6/7*d**g - 2/7 + 2/7*d**3 + x*d = 0.
1
Let o(t) be the second derivative of 3*t**5/70 - t**4/42 - 2*t**3/21 + 3*t. Factor o(p).
2*p*(p - 1)*(3*p + 2)/7
Let i(y) be the third derivative of y**9/181440 - y**7/15120 + y**5/30 + 2*y**2. Let b(f) be the third derivative of i(f). Factor b(w).
w*(w - 1)*(w + 1)/3
Let u(w) = 17*w**2 + 5*w. Let z(n) = 3*n + n - 4*n**2 - 5*n. Let l(f) = 6*u(f) + 26*z(f). Factor l(y).
-2*y*(y - 2)
Suppose -2*a - 4*s = -0*a - 20, -2*a + 12 = 2*s. Factor -3*p + 9/2 + 1/2*p**a.
(p - 3)**2/2
Factor 2*f**4 + 16*f**2 - 10*f**3 - 10*f - 5*f + 2*f**2 + 4 + f.
2*(f - 2)*(f - 1)**3
Let t(j) = -3*j. Let r be t(-2). Suppose f + 6*k - r = 3*k, -2*f - 10 = -5*k. Suppose 1/4*n**3 - 1/4*n + 1/2*n**2 - 1/2*n**4 + f = 0. What is n?
-1, 0, 1/2, 1
Let h(q) = -6*q**3 - 42*q**2 - 144*q - 105. Let g(w) = -w**3 - w**2 + 1. Let p(m) = 3*g(m) - h(m). Factor p(c).
3*(c + 1)*(c + 6)**2
Suppose 2 = 2*r - 4. Find x such that -80*x - 9*x**r + 3*x**5 + 80*x - 6*x**2 = 0.
-1, 0, 2
Let z = 12 + -19. Let m(g) = g**2 - 3*g - 2. Let r(x) be the third derivative of x**5/15 - 3*x**4/8 - x**3 + 4*x**2. Let n(v) = z*m(v) + 2*r(v). Factor n(w).
(w + 1)*(w + 2)
Let m(q) = 25*q**2 + 85*q + 95. Let r(g) = 2*g**2 + 7*g + 8. Let n(l) = -3*m(l) + 35*r(l). Find i, given that n(i) = 0.
-1
Let c be 1*-2 - -6*8/18. Let y(n) be the first derivative of 0*n - 2/9*n**3 + c*n**2 - 3. Let y(s) = 0. Calculate s.
0, 2
Let b(c) be the first derivative of -c**6/66 - c**5/55 + 2*c**4/11 + 8*c**3/33 - 8*c**2/11 - 16*c/11 - 31. Let b(q) = 0. Calculate q.
-2, -1, 2
Let a(b) be the third derivative of -7*b**6/480 + 5*b**5/96 - 13*b**4/192 + b**3/24 + 2*b**2. Factor a(x).
-(x - 1)*(2*x - 1)*(7*x - 2)/8
Let k(t) be the third derivative of t**7/1260 + t**6/180 + t**5/60 + t**4/24 + 3*t**2. Let i(s) be the second derivative of k(s). Factor i(l).
2*(l + 1)**2
Let y = -113 - -113. Let 0*v - 3/7*v**3 + y + 0*v**2 = 0. What is v?
0
Let z(x) = -x**3 + x**2. Let r be (-4 + 0)*9/12. Let n = 4 + r. Let f(c) = -2*c**4 - 10*c**3 + 4*c**2. Let h(p) = n*f(p) - 6*z(p). Factor h(a).
-2*a**2*(a + 1)**2
Factor 0 - 1/5*y + 3/5*y**2 + 4/5*y**3.
y*(y + 1)*(4*y - 1)/5
Find s, given that 2*s**2 - 142*s**2 - 46*s + 156*s**4 + 128*s**3 - 82*s - 16 = 0.
-1, -2/3, -2/13, 1
Find f, given that -3*f**3 - 9/2*f**2 - 3/4*f**4 - 3*f - 3/4 = 0.
-1
Let b be (-5)/