) = 0.
28
Suppose -d + 80 = -q - q, 55 = d + 3*q. Find p, given that -8*p + 265*p**4 + 68*p**2 - 45*p**4 - 14*p**5 - d*p**5 - 196*p**3 = 0.
0, 2/7, 1/3, 1
Let t(w) be the first derivative of 7*w**6/50 - 39*w**5/50 + w**4 + 4*w**3/5 + 18*w - 17. Let y(d) be the first derivative of t(d). Find x, given that y(x) = 0.
-2/7, 0, 2
Let q(l) be the second derivative of 7*l**5/20 - 29*l**4/6 + 50*l**3/3 - 12*l**2 - 14*l + 2. Factor q(z).
(z - 6)*(z - 2)*(7*z - 2)
Suppose 0 = p + 3, 0 = n - 2*n + p + 7. Let -5*d**2 + n*d - d + d - 5*d**3 + 6*d = 0. Calculate d.
-2, 0, 1
Suppose 8/9 + 2*b - 16/9*b**3 - 4/3*b**4 - 2/9*b**5 + 4/9*b**2 = 0. Calculate b.
-4, -1, 1
Let w(a) be the third derivative of a**7/315 + a**6/90 - 2*a**5/45 - 2*a**4/9 + 62*a**2. Factor w(h).
2*h*(h - 2)*(h + 2)**2/3
Let p(u) = -14*u + 15. Suppose -4*c = -19*c - 15. Let x(y) = -y**2 + y - 1. Let j(v) = c*x(v) - p(v). Factor j(d).
(d - 1)*(d + 14)
Suppose h - 4*d - 12 = 11, 4*d = -3*h + 5. Let w = h + -6. Determine a so that -3*a**3 + w + 4 - 3*a**4 - 5 = 0.
-1, 0
Factor -1/5*x**2 - 6561/5 - 162/5*x.
-(x + 81)**2/5
Let o = 13/157 + 839/3140. Let f(c) be the second derivative of 0*c**2 - 27/100*c**5 - c + 0 + 1/5*c**3 + o*c**4. Solve f(u) = 0 for u.
-2/9, 0, 1
Let k(a) = 6*a**4 + 6*a**3 - a**2 + 2*a - 3. Let n(j) = 5*j**4 + 5*j**3 - j**2 + 3*j - 4. Let z = 11 + -14. Let p(l) = z*n(l) + 4*k(l). Factor p(s).
s*(s + 1)*(3*s - 1)*(3*s + 1)
Factor -2/5*b**5 - 2*b**4 + 96/5*b**2 + 16/5*b**3 + 0*b + 0.
-2*b**2*(b - 3)*(b + 4)**2/5
Let i(s) = -3*s - 1. Let f be i(-1). Suppose 0 = -f*p + 6*p. Factor c**3 - 3*c**2 + c**4 - c - 5 + 0*c**3 + p + 7.
(c - 1)**2*(c + 1)*(c + 2)
Let q(j) be the second derivative of 35*j**4/4 - j**3 + 43*j. Let q(p) = 0. Calculate p.
0, 2/35
Let k(q) = q**2 + q - 3. Let r be k(2). Factor 6*s**r + s**5 + 5*s**4 + 0*s**5 - 77*s**2 - 3 + 75*s**2 - 7*s.
(s - 1)*(s + 1)**3*(s + 3)
Suppose 0 = 2*y - 5*n - 11, -y + 4*n = n - 6. Let 106*d**y + 5*d**4 - 106*d**3 = 0. What is d?
0
Let s(b) be the third derivative of -361*b**7/630 + 19*b**6/45 - 4*b**5/45 - 15*b**2 + 13*b. Factor s(m).
-m**2*(19*m - 4)**2/3
Let 32*p**2 + 3*p**4 - 33*p**5 - 30*p**5 + 40*p**3 + p**4 + 59*p**5 = 0. What is p?
-2, -1, 0, 4
Let y(q) = -23*q**4 - 183*q**3 - 224*q**2 - 60*q. Let b(i) = 68*i**4 + 548*i**3 + 674*i**2 + 180*i. Let c(z) = 2*b(z) + 7*y(z). Factor c(j).
-5*j*(j + 1)*(j + 6)*(5*j + 2)
Suppose 7*s = 2*s. Let i(o) = -o**3 + 42*o**2 - 50*o + 371. Let g be i(41). Suppose 3/7*a**3 - 12/7*a**g + s + 9/7*a = 0. Calculate a.
0, 1, 3
Suppose -899*i - 8 = -900*i + 4*a, -13 = -2*i + 5*a. Suppose 4/3*l + 0*l**2 - 2/3 + 2/3*l**i - 4/3*l**3 = 0. Calculate l.
-1, 1
Let b(a) = 405*a**5 + 3060*a**4 - 19240*a**3 + 27520*a**2 - 9524*a + 956. Let h(v) = -v - 1. Let y(i) = b(i) - 4*h(i). Solve y(k) = 0.
-12, 2/9, 2
Let q(j) be the second derivative of j**4/48 - 43*j**3/6 + 1849*j**2/2 + 661*j. Solve q(l) = 0.
86
Let z(r) = -8*r**2 + 17*r. Suppose -3*p + 2*p - 6 = 0. Let o(k) = 8*k**2 - 18*k. Let y(t) = p*z(t) - 5*o(t). Factor y(v).
4*v*(2*v - 3)
Let r(k) be the third derivative of -5*k**8/2016 + 5*k**7/84 - 25*k**6/72 + 35*k**5/36 - 25*k**4/16 + 55*k**3/36 + 317*k**2. Factor r(t).
-5*(t - 11)*(t - 1)**4/6
Let g(j) be the third derivative of -1/18*j**3 + 0*j + 0 + 1/20*j**5 + 1/9*j**4 + 3*j**2. Factor g(k).
(k + 1)*(9*k - 1)/3
Let i(j) = 3*j**4 - 6*j**3 - 15*j**2 + 3. Let f(s) = -6*s**4 + 12*s**3 + 32*s**2 - 7. Let y(g) = -3*f(g) - 7*i(g). Determine u, given that y(u) = 0.
-1, 0, 3
Let j(g) be the third derivative of -13*g**2 + 1/240*g**5 + 0*g + 1/24*g**4 + 1/6*g**3 + 0. Factor j(w).
(w + 2)**2/4
Let q(f) be the third derivative of -f**5/18 + f**4/3 - 4*f**3/9 - 227*f**2. Factor q(d).
-2*(d - 2)*(5*d - 2)/3
Let y be 161/207 + (-2)/(-9). Let v be (y + -1)/(4 - 8). Factor v + 0*l + 3/7*l**2 + 3/7*l**4 - 6/7*l**3.
3*l**2*(l - 1)**2/7
Let y(a) = a**2 - 34*a + 66. Let i be y(2). Let -4 + 2/3*c**i - 2/3*c = 0. Calculate c.
-2, 3
Determine c so that 2028/5 + 156/5*c + 3/5*c**2 = 0.
-26
Suppose 0 = -12*v + 58*v - 41 - 189. Let 10/7*x**v - 8/7 - 62/7*x**2 - 40/7*x - 26/7*x**3 + 2*x**4 = 0. Calculate x.
-1, -2/5, 2
Suppose -11*b = 22*b. Let v(i) be the first derivative of 0*i**3 + 1/12*i**6 + 0*i**2 + 5 + 0*i + b*i**4 + 1/10*i**5. What is n in v(n) = 0?
-1, 0
Let -16*f**2 + f**2 + 300*f - 66*f**2 - 152 + 10*f**2 - 4*f**3 - 73*f**2 = 0. Calculate f.
-38, 1
Factor -2/3*g**3 + 0 + 0*g**2 + 0*g.
-2*g**3/3
Suppose 0 = 3*q - 0 - 6. Find t such that -3 + 3 - 53*t**2 + 8*t + 57*t**q - 4*t**3 = 0.
-1, 0, 2
Let b be (2 - -1) + (-12)/3. Let p be 253/22 + b/(-2). Determine l so that 7*l + p*l**2 + l + 6 + 7*l + 3*l**3 = 0.
-2, -1
Let s(i) = -i**3 - 12*i**2 + 15*i + 7. Let v be s(-13). Let d = v - -22. Let 12*k - 24*k - 7*k**2 + k**2 + d*k**3 + 24 = 0. What is k?
-2, 2
What is g in g**2 + 12642 - 12642 = 0?
0
Factor -4*n**3 + 84886*n**2 - n**3 - 84876*n**2.
-5*n**2*(n - 2)
Let t(d) = -7*d - 42. Let j be t(-6). Let q(i) be the third derivative of 1/18*i**4 + 0 - 2*i**2 + 1/9*i**5 + 5/72*i**6 + 0*i**3 + j*i. Factor q(g).
g*(5*g + 2)**2/3
Factor 765*p**2 - 3*p**3 - 65025*p + 2219544 - 483982 + 106813.
-3*(p - 85)**3
Let c(p) be the third derivative of 9*p**6/40 - 3*p**5/10 - 11*p**4/32 - p**3/8 - 91*p**2. Find r, given that c(r) = 0.
-1/6, 1
Factor 0 + 55/2*y**4 + 0*y + 15*y**2 + 175/2*y**3.
5*y**2*(y + 3)*(11*y + 2)/2
Let q(u) = 6 + 4 + u - 2*u - 8. Let t(w) = 3*w**2 + 21*w. Let p(x) = 6*q(x) + t(x). Suppose p(j) = 0. Calculate j.
-4, -1
Suppose -3*l + 5 + 7 = 0. Suppose -l*p = -2*q + 5*q + 4, 3*q = 5*p - 22. Factor -p*h**4 + 5*h**4 - 3*h**2 - 8*h**3 + 3*h + 5*h**3.
3*h*(h - 1)**2*(h + 1)
Let r(l) be the third derivative of 0 - 1/20*l**5 + 0*l**3 + 5/8*l**4 + 0*l + l**2. Find g, given that r(g) = 0.
0, 5
Let p be 66/42 - 9/(-63). Factor 26/7*x**3 + 8/7*x + 0 + 2/7*x**5 + 24/7*x**2 + p*x**4.
2*x*(x + 1)**2*(x + 2)**2/7
Let q be 4/(-36) - 110/(-450). Let y(i) be the second derivative of 1/3*i**4 + 0*i**5 - 1/3*i**3 - q*i**6 + 1/21*i**7 + 0*i**2 + 0 - 4*i. Factor y(f).
2*f*(f - 1)**3*(f + 1)
Let x be 4/6*(1 - -2). Let -k**2 - k**x - 5*k + 6*k - 6*k**3 - 3*k**2 = 0. Calculate k.
-1, 0, 1/6
Let h(q) = -q**2 - 2. Let i(l) = -2*l**3 - 43*l**2 + 2*l + 34. Let y(n) = -6*h(n) + 2*i(n). Let y(o) = 0. Calculate o.
-20, -1, 1
Factor 2793871 - 1161*p**2 - 3832*p**3 - 149769*p - 9233938 + 3829*p**3.
-3*(p + 129)**3
Let y(k) be the third derivative of 27*k**8/280 + 411*k**7/175 + 3173*k**6/150 + 383*k**5/5 + 155*k**4/4 + 25*k**3/3 + 104*k**2. Factor y(z).
2*(z + 5)**3*(9*z + 1)**2/5
Suppose q = 9 - 13. Let p be 7/(-4)*q*1. Suppose 5*m**4 + 4*m**2 - 9*m**2 + 3*m - p*m**3 + m - 3*m**2 = 0. What is m?
-1, 0, 2/5, 2
Let t(h) = -h**3 + 9*h**2 - 8*h + 4. Let r be t(8). Suppose -r*j + 16 = -2*j. Suppose -2*v + 2*v**3 - 2*v**4 + 0*v**4 + j*v**2 - 6*v**2 + 0*v**3 = 0. What is v?
-1, 0, 1
Let j(q) be the third derivative of q**8/6720 + q**7/420 + q**6/60 + 7*q**5/60 + 2*q**2. Let w(l) be the third derivative of j(l). Find r such that w(r) = 0.
-2
Factor -1/9*m**3 - 143/9*m - 23/9*m**2 - 121/9.
-(m + 1)*(m + 11)**2/9
Let l(z) be the second derivative of 1/50*z**6 - 24*z - 3/20*z**4 - 1/5*z**3 + 0*z**2 + 0*z**5 + 0. Factor l(p).
3*p*(p - 2)*(p + 1)**2/5
Let j = 129201/7 - 18443. Find q, given that -40/7*q - 4/7*q**2 - j = 0.
-5
Let z(b) be the third derivative of -b**7/140 - b**6/10 - 3*b**5/8 + b**4/2 + 4*b**3 - 49*b**2 + 2. Solve z(u) = 0.
-4, -1, 1
Let u(a) be the second derivative of -a**10/10080 + 3*a**8/2240 + a**7/420 - 7*a**4/6 + a. Let r(s) be the third derivative of u(s). Solve r(f) = 0.
-1, 0, 2
Let r(x) be the first derivative of -x**6/3 - 2*x**5/5 + 6*x**4 + 56*x**3/3 + 16*x**2 + 24. Find i such that r(i) = 0.
-2, -1, 0, 4
Let x(y) be the first derivative of y**4/8 + 13*y**3/6 - 7*y**2/2 + 4. Determine r, given that x(r) = 0.
-14, 0, 1
Let l(g) be the first derivative of -3*g**5/5 - 9*g**4 - 36*g**3 + 13. Find w, given that l(w) = 0.
-6, 0
Let n be 97*(-1 - 0 - -2). Let h = n - 481/5. Factor 0 + 2/5*z**2 + h*z.
2*z*(z + 2)/5
Let j(v) be the third derivative of v**6/24 - 5*v**5/6 + 5*v**4 - 191*v**2. Let j(m) = 0. Calculate m.
0, 4, 6
Let z(x) be the second derivative of x**4/24 - 5*x**3/6 - 11*x**2/4 - 84*x. Determine u, given that z(u) = 0.
-1, 11
Le