ve of 0*t**f + 1/30*t**5 - 1/3*t**3 + 0*t - 2*t**2 + 0. Suppose b(r) = 0. What is r?
-1, 1
Let a be -4*(-2 + 1) - 1. Let o be (-209)/(-57) + 10/(-6). Find r such that -1/4*r**a + 0 - 1/4*r - 1/2*r**o = 0.
-1, 0
Let v(d) be the third derivative of d**8/546 + d**7/273 - d**6/260 - d**5/78 - d**4/156 - 14*d**2. Suppose v(m) = 0. Calculate m.
-1, -1/4, 0, 1
Let q(z) be the first derivative of -z**9/3024 - z**8/1680 + z**7/840 + z**6/360 + z**3/3 - 7. Let v(o) be the third derivative of q(o). Factor v(f).
-f**2*(f - 1)*(f + 1)**2
Let o(p) = 2*p**3 - 10*p**2 - 2*p - 6. Let b(s) = -s**3 + s**2 - s + 1. Suppose 5 = 4*g - 11. Let i(d) = g*b(d) + o(d). What is h in i(h) = 0?
-1
Let m = -42 + 127/3. Determine n so that 1/3 + 2/3*n + m*n**2 = 0.
-1
Determine u so that 2*u**3 - 5*u**3 + 2*u**5 - 4*u**2 - 6*u**5 + 4*u**4 + 7*u**3 = 0.
-1, 0, 1
Let x(r) = r**2 - 5*r + 6. Let y be x(8). Let j be 35/y + (-2)/(-12). Factor -2*m + j + 2/3*m**2.
2*(m - 2)*(m - 1)/3
Let 27*j - 48 - 3*j - 22*j**2 + 19*j**2 = 0. Calculate j.
4
Let h(a) be the third derivative of -a**6/180 - a**5/15 - a**4/3 - 8*a**3/9 - 33*a**2. Let h(j) = 0. What is j?
-2
Let u = -33 + 38. Let d(f) be the second derivative of 1/21*f**3 + 0 - 1/7*f**2 - 1/70*f**u + 1/42*f**4 - f. Solve d(n) = 0.
-1, 1
Let j(d) be the third derivative of -d**11/88704 - d**10/28800 - d**9/40320 + d**5/60 - 2*d**2. Let p(r) be the third derivative of j(r). What is l in p(l) = 0?
-1, -2/5, 0
Let k(w) be the second derivative of w**4/42 + 4*w**3/21 + 4*w**2/7 + 3*w. Factor k(n).
2*(n + 2)**2/7
Suppose 429*g = 422*g. Factor 1/4*o**2 + g + 1/4*o.
o*(o + 1)/4
Let m(a) be the first derivative of -a**4/42 - 2*a**3/21 - a**2/7 - 2*a + 5. Let b(u) be the first derivative of m(u). Factor b(c).
-2*(c + 1)**2/7
Let q(s) be the first derivative of s**7/490 - s**6/280 - s**5/140 + s**4/56 + 3*s**2/2 - 4. Let b(w) be the second derivative of q(w). Factor b(i).
3*i*(i - 1)**2*(i + 1)/7
Solve 1 - 23/2*k**3 + 7/2*k**4 - 13/2*k + 27/2*k**2 = 0.
2/7, 1
Let v be 38/8 - 5/(-20). Factor -j**4 - j - j**4 - j**v + j - j**3.
-j**3*(j + 1)**2
Let x(d) = 22*d**3 + 84*d**2 + 158*d + 96. Let s(r) = -7*r**3 - 28*r**2 - 53*r - 32. Let n(u) = 10*s(u) + 3*x(u). Factor n(p).
-4*(p + 1)*(p + 2)*(p + 4)
Determine a so that -9*a**4 - 12*a**2 + 83*a**4 - 12*a**3 + 31*a**4 = 0.
-2/7, 0, 2/5
Suppose 2*c - 4*p = p - 19, -c + 13 = 2*p. Let j = 12 + -8. What is s in 3*s + s - j*s**c - 3*s**4 + s**4 + 2 = 0?
-1, 1
Factor 5*n**4 - 37 + 20*n + 40*n**2 + 37 + 25*n**3.
5*n*(n + 1)*(n + 2)**2
Let j(i) be the first derivative of i**5/10 + i**4/18 - 5*i**2/2 - 3. Let a(y) be the second derivative of j(y). Factor a(d).
2*d*(9*d + 2)/3
Let g(f) = -f**3 + 6*f**2 + 3. Let l be g(6). Suppose s = -l*u - 10, 5*s + 4 = s - 3*u. Factor -2/7*o**s + 0*o - 2/7*o**3 + 0.
-2*o**2*(o + 1)/7
Let d be 6*4/(-32)*-4. Let v(m) be the third derivative of 1/96*m**6 - 2*m**2 + 0 + 0*m + 7/240*m**5 + 1/48*m**4 + 0*m**d. Factor v(w).
w*(w + 1)*(5*w + 2)/4
Suppose -5*k = 3*r + 13, -3*k + 5*k + 3 = r. Let h(w) = -w. Let l(j) = j**2 + 2. Let t(q) = k*l(q) - 6*h(q). Factor t(s).
-2*(s - 2)*(s - 1)
Let c(z) be the third derivative of -7*z**5/60 + z**4/4 - 5*z**3/6 + z**2. Let f(t) = 20*t**2 - 17*t + 14. Let a(q) = -17*c(q) - 6*f(q). What is j in a(j) = 0?
-1, 1
Let m(t) be the second derivative of t**4/6 - 11*t**3/9 + 2*t**2 + 29*t. Factor m(d).
2*(d - 3)*(3*d - 2)/3
Let f(w) be the first derivative of 7*w**6/120 + w**5/40 + 4*w + 5. Let a(n) be the first derivative of f(n). Solve a(o) = 0.
-2/7, 0
Let h = 30 + -18. Let c be 1 - -1*(-4)/h. Solve -1/3*a - a**2 + c = 0 for a.
-1, 2/3
Let l(d) be the third derivative of 1/945*d**7 + 0*d**4 + 0*d**3 - 1/540*d**6 + 1/1512*d**8 - 1/270*d**5 - 2*d**2 + 0 + 0*d. Determine b, given that l(b) = 0.
-1, 0, 1
Let c(i) = 2*i**3 - 2*i**2 + 2*i + 2. Let g be c(2). Suppose 5*n - 6 = g. Factor 0*o + 14/11*o**5 + 0*o**3 + 0 + 0*o**2 - 4/11*o**n.
2*o**4*(7*o - 2)/11
Let c(y) be the first derivative of y**6/2 + 3*y**5/5 - 3*y**4/4 - y**3 - 3. Solve c(g) = 0.
-1, 0, 1
Let j(h) be the third derivative of -h**8/504 - 2*h**7/315 - h**6/144 - h**5/360 - 6*h**2. Find v, given that j(v) = 0.
-1, -1/2, 0
Let h = 260/3 + -2065/24. What is t in 1/2*t - 1/8*t**4 + 0 - t**2 + h*t**3 = 0?
0, 1, 2
Let c(u) be the second derivative of -u**7/4620 + u**6/990 + u**5/220 - 2*u**3/3 - 9*u. Let j(y) be the second derivative of c(y). Factor j(o).
-2*o*(o - 3)*(o + 1)/11
Let i(r) = r + 7. Let a be i(-7). Suppose -3*c + 0*j + 2*j = 0, c - 4*j = a. Factor -4/3*z**3 + c + 0*z - 2/3*z**2 - 2/3*z**4.
-2*z**2*(z + 1)**2/3
Let y = 44 + -70. Let g be ((-1)/(-2))/(y/(-8)). Determine i so that -g*i**2 + 2/13 + 0*i = 0.
-1, 1
Let h(o) be the first derivative of -9/4*o**4 + 0*o**2 + 11 - 6/5*o**5 - o**3 + 0*o. Determine y, given that h(y) = 0.
-1, -1/2, 0
Let y(h) be the first derivative of 0*h - 1/10*h**4 + 0*h**2 - 3 - 2/15*h**3. Let y(z) = 0. Calculate z.
-1, 0
Let d(z) be the first derivative of -z**7/4200 + z**6/1800 + z**5/120 + z**4/40 + 7*z**3/3 - 2. Let c(r) be the third derivative of d(r). Factor c(n).
-(n - 3)*(n + 1)**2/5
Let c be (2 + 1 - 7) + 8 + -2. Factor -3/2*b**c - 3/2*b + 3.
-3*(b - 1)*(b + 2)/2
Let d(b) be the second derivative of -b**9/5040 - b**8/1120 - b**4/6 - 2*b. Let m(o) be the third derivative of d(o). Find z, given that m(z) = 0.
-2, 0
Let u(y) be the second derivative of 2*y + 0 - 3/2*y**3 + 1/4*y**4 - 6*y**2. Factor u(s).
3*(s - 4)*(s + 1)
Factor -24/7*s + 16/7 + 12/7*s**2 - 2/7*s**3.
-2*(s - 2)**3/7
Factor 0 + 1/3*i + 0*i**3 - 1/2*i**2 + 1/6*i**4.
i*(i - 1)**2*(i + 2)/6
Let p = -5 + 7. Solve -x**5 - x**4 + 3*x**5 + p*x**2 - 2*x**3 - x**4 = 0 for x.
-1, 0, 1
Let o(j) be the third derivative of j**8/90 - 13*j**7/1575 - 41*j**6/900 + 11*j**5/450 + 13*j**4/180 + 2*j**3/45 + 2*j**2. What is g in o(g) = 0?
-1, -2/7, -1/4, 1
Solve 2/3*l**2 + 16/3*l - 6 = 0 for l.
-9, 1
Factor -2/11*f**4 + 8/11*f**3 - 10/11*f**2 + 4/11*f + 0.
-2*f*(f - 2)*(f - 1)**2/11
Let k be 4/(-10) + (-104)/(-160). Let x(r) be the second derivative of k*r**3 - 1/2*r**2 - r - 1/24*r**4 + 0. Let x(a) = 0. Calculate a.
1, 2
Let w(b) be the second derivative of -b**4/48 - b**3/24 + b**2/4 - 8*b. Factor w(k).
-(k - 1)*(k + 2)/4
Let o = 27 - 22. Let t(u) be the third derivative of -1/90*u**6 + 0*u**o + 0*u**7 + 1/36*u**4 + 1/504*u**8 + 0 + 0*u**3 + 2*u**2 + 0*u. Factor t(m).
2*m*(m - 1)**2*(m + 1)**2/3
Suppose -2 = 3*h - 17. Factor -21*m**2 + 0*m - h*m - m.
-3*m*(7*m + 2)
Let t = -3 + 7. Let f = 4 - t. Suppose -5*d**2 - 6*d + f*d - 4 + 3*d**2 = 0. Calculate d.
-2, -1
Let g = 34 - 34. Let s(d) be the second derivative of -3*d + 0 + 1/10*d**5 - 1/3*d**4 + 1/3*d**3 + g*d**2. Determine a, given that s(a) = 0.
0, 1
Let s be -1*(3/(-12) + 7/(-28)). Suppose 0 - 1/2*k + s*k**2 = 0. What is k?
0, 1
Let s = -73 - -75. What is y in 0 - y**3 + 0*y**s + 0*y + 7/2*y**4 = 0?
0, 2/7
Solve -2 - 2*t**2 - t**2 - 8*t**3 + 5*t**2 - t + 9*t**3 = 0 for t.
-2, -1, 1
Let w(g) = -g**2 + 2*g. Let s be w(2). Let d(r) be the third derivative of 0*r**4 + s - 1/210*r**7 + 2*r**2 + 1/120*r**6 + 0*r + 0*r**3 + 0*r**5. Factor d(p).
-p**3*(p - 1)
Let n be (108/20 + -9)/((-14)/5). Determine a so that n*a**2 - 15/7*a**4 + 3*a - 3*a**3 + 6/7 = 0.
-1, -2/5, 1
Let k(g) be the third derivative of g**8/112 - 3*g**7/70 + g**6/40 + 3*g**5/20 - g**4/4 + g**2. Factor k(t).
3*t*(t - 2)*(t - 1)**2*(t + 1)
Let s(p) be the second derivative of p**6/40 - 3*p**5/80 - 3*p**4/16 + p**3/8 + 3*p**2/4 - 10*p. Solve s(f) = 0 for f.
-1, 1, 2
Suppose 4*s - 7*s = -204. Find c, given that -9*c + s*c**2 + 9*c**2 + 4 - 15*c - 8*c - 49*c**3 = 0.
2/7, 1
Let b = -3/104 - -125/728. Let a(d) be the first derivative of 0*d - 2/7*d**3 - b*d**2 - 1 - 2/35*d**5 - 3/14*d**4. Let a(f) = 0. Calculate f.
-1, 0
Let v(i) = -3*i**4 + 3*i**3 + 5*i**2 - i - 2. Let t(y) = -3*y**4 + 3*y**3 + 6*y**2 - 3. Let m(p) = -2*t(p) + 3*v(p). Determine k so that m(k) = 0.
-1, 0, 1
Let z(q) = -q**4 - q**2 - q - 1. Let t(s) = -4 + 6*s - 4*s - 8*s**2 - 6*s**3 + 0*s + s**2 - s**4. Let d(m) = -t(m) + 4*z(m). Find b, given that d(b) = 0.
-1, 0, 1, 2
Let x(j) = -j + 3. Let v be x(0). Suppose 6*s + v = 7*s. Suppose -11*g**2 + 2*g**s + g - g + 7*g**2 = 0. Calculate g.
0, 2
Factor 6*r**3 - 3*r - 3*r**2 - 27 + 27.
