). Find v such that c(v) = 0.
5
Factor 0 + 0*t - 2/7*t**3 + 2/7*t**4 - 2/7*t**2 + 2/7*t**5.
2*t**2*(t - 1)*(t + 1)**2/7
Suppose -2*z + 4 = -z. Determine w, given that -5*w**2 - 4 + 0*w**z - w**4 + 5*w - 20*w**3 + 20*w**2 + 6*w**5 - w = 0.
-2, -1/2, 2/3, 1
Let h be 45/30*8/14. Let 0 - 8/7*a - h*a**3 + 16/7*a**2 = 0. What is a?
0, 2/3, 2
Solve 0 + 2/17*w**2 + 0*w - 6/17*w**3 - 2/17*w**5 + 6/17*w**4 = 0 for w.
0, 1
Let s(j) be the third derivative of -j**6/1260 + j**5/210 - j**4/84 + 5*j**3/6 + 5*j**2. Let w(q) be the first derivative of s(q). Suppose w(r) = 0. What is r?
1
Let r(z) be the third derivative of -z**6/300 - z**5/75 + z**4/60 + 2*z**3/15 - 6*z**2. Suppose r(f) = 0. Calculate f.
-2, -1, 1
Factor 30*i**2 + 14*i**3 + 12*i**4 - 10*i**4 + 2*i + 16*i.
2*i*(i + 1)*(i + 3)**2
Let n(s) = s**3 - s**2 + 1. Let r(y) = -12*y**3 + 8*y**2 - 2*y - 11. Let x(a) = 22*n(a) + 2*r(a). Factor x(v).
-2*v*(v + 1)*(v + 2)
Suppose -3*a + 4*z + 16 = -z, 8 = -4*z. Let r = 1 + 2. Factor -4*l + 7*l**2 - 4*l**a - l**2 + 14*l**r + 8*l**2.
2*l*(l + 1)*(7*l - 2)
Let u be (-189)/(-28) - ((-14)/(-2) + -2). Factor u*a**3 - 1/2*a**2 + 0*a + 0.
a**2*(7*a - 2)/4
Let t(c) = -21*c**3 + 9*c - 12. Let z(v) = v**3 + 1. Let y(o) = -o + 7. Let b be y(6). Let n(l) = b*t(l) + 18*z(l). Factor n(w).
-3*(w - 2)*(w + 1)**2
Let b(m) = 4*m - 7. Let d be b(-4). Let j = -153/7 - d. Solve 18/7*a**3 + 6*a**2 - j + 8/7*a = 0.
-2, -2/3, 1/3
Let n(m) be the second derivative of m**7/280 - m**6/360 + m**4/4 - 9*m. Let p(j) be the third derivative of n(j). Factor p(g).
g*(9*g - 2)
Factor -12*f + 38 - 7*f**2 + 9*f**2 - 8*f + 12.
2*(f - 5)**2
Let y = -241 + 243. Find a such that -2/3*a**y + 0 + 0*a = 0.
0
Let r(s) = s**4 + s**2 - s + 1. Let i(q) = 6*q**4 - 4*q**3 + 2*q**2 + 9*q - 3. Let z(k) = i(k) - 5*r(k). Factor z(v).
(v - 4)*(v - 1)**2*(v + 2)
Let w(l) be the first derivative of 5*l**4 + 16*l**3 + 18*l**2 + 8*l + 9. Factor w(f).
4*(f + 1)**2*(5*f + 2)
Let i(l) be the second derivative of 3*l**5/25 + l**4/6 - 8*l**3/15 - 3*l**2/5 - 9*l. Let i(d) = 0. What is d?
-3/2, -1/3, 1
Let k(w) = 2*w - 1. Let g be k(-1). Let p be 4 + 0 + g + 1. Find r, given that 0*r**p + 4*r**2 - 3*r**2 = 0.
0
Let m be -1 + 3 - (-30)/(-5). Let l be (m/5)/(12/(-30)). Factor -2*g - 4*g**l + 4*g + 1 + 5*g**2.
(g + 1)**2
Let h(t) be the first derivative of -2*t**3 + 6/5*t**5 - 4 - 1/2*t**6 + 3/2*t**2 + 0*t**4 + 0*t. Find k such that h(k) = 0.
-1, 0, 1
Suppose -38 + 48*a + 4*a**2 - 7*a**2 - 7 = 0. Calculate a.
1, 15
Let b = -1 + 4. Solve -v**2 - 2*v**3 - 4*v + v**3 + 3*v + b*v**2 = 0 for v.
0, 1
Let v(g) = -g**3 - 6*g. Let r(n) = 7*n**3 + 37*n. Let o(j) = 6*r(j) + 39*v(j). Factor o(w).
3*w*(w - 2)*(w + 2)
Let r(b) be the third derivative of -b**5/150 + b**4/30 + b**3/5 - 8*b**2. Factor r(p).
-2*(p - 3)*(p + 1)/5
Let i be 560/12 - (-4)/(-6). Let y = i + -44. Factor 1 - 1/2*c**y - 1/2*c.
-(c - 1)*(c + 2)/2
Let o(b) be the third derivative of b**6/120 + b**5/30 - b**4/24 - b**3/3 + 10*b**2. What is h in o(h) = 0?
-2, -1, 1
Let t(s) be the first derivative of 2*s**3/21 - 3*s**2/7 - 4. Factor t(v).
2*v*(v - 3)/7
Let j(q) = -q**3. Let g = 5 + -2. Let i be ((-6)/8)/(g/(-24)). Let u(z) = 2*z**4 - 4*z**3 - 2*z**2 - 2*z. Let x(a) = i*j(a) - u(a). Factor x(c).
-2*c*(c - 1)*(c + 1)**2
Let q be (-72)/(-56) + (-2)/7. Let f be 228/(-15)*(-6 + q). Solve -112*n**4 - 250*n**5 + f*n**2 + 17 - 88*n**4 - 88*n + 230*n**3 - 1 = 0 for n.
-1, 2/5
Let n(g) = 8*g**4 - 20*g**3 + 16*g - 4. Let u(l) = -9*l**4 + 21*l**3 - l**2 - 16*l + 5. Let o(i) = -5*n(i) - 4*u(i). Factor o(t).
-4*t*(t - 4)*(t - 1)*(t + 1)
Suppose 16/7 - 4/7*p**3 - 32/7*p + 20/7*p**2 = 0. What is p?
1, 2
Let q(w) = 3*w**2 + 10*w - 15. Let f(c) = 80*c**2 + 270*c - 405. Let i(n) = -2*f(n) + 55*q(n). Factor i(b).
5*(b - 1)*(b + 3)
Let q be 36*2/4*1. Let a be 10/3 - (-12)/q. Factor 4*f**4 + 0*f**2 - 4*f**4 + f**2 - f**a + f**3 - f**5.
-f**2*(f - 1)*(f + 1)**2
Let f(t) be the third derivative of t**6/480 + t**5/120 + t**4/96 - 14*t**2. Factor f(y).
y*(y + 1)**2/4
Let g(m) be the first derivative of -2*m**3/27 + m**2/3 - 4*m/9 - 5. Determine j, given that g(j) = 0.
1, 2
Solve -4/9*k**2 + 2/9*k**3 + 0 + 0*k = 0.
0, 2
Let s(x) = 8*x**4 + 4*x**3 + 2*x**2 + 3. Let o(g) = 7*g**4 + 5*g**3 + 2*g**2 + 2. Let l(d) = -3*o(d) + 2*s(d). Factor l(c).
-c**2*(c + 1)*(5*c + 2)
Let l(v) be the third derivative of -v**8/2400 - v**7/1260 + v**6/900 + v**4/24 - 2*v**2. Let x(z) be the second derivative of l(z). Factor x(c).
-2*c*(c + 1)*(7*c - 2)/5
Let i(p) = 46*p - 92. Let d be i(2). Solve 0*m + 3/5*m**5 + 0 + d*m**4 - 9/5*m**3 - 6/5*m**2 = 0 for m.
-1, 0, 2
Let z = -377999/300 - -1260. Let s(k) be the third derivative of 0*k + z*k**6 - 2*k**2 + 2/15*k**3 + 0 + 2/75*k**5 + 1/12*k**4. Solve s(v) = 0 for v.
-2, -1
Let g be (-20)/8*(-2)/5. Factor -g + 4*q**2 - 5 - 2*q**2 + 0 + 4*q.
2*(q - 1)*(q + 3)
Let x(d) = -d**3 - d**2. Let o(g) = g**3 - 13*g**2 - g + 9. Let v be o(13). Let s(p) = p**3 + p**2. Let c(a) = v*x(a) - s(a). Let c(j) = 0. What is j?
-1, 0
Suppose y + 3 = -2. Let v be 1/(y/(-2) - 2). Find t, given that -4/5*t - 2/5*t**v - 2/5 = 0.
-1
Determine s, given that 8/3*s**3 - 2/3*s**5 + 4/3 + 0*s**4 - 2*s - 4/3*s**2 = 0.
-2, -1, 1
Suppose 4*k = 12, -3*a = -a - k - 7. Let i = 7 - a. Determine b, given that -b - i*b**5 - b**5 + 2*b**3 + 2*b**5 = 0.
-1, 0, 1
Let t be -71 + 2/6*-3. Let s be (-6)/(t/20) - -3. Let 0*l + 14/3*l**3 - 4/3*l**4 + 4/3*l**2 + 0 - s*l**5 = 0. What is l?
-1, -2/7, 0, 1
Let c be 12/(-54) + 20/9. Let s(d) be the second derivative of -3*d + 1/30*d**5 - 1/9*d**3 + 0 - 1/3*d**c + 1/18*d**4. Find t, given that s(t) = 0.
-1, 1
Let i(n) be the second derivative of 6*n**4/11 - 4*n**3/11 + n**2/11 - 7*n. Factor i(a).
2*(6*a - 1)**2/11
Let o = -5 + 10. Suppose 45*s - 41*s = 16. Solve -2/7*h - 4/7*h**s + 4/7*h**2 + 0*h**3 + 0 + 2/7*h**o = 0 for h.
-1, 0, 1
Let v(k) = -3*k**3 - 11*k**2 + 12*k - 16. Let s(d) = -2*d**3 - 10*d**2 + 13*d - 15. Let o(b) = 4*s(b) - 3*v(b). Find h such that o(h) = 0.
2, 3
Suppose -8 + 1 = -y. Let b = y - 4. Factor -b*z**3 - z + 3*z**2 + 3*z**4 + 0*z**4 - 2*z**4.
z*(z - 1)**3
Let n(o) be the second derivative of -o**5/15 - 7*o**4/9 - 22*o**3/9 - 10*o**2/3 - 15*o. Let n(w) = 0. What is w?
-5, -1
Let a(g) = -g**3 - g**2. Let j(k) be the second derivative of -2*k**5/5 - k**4/3 + k**3/3 - k**2 - 2*k. Let d(z) = 6*a(z) - j(z). Let d(u) = 0. Calculate u.
-1, 1
Suppose 35*i = 37*i. Factor 0*x + 1/3*x**2 + i.
x**2/3
Suppose -6 = -17*y + 15*y. Factor 0 - 1/2*g**2 + 1/2*g**y - 1/2*g + 1/2*g**4.
g*(g - 1)*(g + 1)**2/2
Let t(z) = 3*z**3 - z**2 - 9*z - 5. Let d(a) = a**2 - 1. Let s = 5 - 6. Let l(n) = s*t(n) - d(n). Factor l(y).
-3*(y - 2)*(y + 1)**2
Let v be (-10)/4 - 1 - -4. Factor 1/2*n**2 + n + v.
(n + 1)**2/2
Let i(q) be the second derivative of q**6/2 - 13*q**5/4 + 35*q**4/6 + 10*q**3/3 - 20*q**2 - 14*q. Factor i(f).
5*(f - 2)**2*(f - 1)*(3*f + 2)
Let m(v) = v**3 + 27*v**2 - 27*v + 32. Let u be m(-28). Determine k so that 0*k**u + 2/3*k**3 - 1/3*k - 1/3*k**5 + 0*k**2 + 0 = 0.
-1, 0, 1
Let o(w) be the first derivative of 4*w**5/35 + w**4/7 - 8*w**3/7 - 8*w**2/7 + 32*w/7 - 8. Factor o(f).
4*(f - 2)*(f - 1)*(f + 2)**2/7
Find r such that -68/9*r**2 - 8*r**3 + 16/9 + 0*r - 20/9*r**4 = 0.
-2, -1, 2/5
Let h(g) be the first derivative of 0*g + 7/5*g**5 + 4*g**4 + g**2 + 11/3*g**3 - 4. Factor h(w).
w*(w + 1)**2*(7*w + 2)
Let v = 15 - 12. Let q(n) be the third derivative of 0*n**4 + 0 - 1/24*n**v + 2*n**2 + 1/240*n**5 + 0*n. What is l in q(l) = 0?
-1, 1
Let f be -4*(6/4)/3. Let a be 6/f + 31/9. Factor -a*u + 0 - 2/9*u**2.
-2*u*(u + 2)/9
Let f(h) = h**2 + 12*h + 13. Let c be f(-11). Let j be 1*0/((-2)/1). Factor -2/5*a - 2/5*a**c + j.
-2*a*(a + 1)/5
Factor 7 + 0*g**3 - 2 + 0*g**2 + 5*g - 5*g**3 - 5*g**2.
-5*(g - 1)*(g + 1)**2
Let c be (-8)/(-10) - (-2)/(-5). Let l = 272 - 1358/5. Factor l*s**3 - 2/5*s**4 - c*s + 2/5*s**2 + 0.
-2*s*(s - 1)**2*(s + 1)/5
Let x(k) = 3*k**5 - 18*k**4 + 9*k**3 + 12*k**2 - 12*k - 6. Let p(s) = s**4 + 1. Let z(y) = 6*p(y) + x(y). Factor z(l).
3*l*(l - 2)**2*(l - 1)*(l + 1)
Let h(p) be the first derivative of -5*p**6/6 + 5*p**5 - 10*p**4 + 20*p**3/3 - 13. Solve h(r) = 0.
0, 1, 2
Let d(b) be the first derivative of -b**6/15 + 4*b**5/25 - b**4/10 + 2. What is r in d(r