-1/300*k**5 + 1/1050*k**7 + 0 + 3*k**2 + 0*k**4 + 0*k**3 + 1/1680*k**8 + 0*k - 1/600*k**6. Determine j so that r(j) = 0.
-1, 0, 1
Let l = 16 - 7. Solve l*z**2 - 8 + 0 + 2 + 3*z - 3*z**3 - 3*z**2 = 0.
-1, 1, 2
Let k(g) = -3*g**5 - 5*g**4 + 5*g**3 + 3*g**2 + 2*g + 2. Let x(z) = 12*z**5 + 21*z**4 - 21*z**3 - 12*z**2 - 9*z - 9. Let m(t) = -9*k(t) - 2*x(t). Factor m(u).
3*u**2*(u - 1)*(u + 1)**2
Let g(c) be the third derivative of c**8/168 + c**7/105 - c**6/30 - c**5/15 + c**4/12 + c**3/3 + c**2. Solve g(y) = 0.
-1, 1
Let b be 2/(-11) - 14907/(-25905). Let p = b + 1/157. Suppose -p + 0*j + 2/5*j**2 = 0. Calculate j.
-1, 1
Let l(b) be the first derivative of -4*b**5/35 + b**4/14 + 2*b**3/7 - b**2/7 - 2*b/7 + 5. Determine p, given that l(p) = 0.
-1, -1/2, 1
Let j be 235/100 - (-3)/(-4). Determine z so that 2*z**2 - 16/5*z + j - 2/5*z**3 = 0.
1, 2
Let b(a) be the third derivative of a**5/660 + 5*a**4/132 + 25*a**3/66 - 11*a**2. Factor b(i).
(i + 5)**2/11
Suppose -9/2*w**2 + 3/4*w**3 - 6 + 9*w = 0. Calculate w.
2
Factor 1/2*l**4 + 13/2*l + 2 + 7/2*l**3 + 15/2*l**2.
(l + 1)**3*(l + 4)/2
Let k(b) = 4*b**4 - 7*b**3 + 6*b**2 + 7*b. Let o(v) = -5*v**4 + 8*v**3 - 7*v**2 - 8*v. Let i(n) = -6*k(n) - 5*o(n). Suppose i(q) = 0. Calculate q.
-2, -1, 0, 1
Let j(a) = -a + 11. Let b be j(9). Solve 0*x**4 + 0*x**2 + 2*x + 2*x**4 - b*x**3 - 2*x**2 = 0 for x.
-1, 0, 1
Let d(p) be the third derivative of p**5/12 + 5*p**4/6 + 10*p**3/3 + 3*p**2. Solve d(m) = 0.
-2
Let d(m) = 2*m**2 + 8*m - 10. Let q be d(-5). Suppose 1/4*b**5 + 0 + q*b - 1/4*b**2 + 1/4*b**4 - 1/4*b**3 = 0. Calculate b.
-1, 0, 1
Let i(h) = h**4 - h**3 + h. Suppose 3*w + w + 2*k = 0, 5*w + 4*k - 3 = 0. Let s(t) = 11*t**4 - 13*t**3 + 2*t**2 + 5*t. Let a(b) = w*s(b) + 5*i(b). Factor a(p).
-2*p**2*(p - 1)*(3*p - 1)
Let n(a) be the second derivative of -1/6*a**4 + 0 - 1/3*a**3 + 0*a**2 - a. Let v(z) = z**2 + z. Let r(d) = -n(d) - 4*v(d). Let r(k) = 0. What is k?
-1, 0
Let z(p) be the third derivative of p**5/240 - p**4/32 + p**3/12 + 41*p**2. Factor z(x).
(x - 2)*(x - 1)/4
Let d(f) = 4*f**2 + 3*f. Let y = -5 - -8. Let r(k) = -k + y*k + 3*k**2 + 0*k. Let o(c) = -2*d(c) + 3*r(c). Solve o(t) = 0.
0
Let s(a) be the second derivative of 0*a**3 + 0 + 0*a**2 - 1/24*a**4 - 1/120*a**6 - 2*a - 3/80*a**5. What is m in s(m) = 0?
-2, -1, 0
Let t(o) = -3*o - 2. Let f be -1*(1 - (2 + -3)). Let b be t(f). Suppose 0*i**2 - 1/4*i**3 + 0*i**b + 1/4*i**5 + 0 + 0*i = 0. What is i?
-1, 0, 1
Let p = 5 + -5. Suppose 0 = -2*d + 3*n + n + 46, -5*d - 2*n + 79 = p. What is y in 16*y**2 + 1 - y + 1 - d*y**2 = 0?
-2, 1
Factor -8/7 + 36/7*m + 44/7*m**2.
4*(m + 1)*(11*m - 2)/7
Let f be -2 + 147/54 + 1/6. Suppose 8/9*p**3 - 34/9*p**2 - f + 40/9*p = 0. What is p?
1/4, 2
Let k be (1 - -1)/(1 - -1). Suppose -r + 1 = -k. Factor -12*o**3 - 5*o**4 + 3*o**2 - o**4 - 11*o**r - 4*o**3.
-2*o**2*(o + 2)*(3*o + 2)
Let v(t) be the second derivative of 0 + 0*t**2 + 6*t - 1/15*t**6 + 1/8*t**5 - 1/12*t**4 + 1/84*t**7 + 0*t**3. Let v(c) = 0. Calculate c.
0, 1, 2
Let m(l) be the first derivative of -l**4/6 - 4*l**3/3 - 4*l**2 + 4*l - 6. Let x(k) be the first derivative of m(k). Factor x(b).
-2*(b + 2)**2
Let z = 2/785 + 773/4710. Factor -z*u**2 - 2/3 + 2/3*u.
-(u - 2)**2/6
Let u(m) = -m**5 - m**4 - m**3 - m**2 - m. Let q(k) = -5*k**5 - 3*k**4 - 3*k**3 - 5*k**2 - 6*k. Let v(z) = q(z) - 6*u(z). Factor v(i).
i**2*(i + 1)**3
Let r(l) be the second derivative of -2*l + 0 + 1/21*l**3 + 0*l**2 - 1/21*l**4. Find k, given that r(k) = 0.
0, 1/2
Let c(i) be the third derivative of -i**9/120960 - i**8/40320 + i**5/20 - 3*i**2. Let h(k) be the third derivative of c(k). Factor h(a).
-a**2*(a + 1)/2
Suppose 5*z - 163 + 24 = 4*k, -4*k = -4*z + 140. Let b be k/(-8)*(-2)/(-3). Factor 4*c + c**2 + 2*c**2 - 2*c**2 - 3*c**2 - 2*c**b.
-2*c*(c - 1)*(c + 2)
Let u(g) = 3*g**4 + 6*g**3 + 3*g**2 - 6*g. Let b(f) = 3*f**4 + 6*f**3 + 3*f**2 - 5*f. Let l be 2*(-6)/4 + 8. Let w(d) = l*u(d) - 6*b(d). Solve w(h) = 0.
-1, 0
Suppose 3*w = 2*w + 5*b - 21, -2*w + 18 = 2*b. Factor -l**3 + 2*l**w + 5*l**2 - l**3 - l**4 - 4*l**2.
l**2*(l - 1)**2
Let l(y) = y**2 + 4*y + 1. Let f be (1 + -5)*1/(-2). Suppose 0 - 4 = f*p. Let j(k) = 2*k**2 + 5*k + 2. Let h(v) = p*j(v) + 3*l(v). Factor h(a).
-(a - 1)**2
Factor 3*z - 3/5*z**3 + 3/5*z**2 + 9/5.
-3*(z - 3)*(z + 1)**2/5
Let p = -3 + 3. Let g(d) be the first derivative of -1/9*d**4 + 0*d**3 - 1 + p*d + 0*d**2 + 2/15*d**5. Factor g(r).
2*r**3*(3*r - 2)/9
Let k be 14/49 - 10/(-14). Determine j, given that -11*j**3 - k + 4*j**4 + 7*j - 3*j**2 + 3 + 4*j**3 - 3*j**2 = 0.
-1, -1/4, 1, 2
Let t(y) be the first derivative of -y**3/12 + y**2/8 + y/2 + 33. Solve t(i) = 0.
-1, 2
Let x(l) = 5*l**3 + l**2 + 2*l - 2. Let t be x(1). Let k(g) be the first derivative of 18*g + 2/3*g**3 - 4 + t*g**2. Suppose k(s) = 0. Calculate s.
-3
Let p = -370 + 373. Suppose 0 = -2*w + 4*w - 4. Find j such that -2*j**w - 2*j - 2/3*j**p - 2/3 = 0.
-1
Let u be (-12)/(-16) + 15/(-20). Let o(a) be the third derivative of 4/39*a**4 + 0*a + 4/39*a**3 + a**2 + u + 1/30*a**5 + 1/260*a**6. Factor o(r).
2*(r + 2)**2*(3*r + 1)/13
Suppose 12 = i + 2*i. Let b = i - 1. Let p(d) = -d**2 + 5*d - 3. Let h(w) = -2*w**2 + 6*w - 4. Let v(r) = b*h(r) - 4*p(r). Factor v(t).
-2*t*(t + 1)
Let u(z) be the second derivative of -2*z**7/63 - 4*z**6/45 - z**5/15 + 11*z. Factor u(c).
-4*c**3*(c + 1)**2/3
Let f(y) be the third derivative of -y**6/60 - y**5/15 + y**4/12 + 2*y**3/3 + 13*y**2. Factor f(i).
-2*(i - 1)*(i + 1)*(i + 2)
Let c(g) = -g**2 + 0 + 1 - g**2 + 3*g**2. Let j be c(-1). Factor 2*r**2 - 1 - j + r + r**3 + 3.
r*(r + 1)**2
Let d = 44 - 47. Let c be -1 - (3 + d*2). Suppose 2/3 - 2/3*j**c + 0*j = 0. What is j?
-1, 1
Solve 2/3*o**2 + 28*o + 294 = 0 for o.
-21
Let a = 15 + -11. Factor -2*t**4 + 5*t**3 + 2*t**4 - 3*t**3 - t**a.
-t**3*(t - 2)
Let x(z) be the second derivative of 0 + 1/150*z**5 + 1/60*z**4 - z**2 + z - 2/15*z**3. Let h(o) be the first derivative of x(o). Factor h(t).
2*(t - 1)*(t + 2)/5
Factor 0 + 0*u - 4/5*u**4 - 4/5*u**2 - 8/5*u**3.
-4*u**2*(u + 1)**2/5
Let i(o) be the first derivative of -o**4/2 - 8*o**3/9 + 5*o**2/3 + 4*o/3 - 5. Suppose i(k) = 0. What is k?
-2, -1/3, 1
Let z(m) be the third derivative of m**5/20 - 19*m**4/4 + 361*m**3/2 - m**2 - 1. Factor z(h).
3*(h - 19)**2
Let v(l) be the third derivative of -1/6*l**4 + 4*l**2 + 0*l + 7/30*l**5 - 1/20*l**6 + 0*l**3 + 0. Factor v(z).
-2*z*(z - 2)*(3*z - 1)
Let g = -235 - -471/2. Factor g*o + 1/4*o**2 + 1/4.
(o + 1)**2/4
Let u be -4 + 2 - -4 - (-7)/(-4). Factor 0*a - u + 1/4*a**2.
(a - 1)*(a + 1)/4
Let d(c) = c**5 - c**4 - c**3 + c**2 - c - 1. Let u(m) = -8*m**5 + 8*m**4 + 6*m**3 - 6*m**2 + 12*m + 8. Let l(k) = -10*d(k) - u(k). Let l(t) = 0. What is t?
-1, 1
Factor 0 + 2/9*l**3 - 2/9*l**4 - 2/9*l**5 + 0*l + 2/9*l**2.
-2*l**2*(l - 1)*(l + 1)**2/9
Suppose -2*a - d = a - 17, 2*d - 9 = -a. Let u = a - 3. Factor -6*z - u*z**2 - 3*z + 7*z + 2*z**3 + 2*z**4.
2*z*(z - 1)*(z + 1)**2
Let f = -1394/3 - -466. Factor -2/3 + 2/3*j**5 - f*j**2 + 4/3*j**3 - 2*j + 2*j**4.
2*(j - 1)*(j + 1)**4/3
Let g = -7 - -12. Factor 1 - 7*z**2 - 4*z**3 - g*z**2 + z**3 - 15*z - 7.
-3*(z + 1)**2*(z + 2)
Let s(o) be the first derivative of -o**6/280 - o**5/35 - 5*o**4/56 - o**3/7 + o**2/2 - 2. Let p(d) be the second derivative of s(d). Factor p(t).
-3*(t + 1)**2*(t + 2)/7
Let r(y) be the first derivative of -1/9*y**2 + 0*y - 2/27*y**3 + 4. Let r(k) = 0. What is k?
-1, 0
Let o(r) = -13*r**4 + 11*r**3 + 13*r**2 + 9*r - 5. Let s(y) = -6*y**4 + 5*y**3 + 7*y**2 + 4*y - 2. Let f(q) = -6*o(q) + 15*s(q). Factor f(b).
-3*b*(b - 2)*(b + 1)*(4*b + 1)
Let i(m) = -2*m**4 - 5*m**3 + m**2 + 3*m. Let f(o) = -3*o**4 - 6*o**3 + o**2 + 4*o. Let t = 4 - 0. Let q(y) = t*i(y) - 3*f(y). Factor q(p).
p**2*(p - 1)**2
Let l be 5 - (-7 + 240/42). Let s be -1 - (-32)/14 - 1. Solve -s - 48/7*x**3 - 16/7*x - 18/7*x**4 - l*x**2 = 0.
-1, -1/3
Let m(k) be the third derivative of 13*k**5/60 - k**4/12 - k**3/6 + 2*k**2. Let t be m(-1). Factor 12*f + 4 - f**3 + 4*f**2 + 9*f**3 - 2 + t*f**2.
2*(f + 1)**2*(4*f + 1)
Find v, given that 0 + 1/7*v**3 + 2/7*v - 3/7*v**2 = 0.
0, 1, 2
Let j(b) be the second derivative of -b**6/210 - b**5/70 + b**4/21 + b**3/21 - 3*b**2/14 - 5*b. Solve j(z) = 0.
-3, -1, 1
Let n(d) = d -