b - 5. Let d be n(-8). Let j be 3/42*(d - -1). Factor j*f - 4/7 + 2/7*f**3 - 8/7*f**2.
2*(f - 2)*(f - 1)**2/7
Determine x, given that 6*x**3 + 4 + 3*x**5 - 9*x**4 + 6*x**2 - 15*x + 3 - 4 + 6*x = 0.
-1, 1
Let v(b) be the first derivative of -1/10*b**5 + 0*b**3 + 0*b**2 - 1/8*b**4 - 3 + 0*b. Find w such that v(w) = 0.
-1, 0
Let i(h) = -h**3 + 8*h**2 - 5*h - 10. Let y be i(7). Suppose 8 + 12 = y*l. Determine s, given that 0*s + 1/3*s**3 + 2/3*s**4 + 0 + 0*s**2 + 1/3*s**l = 0.
-1, 0
Suppose 0 = -0*k - 5*k. Find w such that 4/11*w**2 + k + 0*w**3 + 2/11*w - 2/11*w**5 - 4/11*w**4 = 0.
-1, 0, 1
Solve 5*b + 0*b**2 - 9 - b**2 + 4*b**2 + b = 0 for b.
-3, 1
Let k(x) = -x + 9. Let m be k(4). Determine g so that -72*g**2 - 50*g**5 - 48*g**m - 8*g - 218*g**3 + 0 + 0 - 252*g**4 = 0.
-1, -2/7, 0
Suppose 2*x = m + 4 + 4, -x - 1 = -3*m. Factor k**x + 5*k**4 + 7*k**3 - k**2 + 1 - 4 - 8*k - 3 + 2.
(k - 1)*(k + 1)**2*(k + 2)**2
Let i(f) be the second derivative of -f**7/120 - f**6/720 + f**5/60 - f**4/12 + 3*f. Let k(g) be the third derivative of i(g). Suppose k(q) = 0. What is q?
-1/3, 2/7
Suppose -1 - 2 = -o. Factor o*n - 2 + 8 - n**2 - 2*n**2.
-3*(n - 2)*(n + 1)
Let v(i) = -3*i**2 - 1 - 3*i - i**2 + 5*i + 3*i**2. Let h(z) = z - 1. Let r(y) = 3*h(y) - 3*v(y). Let r(g) = 0. Calculate g.
0, 1
Suppose 0 = 2*j - 6. Determine d, given that -d**j - 2*d - 2*d**4 + d**2 - 5*d**3 - 6*d**2 - d**2 = 0.
-1, 0
Suppose d**3 + 3*d - 2 + 8*d**2 + 6 - 3 - 5*d**2 = 0. Calculate d.
-1
Suppose -6*y + 2*y + 8 = 0. Solve 2*j**3 - 2*j**5 - 16*j + 16*j - 2*j**4 + y*j**2 = 0 for j.
-1, 0, 1
Suppose -4*u - 96 = 3*z - 21, -u - 84 = 3*z. Let y = -19 - z. Find k such that y*k**3 + 13*k**2 + 4 + 5*k**2 + 5*k**2 + 14*k - 5*k**2 + 2*k**4 = 0.
-2, -1
Let f = 6 - -1. Suppose 2*j + 2*t + 5 = f, -5*t = -j + 7. Find s such that j*s - 2*s**2 + 2 - 3 + 1 = 0.
0, 1
Suppose 2*n - 63 = -k, -5*n + 4*n = 5*k - 18. Let u be 26/143 - (-71)/n. Factor 13/3*o**2 - 2/3*o + 23/3*o**4 - u*o**5 - 9*o**3 + 0.
-o*(o - 1)**3*(7*o - 2)/3
Let z = 6 - 7. Let y be 1*3*z/(-9). Factor y*p**4 - 1/3*p**2 + 0 + 0*p**3 + 0*p.
p**2*(p - 1)*(p + 1)/3
Let x = 405 - 2833/7. Factor -x*w + 0 + 1/7*w**2.
w*(w - 2)/7
Suppose -7*u - 2*q = -2*u - 16, 23 = 4*u + 5*q. Find c such that -4*c**2 + 3*c**2 + 4*c**u - 4*c**2 = 0.
0
Suppose w - 2*n = 13, -5*w + 2*n + 40 = 7. Let c = -2 + w. Find i, given that 11*i**2 - 2 + c*i - 14*i**2 + 8 = 0.
-1, 2
Let o(q) be the third derivative of -q**9/1512 + q**8/420 - q**6/90 + q**5/60 + q**3/3 - q**2. Let k(w) be the first derivative of o(w). What is p in k(p) = 0?
-1, 0, 1
Let k(p) be the third derivative of -7*p**6/540 + 23*p**5/270 - 5*p**4/27 + 4*p**3/27 + 3*p**2 - 4*p. Solve k(b) = 0.
2/7, 1, 2
Factor -8/5*f + 2/5*f**2 + 8/5.
2*(f - 2)**2/5
Let g = -9 + 12. Suppose -8*a + g*a = -15. Factor -2/7*r**5 + 0 + 0*r**a + 2/7*r + 4/7*r**4 - 4/7*r**2.
-2*r*(r - 1)**3*(r + 1)/7
Let y = -83 + 85. Let w(t) be the second derivative of 1/40*t**5 - 1/24*t**4 + 0 + 0*t**3 + 0*t**y + 3*t. Factor w(q).
q**2*(q - 1)/2
Factor -10*k**3 + 0*k**4 - 5*k**2 + 0*k**4 - k**4 - 4*k**4.
-5*k**2*(k + 1)**2
Let p(y) be the first derivative of -2*y**3/15 + 6*y**2/5 - 18*y/5 + 9. Determine m so that p(m) = 0.
3
Determine i, given that -3/5*i**2 + 4/5 + 1/5*i**3 + 0*i = 0.
-1, 2
Let l(x) be the third derivative of x**7/420 - x**6/60 + x**5/60 + x**4/12 - x**3/4 + 4*x**2. Let l(a) = 0. What is a?
-1, 1, 3
Suppose -2*k + 6*k - 4*z = 8, -6 = 2*k + 3*z. Let m(j) be the second derivative of k*j**2 + j - 11/48*j**4 - 9/80*j**5 + 0 - 1/12*j**3. Factor m(v).
-v*(v + 1)*(9*v + 2)/4
What is u in 12*u**3 - 15/2*u + 8*u**4 - 23/2*u**2 - 1 = 0?
-2, -1/4, 1
Let u(k) = 2*k + 14. Let w be u(-7). Let d(p) be the second derivative of 3*p + 0*p**4 + 1/10*p**5 + 0 + 0*p**3 + w*p**2 + 2/15*p**6. Factor d(t).
2*t**3*(2*t + 1)
Solve 12*s + 12*s**2 + 12*s**2 - 3*s**3 + 3*s**4 + 7*s**3 + 11*s**3 = 0 for s.
-2, -1, 0
Let m = -2267 - -38526/17. Let w = 177/187 + m. Factor 0*g - w + 2/11*g**2.
2*(g - 1)*(g + 1)/11
Let c = -8 + 5. Let k = 6 + c. Factor k + 3*w + w**2 - 1 + 0*w.
(w + 1)*(w + 2)
Let f = 277 + -553/2. Determine d, given that -1/4*d**2 + f - 1/4*d = 0.
-2, 1
Let j(k) be the first derivative of -k**7/490 - 3*k**6/280 - 3*k**5/140 - k**4/56 + 7*k**3/3 - 7. Let f(v) be the third derivative of j(v). Factor f(u).
-3*(u + 1)**2*(4*u + 1)/7
Let y(x) = 10*x**4 + 5*x**3 - 5*x**2 - 10*x + 5. Let j(a) = -5*a**4 - 2*a**3 + 2*a**2 + 5*a - 3. Let v(k) = -5*j(k) - 3*y(k). Suppose v(q) = 0. Calculate q.
-1, 0, 1
Let n be -7 + 3 + 162/36. Factor 0 - 1/2*u**2 + 0*u + n*u**3.
u**2*(u - 1)/2
What is l in 0*l - 4/7*l**3 + 4/7*l**5 + 8/7*l**2 - 2/7 - 6/7*l**4 = 0?
-1, -1/2, 1
Factor 6/7*l**2 - 39/7*l + 18/7.
3*(l - 6)*(2*l - 1)/7
Let c(l) be the third derivative of 6*l**2 + 0*l**3 + 0*l**7 + 0*l + 1/168*l**8 + 0 - 1/20*l**6 + 0*l**4 + 1/15*l**5. Factor c(b).
2*b**2*(b - 1)**2*(b + 2)
Let t(k) = 17*k**2 - 17*k - 5*k**3 - 3*k**2 + 8 - 8*k**2. Let h(o) = 3*o**3 - 4*o**2 + 11*o - 5. Let b(c) = 8*h(c) + 5*t(c). Let b(f) = 0. What is f?
-3, 0, 1
Let g be (-104)/(-24)*42/(-4). Let s = g - -47. Factor s*q**2 + 0 - q - 1/2*q**3.
-q*(q - 2)*(q - 1)/2
Let m(q) be the second derivative of 1/10*q**3 - 1/20*q**4 + 3*q + 0 + 0*q**2. Factor m(i).
-3*i*(i - 1)/5
Let z(c) = 2*c**2 - 3*c - 9. Let i(g) = 2*g**2 - 4*g - 10. Let o(q) = -5*i(q) + 6*z(q). Solve o(u) = 0 for u.
-2, 1
Let w(x) be the second derivative of 0 + 1/6*x**4 + 2*x**2 - 10*x - x**3. Determine u, given that w(u) = 0.
1, 2
Let t(l) be the third derivative of -l**6/360 + l**5/180 - 16*l**2. Let t(o) = 0. Calculate o.
0, 1
Factor 0*n + 0 + 2/9*n**4 - 2/3*n**5 + 4/9*n**3 + 0*n**2.
-2*n**3*(n - 1)*(3*n + 2)/9
Let n(q) = q**2 + 2. Let b be 18/6 + (-1 - -5). Let a(j) = -3*j**2 - 4. Let u(h) = b*n(h) + 3*a(h). Find v such that u(v) = 0.
-1, 1
Let l = 279/148 - 5/37. Factor -1 + 27/4*m**2 - 13/2*m**3 + l*m**4 - m.
(m - 2)*(m - 1)**2*(7*m + 2)/4
Let f(g) be the third derivative of g**6/120 - g**5/60 - g**4/8 + g**3/3 - 5*g**2. Let p be f(2). Solve p + h**3 - 2/3*h + h**2 + h**5 - 7/3*h**4 = 0.
-2/3, 0, 1
Let v(b) be the third derivative of -1/105*b**5 - 1/84*b**4 - 2*b**2 + 0*b + 1/1176*b**8 + 0 + 0*b**3 + 0*b**6 + 2/735*b**7. Factor v(y).
2*y*(y - 1)*(y + 1)**3/7
Let x(r) = r + 2. Let l be x(3). Suppose -5*g + 2*f = -26, -l*g - f = -10 - 7. Solve 2 - 30*q**3 + 78*q**3 + 32*q**g + 2*q**2 - 12*q + 0 = 0.
-1, 1/4
Let f(n) be the second derivative of -n**4/4 - n**3/2 + 3*n**2 + 16*n. Factor f(t).
-3*(t - 1)*(t + 2)
Find u such that -8/13*u + 0 + 2/13*u**2 - 2/13*u**4 + 8/13*u**3 = 0.
-1, 0, 1, 4
Suppose 2*p + 4*x - 2 = 0, -p + 40 = 3*p - x. Let m be ((-2)/(-3))/(24/p). Find a, given that 0 - 5/4*a**3 + 1/2*a - m*a**4 + 1/4*a**2 + 3/4*a**5 = 0.
-1, -2/3, 0, 1
Let t(a) be the third derivative of a**6/200 + 7*a**5/100 + 3*a**4/8 + 9*a**3/10 - 13*a**2. Factor t(j).
3*(j + 1)*(j + 3)**2/5
Let b(h) be the second derivative of h**4/4 + 3*h**3/2 + 3*h**2/2 + 2*h. Let o(u) = 2*u**2 + 8*u + 2. Let l(g) = 4*b(g) - 5*o(g). What is f in l(f) = 0?
1
Let h(p) be the first derivative of 2*p**4 - 19*p**3/3 + 25*p**2/2 - 5*p + 1. Let c(a) = -7*a**3 + 20*a**2 - 26*a + 6. Let n(m) = -3*c(m) - 2*h(m). Factor n(t).
(t - 2)**2*(5*t - 2)
Suppose -6*m = -12*m. Let l(h) be the third derivative of 1/1344*h**8 + 1/96*h**4 + 0*h - 4*h**2 + 0*h**5 + m*h**3 + 0*h**7 + 0 - 1/240*h**6. Factor l(a).
a*(a - 1)**2*(a + 1)**2/4
Let y be (-6)/(-108) - (-1)/6. Let a(h) be the first derivative of 2/9*h**2 - 1/9*h**4 + 2 + 2/45*h**5 - y*h + 0*h**3. Let a(i) = 0. What is i?
-1, 1
Let a(g) = 16*g**4 - 18*g**3 + 2*g**2. Let t(m) = -5*m**4 + 6*m**3 - m**2. Let s(y) = -3*a(y) - 10*t(y). Determine d so that s(d) = 0.
0, 1, 2
Let j be (6/(0 - 3))/(-9). Let u = 5/18 + j. Let 0*h - 1/2*h**3 + 0 - u*h**2 = 0. Calculate h.
-1, 0
Factor -4 - 4*c**2 + 11 - 7.
-4*c**2
Suppose 2*p**4 - 2*p**2 + 0 - 4/7*p - 6/7*p**3 + 10/7*p**5 = 0. What is p?
-1, -2/5, 0, 1
Let t(c) = -4*c**3 + 7*c**2 - 11*c + 5. Let k = 7 + -4. Let w(x) = x**2 + x - 1. Let h(y) = k*w(y) + t(y). Factor h(n).
-2*(n - 1)**2*(2*n - 1)
Factor -5*a**2 + 113 - 113 - 5*a**3.
-5*a**2*(a + 1)
Let v(w) = w - 4. Let z(r) = -r**3 - 4*r**2 - r + 3. Let b be z(-4). Let k be v(b). Factor -3*y**4 - 36*y**2 + 5*y - 16 + 12*y**3 + 35