 0*u**z + 3*u**2.
u**2*(u - 1)
Let r(a) be the third derivative of a**7/210 + a**6/40 + a**5/20 + a**4/24 + 7*a**2. Find c, given that r(c) = 0.
-1, 0
Let q(a) = a**2 + 7*a - 5. Let j(u) = 4*u**2 + 36*u - 24. Let k(v) = -3*j(v) + 16*q(v). Solve k(w) = 0.
-2, 1
Let l(m) = 4*m - 40. Let r be l(11). Let u(j) be the first derivative of 1/5*j + 0*j**2 + r + 0*j**4 - 2/15*j**3 + 1/25*j**5. Suppose u(z) = 0. What is z?
-1, 1
Let r(f) be the third derivative of 0*f - 2*f**2 + 1/12*f**3 + 1/32*f**4 - 1/480*f**6 + 0 + 0*f**5. Let r(s) = 0. What is s?
-1, 2
Let s(r) be the first derivative of r**9/1008 - r**8/560 - r**7/280 + r**6/120 - r**3 + 1. Let j(b) be the third derivative of s(b). Factor j(a).
3*a**2*(a - 1)**2*(a + 1)
Let y(v) = -v - 1. Let i be y(-4). Find k, given that -1/2*k**5 - k**2 + k**i + 1/2*k**4 - 1/2*k + 1/2 = 0.
-1, 1
Let m(i) be the second derivative of -i**4/3 + 2*i**3 + 8*i**2 - 7*i. What is s in m(s) = 0?
-1, 4
Let y(x) be the third derivative of -1/60*x**4 + 0*x**3 - 1/150*x**7 + 1/300*x**6 + 0 + 7/300*x**5 - 3*x**2 + 0*x. Factor y(v).
-v*(v - 1)*(v + 1)*(7*v - 2)/5
Let s be 4 + -6 + 3/1. Let k be 3 - (s + -2) - 1. Suppose u**2 - 1 - u**k + 0*u + 2*u - u = 0. What is u?
-1, 1
Let y = 2 - 0. Let 2*j**3 - 4*j**y - 6*j - j**3 + 2*j**3 + j**2 = 0. Calculate j.
-1, 0, 2
Let a(m) be the second derivative of 0*m**2 - 2*m + 0 + 1/40*m**5 - 1/24*m**4 - 1/6*m**3. Suppose a(r) = 0. Calculate r.
-1, 0, 2
Let a(f) = -10*f**5 + 22*f**4 - 84*f**3 + 172*f**2 - 170*f + 46. Let p(m) = m**5 - m**3 + m**2 + m + 1. Let g(x) = a(x) + 8*p(x). Let g(s) = 0. What is s?
1, 3
Let y(a) = -a**3 - 6*a**2 - 4*a + 2. Let c(x) = 1. Let d(f) = -c(f) - y(f). Let n be d(-5). Let 1 - n*z**2 + 3*z**2 + 2*z + 0 = 0. Calculate z.
-1
Let u(o) be the third derivative of -o**8/28 - o**7/70 + 3*o**6/5 + 19*o**5/10 + 5*o**4/2 + 3*o**3/2 - 12*o**2. Determine x, given that u(x) = 0.
-1, -1/4, 3
Let x = 5 + -2. Factor -s**2 - 3*s - x + 3 + 5*s - 1.
-(s - 1)**2
Suppose -2*u + 3*u - 3 = 0. Factor q**3 - 6 - 3*q + 2 - q**4 - q + 3*q**2 + q**u.
-(q - 2)**2*(q + 1)**2
Let f = -74/3 + 25. Let a = f - -4/15. Factor a*b + 0 + 3/5*b**5 + 12/5*b**2 + 18/5*b**3 + 12/5*b**4.
3*b*(b + 1)**4/5
Let v be 4/(-6) - 2/6. Let b be (-2)/v - (4 - 4). Factor 0*u + 0*u**b - 2/7*u**3 - 2/7*u**5 + 4/7*u**4 + 0.
-2*u**3*(u - 1)**2/7
Let x(o) be the second derivative of -o**5/160 - o**4/96 + 4*o. Factor x(d).
-d**2*(d + 1)/8
Let f(q) = -q**2 - 1. Let g(a) = 15*a**2 + 20. Let w(j) = -20*f(j) - g(j). Solve w(r) = 0 for r.
0
Let n(d) be the first derivative of -d**6/300 + d**5/75 - d**4/60 + 3*d**2/2 + 3. Let y(b) be the second derivative of n(b). Factor y(u).
-2*u*(u - 1)**2/5
Suppose -56 = -8*u - 20*u. Factor -3/4*n + 1/4*n**u + 1/2.
(n - 2)*(n - 1)/4
Let y(z) = -z**2 + 4*z. Let t be y(2). Suppose t*f + 0 = 8. Factor -2*s**3 - s**f + 0*s**3 + s**3.
-s**2*(s + 1)
Let i(c) = c**3 + 7*c**2 + 8*c - 8. Let j be i(-5). Let r(w) be the second derivative of 0 - 1/12*w**4 + 3*w + 2/3*w**3 - j*w**2. Determine q so that r(q) = 0.
2
Let u(n) = -3*n**3 + 18*n**2 - 9*n. Let z(o) = 6*o**3 - 37*o**2 + 17*o + 1. Suppose 0 = 2*w - 5*w + 18. Let x(r) = w*z(r) + 13*u(r). Factor x(y).
-3*(y - 2)*(y - 1)**2
Let f(a) be the second derivative of -1/10*a**5 + 1/3*a**3 - 3*a + 0*a**2 + 1/15*a**6 + 0 - 1/6*a**4. Suppose f(j) = 0. Calculate j.
-1, 0, 1
Factor 0 + 1/3*j - j**2 + j**3 - 1/3*j**4.
-j*(j - 1)**3/3
Let s be (-6)/(6/(-5)) + 2. Let y be ((-4)/s)/(6/(-7)). Factor 2/3*a**2 + 0 - y*a**3 + 4/3*a.
-2*a*(a - 2)*(a + 1)/3
Let b(l) be the second derivative of -1/4*l**3 + 0 - 1/16*l**4 - 3/8*l**2 + 2*l. Factor b(x).
-3*(x + 1)**2/4
Suppose -y = -6*y. Let a = -159/4 - -40. Solve -a*c + y*c**2 + 1/4*c**3 + 0 = 0 for c.
-1, 0, 1
Determine w so that 684*w + 5*w**5 - 11*w**3 - 40*w**2 + 10*w**4 - 4*w**3 - 704*w = 0.
-2, -1, 0, 2
Factor -8/7 - 2/7*i**2 + 10/7*i.
-2*(i - 4)*(i - 1)/7
Let i(p) be the second derivative of -p**8/6720 - p**7/1260 - p**6/720 + p**4/6 + 2*p. Let w(x) be the third derivative of i(x). Let w(q) = 0. What is q?
-1, 0
Let g = -2 + 10/3. Let -g*y + 53/3*y**3 - 4/3 + 53/3*y**2 - 49/3*y**4 - 49/3*y**5 = 0. What is y?
-1, -2/7, 2/7, 1
Let n(w) be the third derivative of -w**7/6 + 11*w**6/6 - 47*w**5/12 + 25*w**4/12 - 25*w**2. Find f, given that n(f) = 0.
0, 2/7, 1, 5
Suppose 3*g = 4*o - 7 + 19, 5*g + o + 3 = 0. Factor -1/4*j**3 + 0 + 1/4*j + g*j**2.
-j*(j - 1)*(j + 1)/4
Let r(h) be the third derivative of h**7/350 - 6*h**6/25 + 216*h**5/25 - 864*h**4/5 + 10368*h**3/5 - 29*h**2. Factor r(b).
3*(b - 12)**4/5
Let h = 0 + 3. Let n be (h + -1 + -2)*-1. Solve 0*i**2 + n + 2/9*i**3 + 0*i**4 - 2/9*i**5 + 0*i = 0 for i.
-1, 0, 1
Let y(c) = 20*c + 6. Let k be y(3). Let -21 - 46*j - 24*j**2 - 62*j - k*j**2 - 3 - 21*j**3 = 0. Calculate j.
-2, -2/7
Suppose 0*f + 2*f = 5*c - 23, -5*c - 1 = 4*f. Let b be (-8)/28 - 74/(-14). Find t such that -t**2 - b - t + 2*t - t**c + 6 = 0.
-1, 1
Let c(a) be the first derivative of -a**7/560 - a**6/120 - a**5/80 - a**3 + 1. Let u(t) be the third derivative of c(t). Let u(s) = 0. What is s?
-1, 0
Let a(v) be the second derivative of -v**5/5 + v**4/3 + 2*v**3/3 - 2*v**2 - 19*v. Factor a(y).
-4*(y - 1)**2*(y + 1)
Let i = 161 + -1125/7. Solve -2/7*j + 0 - i*j**2 = 0.
-1, 0
Let u(o) be the second derivative of -o**4/2 - 2*o**3/3 - 11*o**2 + o. Let q = -19 + 14. Let r(i) = 2*i**2 + i + 7. Let v(w) = q*u(w) - 16*r(w). Factor v(j).
-2*(j - 1)**2
Let w(m) be the second derivative of m**6/75 - m**5/50 - m**4/30 + m**3/15 + 4*m. Factor w(r).
2*r*(r - 1)**2*(r + 1)/5
Suppose -15 = 5*z, -69 - 116 = 2*q - 5*z. Let t be (-115)/q - (-6)/(-8). Factor 2/5*k**2 + t - 4/5*k.
2*(k - 1)**2/5
Let k(h) = -4*h - 11. Let f be k(-5). Let z be (1/7)/(f/18). Factor 0 + 0*j + z*j**2.
2*j**2/7
Factor -3/2*i**2 - 1/2*i**3 - 3/2*i - 1/2.
-(i + 1)**3/2
Suppose -4*x = -6*x + 8. Let a(r) be the first derivative of 0*r - 1/6*r**x + 2 - 1/3*r**2 - 4/9*r**3. Factor a(d).
-2*d*(d + 1)**2/3
Let h(m) be the third derivative of m**6/720 + m**5/180 - m**4/144 - m**3/18 - 2*m**2. Factor h(a).
(a - 1)*(a + 1)*(a + 2)/6
Let a(j) be the second derivative of -j**5/10 + j**4/2 - j**3 + j**2 - 18*j. Solve a(x) = 0 for x.
1
Let n(r) be the third derivative of 5*r**2 - 1/12*r**6 - 1/4*r**4 - 1/70*r**7 + 0 - 1/6*r**3 - 1/5*r**5 + 0*r. Factor n(d).
-(d + 1)**3*(3*d + 1)
Let c(g) = -1 - g - 6 - 5 - 2. Let a be c(-17). Determine j so that 1/3*j**5 + 0 + 0*j**2 - 2/3*j**4 + 0*j + 1/3*j**a = 0.
0, 1
Let q be ((-529)/483 - 2/6) + 2. Factor 2/7*w**4 + q + 2*w + 10/7*w**3 + 18/7*w**2.
2*(w + 1)**3*(w + 2)/7
Let i(r) be the third derivative of 0*r - r**2 - 1/72*r**4 + 0 + 1/1008*r**8 + 0*r**6 - 1/90*r**5 + 1/315*r**7 + 0*r**3. Factor i(g).
g*(g - 1)*(g + 1)**3/3
Determine k, given that -8/5*k + 0 - 2/5*k**3 - 8/5*k**2 = 0.
-2, 0
Suppose 6 = d + d. Let t(l) = -l**3 + 9*l**2 - l + 11. Let j be t(9). Factor -j*k**2 + 3*k**4 + 1 - 6*k**3 + 2*k**d - 2 + 4*k.
(k - 1)**2*(k + 1)*(3*k - 1)
Let w be (3/4)/((-143)/(-520)). Suppose 26/11*i**3 + w*i**2 + 0 + 4/11*i = 0. Calculate i.
-1, -2/13, 0
Let q(u) = 12*u**4 + 10*u**3 - 4*u**2 + 10*u + 12. Let a(l) = -l**4 - l**3 - l - 1. Let k(h) = -10*a(h) - q(h). Determine d so that k(d) = 0.
-1, 1
Let t(k) be the first derivative of -4*k**3/27 - 8*k**2/9 - 16*k/9 + 3. Factor t(j).
-4*(j + 2)**2/9
Let c be (0 + 24)/(-1 + 0). Let h = c + 24. Factor 1/2*f**3 + 0 - 1/2*f**4 + h*f + 1/2*f**2 - 1/2*f**5.
-f**2*(f - 1)*(f + 1)**2/2
Suppose 3*w = -5*v + 180, 3*v + 4*w = v + 72. Suppose v = 3*d - 3*f + 3, -40 = -4*d + 2*f. Let 10 + d*l - l - 2 + 2*l**2 = 0. What is l?
-2
Factor 0 - 2/11*f**2 + 2/11*f**3 + 0*f.
2*f**2*(f - 1)/11
Let s(j) be the second derivative of -3/10*j**5 + 0*j**3 - 4/15*j**6 + 1/6*j**4 + 6*j + 0*j**2 + 0. Find c, given that s(c) = 0.
-1, 0, 1/4
Let x(f) be the first derivative of f**8/336 + f**7/105 - f**5/30 - f**4/24 + f**2 + 3. Let s(j) be the second derivative of x(j). Factor s(r).
r*(r - 1)*(r + 1)**3
Factor 3*s - 3*s**3 + 41*s**4 - s**2 - 32*s**4 - 8*s**2.
3*s*(s - 1)*(s + 1)*(3*s - 1)
Let t(p) = -p**3 - 1. Let c(x) = -6*x**2 - 12*x - 7. Let f(v) = -5*c(v) - 5*t(v). Factor f(m).
5*(m + 2)**3
Suppose -4*j + 3 = -5. Let n be (-1 + j)*6/4. Let 7/2*c + 1 + n*c**2 = 0. What is c?
-2, -1/3
Let d be (6/4)/((-6)/(-