f) = 0?
-1, 0, 2
Let y(g) be the third derivative of 0*g - 3*g**2 + 0*g**3 + 0 - 1/15*g**5 - 1/48*g**4 - 3/224*g**8 - 11/120*g**6 - 2/35*g**7. Factor y(k).
-k*(k + 1)**2*(3*k + 1)**2/2
Let k(p) be the second derivative of -p + 2*p**3 + 0 - 9/2*p**2 - 1/4*p**4. What is r in k(r) = 0?
1, 3
Suppose 2*x - 2 = 2*b + 2, 4*x - b = 23. Let m be (x/(-14))/(2/(-40)). Find u such that 2*u + 18 - 4*u - m*u + 2*u**2 = 0.
3
Let a(i) = 3*i**3 + 8*i**4 + 2*i**2 + i**3 + 4*i + 2*i. Let r(d) = d**4 + d. Let s(w) = w**2 - 8*w + 6. Let c be s(7). Let v(p) = c*a(p) + 6*r(p). Factor v(b).
-2*b**2*(b + 1)**2
Let y(s) be the third derivative of s**7/2205 - s**6/315 + s**5/126 - s**4/126 - s**2 + 7. Solve y(h) = 0.
0, 1, 2
Solve -2*t**4 - 1398*t**3 + t - t + 1394*t**3 = 0 for t.
-2, 0
Let f(d) be the second derivative of -d**6/10 - 3*d**5/4 - 9*d**4/4 - 7*d**3/2 - 3*d**2 - 7*d. Suppose f(g) = 0. What is g?
-2, -1
Let r be (-1)/4 - (-18)/8. Solve -3*w**3 + 0*w**2 - 2*w + r*w**2 - 2 + 5*w**3 + 0*w**3 = 0 for w.
-1, 1
Let c(k) be the third derivative of k**7/4725 + 7*k**6/5400 - k**5/450 + k**4/8 - 3*k**2. Let z(t) be the second derivative of c(t). Solve z(x) = 0.
-2, 1/4
Let z(v) = v**3 - v**2 - v + 1. Suppose 5*n + 0*n - 10 = 0. Let o be z(n). Solve 0*m + 2/5*m**2 + 2/5*m**o + 0 = 0 for m.
-1, 0
Let y(s) = s**2 + 4. Let n be y(0). Suppose -3*z = -3*b, 3*b + 5*z - 24 = -0*b. Suppose -3/2*o**n + 0*o - 5/2*o**b - o**2 + 0 = 0. Calculate o.
-1, -2/3, 0
Let o(i) be the first derivative of i**4/22 + 2*i**3/33 + 2. Solve o(l) = 0.
-1, 0
Suppose 2*p - 12 = -0. Let d(z) = 7*z**2 + 9*z + 2. Let w(a) = a + 0*a**2 - 2*a**2 + 3*a**2. Let g(v) = p*w(v) - d(v). Determine y, given that g(y) = 0.
-2, -1
Let k(s) be the second derivative of s**7/462 + s**6/110 - s**5/220 - 7*s**4/132 + 2*s**2/11 - 10*s. Let k(h) = 0. Calculate h.
-2, -1, 1
Let f be -1*(0 - -1) - -4. Factor -3*t**2 + 8*t**3 + 4*t**4 - 4*t**f - t**2 - 4*t.
4*t*(t - 1)*(t + 1)**2
Let a be 0*(0 + 3)/3. Let s(m) be the third derivative of 0*m + m**2 - 1/240*m**5 - 1/24*m**4 + a - 1/6*m**3. Factor s(y).
-(y + 2)**2/4
Let g(v) be the third derivative of 49*v**6/180 - 7*v**5/15 + v**4/4 - 19*v**2. Let g(x) = 0. Calculate x.
0, 3/7
Suppose 3*k - k = 6, 3*k - 64 = -5*h. Factor -5*y + 9*y**2 - h*y**2 - 6*y - 8 + 3*y.
-2*(y + 2)**2
Let p(r) = r - 1. Let w be p(6). Factor -2*t**5 - 5*t**3 + 5*t**w + 3*t - t**3.
3*t*(t - 1)**2*(t + 1)**2
Let f(s) = -s**2 + 6*s + 2. Let t(k) = k**3 - 4*k**2 - 4*k + 1. Let y be t(5). Let h be f(y). Determine x, given that -14/3*x**h - 4/3 - 6*x = 0.
-1, -2/7
Let l(u) be the third derivative of u**8/840 - 4*u**7/525 - u**6/50 + 2*u**5/75 + u**4/12 + 4*u**2 - 2*u. Find x such that l(x) = 0.
-1, 0, 1, 5
Find j such that -3/2*j + 3/4*j**2 - 9/4 = 0.
-1, 3
Let s(y) be the second derivative of y**6/90 - y**5/30 - y**4/36 + y**3/9 + 21*y. Suppose s(k) = 0. What is k?
-1, 0, 1, 2
Find l, given that -3*l**2 + 4*l**2 - l**2 - 4*l + 16*l**2 = 0.
0, 1/4
Let z(j) = j**2 + 4*j + 11. Let b be z(-3). Factor 0 - 4*o**3 + b*o**2 + 2/3*o**4 - 16/3*o.
2*o*(o - 2)**3/3
Let y(a) be the first derivative of -a**5/120 + a**4/24 + 7*a**2/2 - 2. Let i(q) be the second derivative of y(q). Find x, given that i(x) = 0.
0, 2
Let b(q) = 27*q**2 + 18*q + 4 - 33*q - 19. Let p(s) = 7*s**2 - 4*s - 4. Let v(a) = 4*b(a) - 15*p(a). Factor v(i).
3*i**2
Find p, given that -2/3 - 1/3*p + 1/3*p**2 = 0.
-1, 2
Let k(f) = -f**2 - f - 1. Let c be 28/16 - (-2)/8. Let n(r) = -2*r**2 + 5*r**2 + c*r + 0 - 2. Let z(l) = -2*k(l) - n(l). Solve z(s) = 0 for s.
-2, 2
Let k be (3*1/4)/((-198)/(-176)). Let m(t) be the first derivative of -1/2*t**2 - k*t**3 + 0*t + 2. Factor m(u).
-u*(2*u + 1)
Let p = -447 - -447. Let 3/7*j**2 + 0 + p*j + 12/7*j**4 - 15/7*j**3 = 0. What is j?
0, 1/4, 1
Let t(v) be the second derivative of 0 - 15/2*v**3 + 4*v + 27/2*v**2 - 3/20*v**5 + 7/4*v**4. Factor t(u).
-3*(u - 3)**2*(u - 1)
Let o = -4 + 3. Let k(h) = h**4 + h**2 - h + 1. Let x(y) = -5*y**4 + 2*y**3 - y**2 + y - 3. Let w(d) = o*x(d) - 3*k(d). Factor w(f).
2*f*(f - 1)**2*(f + 1)
Determine g, given that -2/3*g**2 + 2/3 + 0*g = 0.
-1, 1
Let l(o) = -9*o**2 + 47*o - 36. Let g be 116/30 + (-4)/(-30). Let j(w) = -3*w**2 + 16*w - 12. Let y(u) = g*l(u) - 11*j(u). Factor y(c).
-3*(c - 2)**2
Let z(i) be the first derivative of 0*i - 1/3*i**3 + i**2 + 1/5*i**5 + 3 - 1/2*i**4. Factor z(t).
t*(t - 2)*(t - 1)*(t + 1)
Let d(u) be the second derivative of -u**5/5 + u**4/3 + 2*u**3/3 - 2*u**2 + 2*u. Suppose d(k) = 0. What is k?
-1, 1
Suppose -5*k + k = -3*k. Let 0 - 2/3*j**2 + k*j**3 + 8/9*j**4 - 2/9*j = 0. What is j?
-1/2, 0, 1
Let u(g) be the third derivative of -g**5/120 - g**4/24 - g**3/12 + 2*g**2. Factor u(x).
-(x + 1)**2/2
Let o = 437/6 + -218/3. Factor 1/6 - o*l**4 + 1/3*l - 1/3*l**3 + 0*l**2.
-(l - 1)*(l + 1)**3/6
Let u(l) be the first derivative of l**6/540 - l**5/90 + l**4/36 - 2*l**3/3 + 5. Let a(g) be the third derivative of u(g). Factor a(r).
2*(r - 1)**2/3
Factor -2*r**3 - r**3 + r**2 - 2 - r**4 + 2*r**4 + 3*r.
(r - 2)*(r - 1)**2*(r + 1)
Let t(u) = 3*u**4 - 5*u**3 - 20*u**2 - 12*u. Let i(j) = -2*j**4 + 3*j**3 + 13*j**2 + 8*j. Let w(f) = 8*i(f) + 5*t(f). Factor w(v).
-v*(v - 2)*(v + 1)*(v + 2)
Let z be 0 - -8 - (-3)/(-1). Let k(m) be the third derivative of -m**2 + 0*m + 0 - 1/60*m**6 + 1/12*m**4 + 1/30*m**z - 1/3*m**3. Factor k(p).
-2*(p - 1)**2*(p + 1)
Let a(u) be the first derivative of u**4/10 - u**2/5 - 8. Suppose a(s) = 0. Calculate s.
-1, 0, 1
Let b(w) = -1 - 3 - 16*w + 18*w. Let y be b(2). Let 2/5*o**3 + y + 0*o - 2/5*o**4 + 0*o**2 = 0. Calculate o.
0, 1
Determine y, given that 2/7*y - 2/7*y**3 + 2/7*y**2 - 2/7 = 0.
-1, 1
Suppose -4*j = 8, -2*y - 3*j + 1 = 7. Let c be (-22)/(-33)*(1 + 2). Factor -3*i**3 + y*i**4 - c*i**5 + 5*i**3 - 2*i**4 + 2*i**2.
-2*i**2*(i - 1)*(i + 1)**2
Let u(i) be the third derivative of -i**8/1680 - i**7/350 - i**6/600 + i**5/100 + i**4/60 + 2*i**2. Determine h, given that u(h) = 0.
-2, -1, 0, 1
Let i = 261 - 259. Factor -2/3*k**3 + 0*k - 2/3*k**5 + 0*k**i + 0 + 4/3*k**4.
-2*k**3*(k - 1)**2/3
Let w(d) be the third derivative of d**8/1512 + 2*d**7/945 - d**6/135 - 4*d**5/135 + 37*d**2. Factor w(v).
2*v**2*(v - 2)*(v + 2)**2/9
Let h(c) be the first derivative of -c**5/3 + 6. Determine b so that h(b) = 0.
0
Let n(v) = -v**4 + v**3 + v**2 + v + 1. Let o(r) = -3*r**2 - 3*r - 3. Let z = -12 - -15. Let d(a) = z*n(a) + o(a). Factor d(t).
-3*t**3*(t - 1)
Let m(v) be the second derivative of v**4/78 + 8*v**3/39 + 16*v**2/13 - 6*v. Find n such that m(n) = 0.
-4
Let 5*y**4 - 3*y**2 - 171*y**3 + 3*y**2 + 206*y**3 = 0. Calculate y.
-7, 0
Suppose -3*o + 6*o = 0. Let w(r) be the second derivative of o - 1/4*r**2 + 5/48*r**4 - 2*r - 1/8*r**3. Find b, given that w(b) = 0.
-2/5, 1
Find d, given that 8/3 - 8/3*d**2 + 4/3*d - 4/3*d**3 = 0.
-2, -1, 1
Let d(v) = v**2 + 4*v - 2. Let k be d(-5). Factor c**3 + k*c**4 - 4*c**3 - 3*c**3 + 3*c**2.
3*c**2*(c - 1)**2
Let i(k) be the second derivative of 0*k**4 - 1/5*k**3 - k + 2/25*k**5 + 0 + 1/5*k**2. Factor i(j).
2*(j + 1)*(2*j - 1)**2/5
Find r, given that 5/4*r + 5/4*r**2 - 5/4 - 5/4*r**3 = 0.
-1, 1
Let n(w) be the first derivative of 2*w**5/55 - w**4/11 + 2*w**2/11 - 2*w/11 + 1. Factor n(h).
2*(h - 1)**3*(h + 1)/11
Let h(j) be the second derivative of -5*j**5 + 5*j**4/12 - 8*j - 3. Factor h(f).
-5*f**2*(20*f - 1)
Suppose -3*l + 20 = -l. Solve 2*q**3 - 11*q**2 + 2*q**4 + 24*q + 37*q**2 + 8 + l*q**3 = 0 for q.
-2, -1
Suppose 11*r = 82 - 27. Factor a**2 + 0*a**3 + 0 - 1/2*a**r - a**4 + 1/2*a.
-a*(a - 1)*(a + 1)**3/2
Let k(x) be the second derivative of 0*x**4 + 0 - 1/3*x**3 + 1/10*x**5 - 1/30*x**6 + 1/2*x**2 - x. Find n, given that k(n) = 0.
-1, 1
Let p = 5666/21135 - 2/1409. Factor 2/15*x**4 - p*x**3 + 0 + 0*x**2 + 0*x.
2*x**3*(x - 2)/15
Let z(a) be the first derivative of a**3/15 + 3*a**2/10 - 12. What is k in z(k) = 0?
-3, 0
Let v = 16 - 12. Suppose -21*l + 23*l - v = 0. Factor 0 + 2/5*u + 2/5*u**4 + 6/5*u**3 + 6/5*u**l.
2*u*(u + 1)**3/5
Let z(k) be the first derivative of 2*k**3/15 - k**2/3 - 4*k/15 - 17. Factor z(y).
2*(y - 2)*(3*y + 1)/15
Let p(r) be the second derivative of r**4/12 - r**3/6 - r**2 + 9*r. Find i, given that p(i) = 0.
-1, 2
Let y(c) = 8*c**2 + 13*c - 8. Let o(i) = -7*i**2 - 12*i + 7. Let n(p) = -7*o