) = -6*c**4 + 5*c**3 - 5*c**2 + 5*c - 5. Let n(s) = s**4 - s**3 + s**2 - s + 1. Let a(r) = 20*n(r) + 4*x(r). Determine w, given that a(w) = 0.
0
Let i = -7 - -11. Factor -s + 5*s**3 + 0*s**3 - i*s**3.
s*(s - 1)*(s + 1)
Let f = -11 + 6. Let c = f + 8. Factor -u**4 - u**3 - 4*u**3 + 2*u**c + 4*u**3.
-u**3*(u - 1)
Let y(d) = -2*d**3 - d**2 + 2*d - 4. Let v be y(-2). Let k(q) be the first derivative of 0*q**v + 0*q**2 - 1/3*q**3 - 1 + 1/5*q**5 + 0*q. What is w in k(w) = 0?
-1, 0, 1
Let m(q) = -q**2 + q. Let j(g) = 6*g**2 - 6*g. Let h be 14/(-3*(-2)/(-6)). Let a(p) = h*m(p) - 2*j(p). Suppose a(r) = 0. Calculate r.
0, 1
Suppose 4*c - 4*q - 176 = 0, -3*q + 155 = c + 3*c. Determine r so that -324*r - c - 36*r**3 + 162*r**2 + 2*r**4 + r**4 + 166 + 118 = 0.
3
Let 0*a - 6*a - 2*a**2 + 0*a**2 = 0. Calculate a.
-3, 0
Suppose 0 = 3*g + 188 - 194. Factor -2/11*b**g + 2/11*b + 0.
-2*b*(b - 1)/11
Let o(m) = -9 + 2 - 4*m + m**3 - 1 + 12 + 4*m**2. Let c be o(-4). Solve -c*w**3 + 50/3*w**4 + 8*w + 8/3 - 22/3*w**2 = 0.
-2/5, 1
Let y(h) be the third derivative of 0*h**4 + 0 + 7*h**2 + 1/90*h**6 + 1/315*h**7 + 0*h + 0*h**3 + 1/90*h**5. Find m such that y(m) = 0.
-1, 0
Let p be (-8 + 490/30)*2/5. Let -p*h - 2/9*h**3 + 14/9*h**2 + 2 = 0. Calculate h.
1, 3
Suppose 3*f = -2*t - 2*t - 10, 0 = 5*f - 3*t - 22. Factor 4 - 2 + 5*g**3 + f*g + 6*g + 9*g**2 + g**4 - g.
(g + 1)**3*(g + 2)
Let x = 1/4 + 1/4. Let p(u) be the first derivative of -5/2*u**4 - 1/24*u**6 - x*u**5 - 8*u + 2 - 10*u**2 - 20/3*u**3. Determine v, given that p(v) = 0.
-2
Let t(l) be the first derivative of l**5/10 - 3*l**4/8 + l**3/2 - l**2/4 + 15. Determine q, given that t(q) = 0.
0, 1
Let n(j) be the third derivative of -j**8/6720 + j**6/720 - j**4/96 + j**3/3 + 2*j**2. Let y(l) be the first derivative of n(l). Factor y(z).
-(z - 1)**2*(z + 1)**2/4
Let d(j) be the first derivative of -j**6/40 - 3*j**5/40 + j**3/4 + 3*j**2/8 + 2*j - 5. Let m(n) be the first derivative of d(n). Determine s so that m(s) = 0.
-1, 1
Let v be 3/2*8/3. Let a(z) be the third derivative of 0*z**3 + 1/60*z**5 + 0*z**v - z**2 + 0 + 0*z. Suppose a(q) = 0. Calculate q.
0
Let f(c) be the third derivative of c**7/630 - c**6/90 + c**5/60 + c**4/18 - 2*c**3/9 - 47*c**2. Factor f(p).
(p - 2)**2*(p - 1)*(p + 1)/3
Suppose 25 = r - 5*b, -4*r - b + 0 = 5. Factor 1/2*y**5 + 4*y**3 - 5/2*y**4 - 2*y**2 + r*y + 0.
y**2*(y - 2)**2*(y - 1)/2
Let a(p) = 2*p**2 + 4*p - 6. Let s(w) = -w + 1. Let o(y) = a(y) + 6*s(y). Factor o(m).
2*m*(m - 1)
Let l(t) be the first derivative of 0*t**2 + 1/10*t**4 + 4/15*t**3 - 6 + 0*t. Factor l(f).
2*f**2*(f + 2)/5
Let d(c) = c**3 - 17*c**2 - 17*c - 15. Let p be d(18). Let -2*k**2 - 21/2*k**4 + 0 + 0*k + 8*k**p + 9/2*k**5 = 0. What is k?
0, 2/3, 1
Let i(k) be the third derivative of k**7/630 - k**5/180 + 5*k**2. Factor i(g).
g**2*(g - 1)*(g + 1)/3
Suppose -3*s + 83 = -4*u, -3*u - 8 = -2. Let i = 76/3 - s. Suppose i*a**2 - 1/3*a**4 + 0 + 1/3*a**3 - 1/3*a = 0. Calculate a.
-1, 0, 1
Let x(w) be the third derivative of 1/210*w**5 + 4*w**2 + 0 + 1/84*w**4 + 0*w + 0*w**3. Factor x(i).
2*i*(i + 1)/7
Let q be 1/1 + 0 - (0 - 1). Let m(g) be the first derivative of 0*g**2 + q - 1/9*g**3 + 1/3*g. Factor m(x).
-(x - 1)*(x + 1)/3
Let y(s) = 4*s**2 + 1 - 2*s**4 - s**3 + 0 - 3*s**2. Let w = 62 - 63. Let t(d) = -d**3 - d**2 + 1. Let l(q) = w*t(q) + y(q). What is k in l(k) = 0?
-1, 0, 1
Let x(l) be the second derivative of -l**2 - 3*l + 1/12*l**4 + 0 + 1/6*l**3. Solve x(j) = 0 for j.
-2, 1
Let a(y) = y**2 + y - 1. Let u(v) = 4*v**3 + 6*v**2 + 5*v - 5. Let f(n) = -5*a(n) + u(n). Factor f(b).
b**2*(4*b + 1)
Factor 2/13*l**2 - 8/13*l + 8/13.
2*(l - 2)**2/13
Let s(w) = w. Let x(z) = 2*z**2 + 11*z. Let u(h) = -14*s(h) + 2*x(h). Find r such that u(r) = 0.
-2, 0
Let b(c) = -2*c**4 - c**3 - 7*c**2 - c. Let t(g) = g**4 + 3*g**2 + g. Let l(j) = 6*b(j) + 14*t(j). Factor l(i).
2*i*(i - 2)**2*(i + 1)
Let d(r) be the third derivative of r**8/2856 + 2*r**7/1785 - r**5/255 - r**4/204 - 10*r**2. What is w in d(w) = 0?
-1, 0, 1
What is d in 16/3*d - 4/3*d**2 - 4 = 0?
1, 3
Let y(c) be the second derivative of 0*c**3 + 0 - 3*c - 1/6*c**4 + 4/3*c**2 - 1/30*c**5. Factor y(v).
-2*(v - 1)*(v + 2)**2/3
Let n = 1 - 2. Let p be (0/3)/n + 3. Find j, given that j**3 + j**p - 6*j**4 + j**3 = 0.
0, 1/2
Let g = 18 - 12. Let i(l) = l**3 - 5*l**2 - 6*l + 3. Let t be i(g). Solve -o**2 + o**3 + 4*o**t - o**4 - 3*o**3 = 0.
0, 1
Find u, given that -6/5 + 6/5*u**2 - 9/5*u = 0.
-1/2, 2
Let g(q) be the third derivative of q**7/210 + q**6/120 - 4*q**2. Factor g(p).
p**3*(p + 1)
Let m = 8 + -2. Let i = 4 + 1. Factor -5*l**3 - 4*l**3 - l + 8*l**2 + 16*l**i - m*l**3 - 8*l**4.
l*(l - 1)*(l + 1)*(4*l - 1)**2
Let s(u) be the second derivative of -u**4/4 - 13*u. Suppose s(k) = 0. What is k?
0
Let x(o) be the first derivative of 0*o + 2/3*o**2 + 2 - 7/9*o**6 - 6/5*o**5 + 5/6*o**4 + 2*o**3. Solve x(r) = 0.
-1, -2/7, 0, 1
Let b(a) = a - 4. Let z be b(11). Let p be -5*z/((-35)/2). Suppose -2/3*i**3 - 2/3*i**4 + 0 + 2/3*i + 2/3*i**p = 0. Calculate i.
-1, 0, 1
Let k(m) be the third derivative of m**6/420 + m**5/70 + m**4/28 + m**3/21 + 7*m**2. Factor k(u).
2*(u + 1)**3/7
Let h(m) be the first derivative of -6*m**3 - 3*m**4 - 3/5*m**5 - 8 - 3*m - 6*m**2. Factor h(w).
-3*(w + 1)**4
Let -14*r**5 + 2*r**5 + 108*r + 33*r**3 - 129*r - 6 + 21*r**2 - 15*r**4 = 0. What is r?
-2, -1, -1/4, 1
Let v(k) = -k**3 - 9*k**2 - 9*k - 6. Suppose -j - 31 = 4*u, 5*j = -0 + 5. Let y be v(u). Factor 3*s**3 - s**2 + 0*s**2 - y*s**3.
s**2*(s - 1)
Let 6/7*f**2 + 0*f**3 - 3/7 - 3/7*f**4 + 0*f = 0. What is f?
-1, 1
Solve -12*r**3 - 8*r**2 + 4*r - 4*r + 32*r**4 - 12*r**5 = 0.
-1/3, 0, 1, 2
Let w be (8/(-6))/(0 + -2). Let n be 96/(-54) - (1 + -3). Factor -2/3*t**3 + 0 + 0*t - n*t**2 - 2/9*t**5 - w*t**4.
-2*t**2*(t + 1)**3/9
Let y(q) be the first derivative of q**6/6 - 2*q**5/5 + 2*q**3/3 - q**2/2 - 3. Let y(b) = 0. What is b?
-1, 0, 1
Let q be -1*0/(-4 - 6). Factor q + 3/2*d**2 + 0*d - 1/2*d**4 + d**3.
-d**2*(d - 3)*(d + 1)/2
Let s(h) = -5*h**2 - 2*h + 6. Let m(o) = 9*o**2 + 5*o - 11. Let f(a) = -4*m(a) - 7*s(a). Let x be f(-6). Factor 10/9*q**x + 4/9*q + 8/9*q**3 + 0 + 2/9*q**4.
2*q*(q + 1)**2*(q + 2)/9
Let y(o) be the third derivative of -o**7/210 + o**5/60 + 15*o**2. Find x such that y(x) = 0.
-1, 0, 1
Let d = 3 - 1. Suppose 0 = -2*o + 8 - d. Factor 4*a**2 - 3*a**2 + 0*a**4 + a**4 - 2*a**o.
a**2*(a - 1)**2
Let h(x) be the second derivative of -x**5/4 + 25*x**4/4 - 105*x**3/2 + 245*x**2/2 - 27*x - 1. Factor h(y).
-5*(y - 7)**2*(y - 1)
Let g(s) = s**2 + 12*s + 22. Let k be g(-10). What is j in 3/5*j**3 + 0 - 6/5*j**k + 0*j = 0?
0, 2
Let q(c) be the second derivative of -c**4/6 + 5*c**3/3 - 4*c**2 + 7*c. Factor q(n).
-2*(n - 4)*(n - 1)
Let o(l) = -5 - 3*l**2 + 8*l + 13*l**3 - 12*l**3 - 1. Let y(f) = f - 1. Let k(z) = -3*o(z) + 15*y(z). Determine m, given that k(m) = 0.
1
Suppose -4*a**3 + 7*a**2 + 5*a**2 + 26 - 24 - 9*a = 0. What is a?
1/2, 2
Let u(r) be the second derivative of 0 - 1/36*r**4 + 1/18*r**3 + 1/3*r**2 - 3*r. Suppose u(z) = 0. Calculate z.
-1, 2
Determine v so that 286*v**3 + v**4 - 284*v**3 + v**4 = 0.
-1, 0
Let m(z) be the first derivative of -z**6/90 + 7*z**5/60 - z**4/2 + 10*z**3/9 - 4*z**2/3 - 9*z + 4. Let k(v) be the first derivative of m(v). Factor k(d).
-(d - 2)**3*(d - 1)/3
Let f(z) be the third derivative of -z**6/1440 - z**5/240 - z**4/96 - z**3/6 - z**2. Let d(k) be the first derivative of f(k). Let d(s) = 0. What is s?
-1
Factor 0*f + 1/4*f**5 + 0 - 1/4*f**2 + 3/4*f**3 - 3/4*f**4.
f**2*(f - 1)**3/4
Suppose 6*t = 4*t. Suppose 20 = -t*w + 5*w. Find q such that 2/3*q**5 + 0*q + 0*q**2 + 0 + 2/3*q**3 + 4/3*q**w = 0.
-1, 0
Let s(r) be the third derivative of 0*r + 1/42*r**4 + 0*r**3 + 0 - 1/168*r**6 - 5*r**2 - 1/490*r**7 + 1/105*r**5. Factor s(v).
-v*(v - 1)*(v + 2)*(3*v + 2)/7
Let h(x) be the first derivative of -x**4/2 - 14*x**3/9 - 5*x**2/3 - 2*x/3 + 24. Factor h(q).
-2*(q + 1)**2*(3*q + 1)/3
Let b(s) = -3*s + 10. Let y(m) = 4*m - 11. Let i(q) = -5*b(q) - 4*y(q). Let n be i(-6). Factor n*p + 0*p**3 + 1/3*p**4 - 1/3*p**2 + 0.
p**2*(p - 1)*(p + 1)/3
Factor 2*g**2 - g**3 + 0 - 3*g + 4*g + 0*g**2 - 2.
-(g - 2)*(g - 1)*(g + 1)
Let g(i) = 8*i - 7*i**2 + i**3 - 12*i - 3*i - 3 - 2*i**3. Let r be g(-6)