t p(m) = 0.
0, 1
Suppose 0*r - r - 15 = 3*g, -5*r - 3*g = 51. Let l = r + 11. Factor 6/5*z + 4/5 + 2/5*z**l.
2*(z + 1)*(z + 2)/5
Find b, given that -1 + 2*b**2 + 9 - 7*b**2 - 3 = 0.
-1, 1
Let a(z) = 10*z**2 + 3*z - 15*z**2 - 6 - 5*z - 5*z. Let v(o) = -o**2 - o - 1. Let i(s) = a(s) - 6*v(s). Find r, given that i(r) = 0.
0, 1
Let s(u) be the first derivative of 5*u**3/3 + 7*u**2/2 + 2*u - 9. Factor s(y).
(y + 1)*(5*y + 2)
Let z(o) be the first derivative of 2*o**6/27 + 16*o**5/45 + o**4/3 - 16*o**3/27 - 8*o**2/9 - 28. Find w, given that z(w) = 0.
-2, -1, 0, 1
Let p = -151 - -1367/9. Let w = -5 - -7. Let -w*s - 4/9 - p*s**2 = 0. Calculate s.
-2, -1/4
Let t(l) = -l**3 + 7*l**2 - 4*l - 6. Let p be t(6). Factor -p*k**2 - 1 - 5*k - k - 2*k**3 - 1.
-2*(k + 1)**3
Let q(y) = y**3 + 3*y**2 + y. Let o be q(-3). Let r be o + 2/(8/12). Factor -2/9*u**2 + r + 2/9*u.
-2*u*(u - 1)/9
Let s(l) = -3*l**4 + 3*l**3 + 3*l - 3. Let y(h) = -6*h**4 + 6*h**3 + 5*h - 5. Let i(k) = -5*s(k) + 3*y(k). Let i(u) = 0. Calculate u.
0, 1
Let h(d) = d + 4. Let f be h(-4). Let m = -177 - -1241/7. Suppose f - 2/7*y + m*y**4 - 2/7*y**2 + 2/7*y**3 = 0. What is y?
-1, 0, 1
Let r be 1/((-3)/6*-1). Suppose 6*m**r - 3 + 4*m - 4*m**2 + 3 = 0. What is m?
-2, 0
Suppose 10/9*l - 4/9 - 2/3*l**2 = 0. Calculate l.
2/3, 1
Let d = 15/8 + 21/8. Let j = 29/6 - d. Factor j*z - 1/3 + 16/3*z**2 - 16/3*z**3.
-(z - 1)*(4*z - 1)*(4*z + 1)/3
Suppose 4*o = 12 - 0. Suppose o*b - 3*j - 6 = 0, -2*b + 4*b + 2*j - 4 = 0. Let 2/3*z**3 - 2/3*z + 0 + 7/3*z**4 - 7/3*z**b = 0. Calculate z.
-1, -2/7, 0, 1
Let u = -34 + 34. Let h(s) be the third derivative of 1/3*s**4 + 1/6*s**5 + u - 3*s**2 + 0*s - 1/3*s**3. Factor h(c).
2*(c + 1)*(5*c - 1)
Let y = 11 + -9. Factor -5*a + 3*a + 4 + 2*a**y - 4.
2*a*(a - 1)
Let k be (-10)/(-16)*(7 + -3). Determine t, given that 0 - t**2 + 7/2*t**3 - k*t**4 + 0*t = 0.
0, 2/5, 1
Let z = 12 + -7. Suppose 2*a = z + 3. Factor 12*b**2 - 8*b**3 - 5*b - 3*b + 2*b**a + 0 + 2.
2*(b - 1)**4
Let y(l) be the third derivative of -l**8/588 - 2*l**7/105 - l**2 - 5*l. Factor y(k).
-4*k**4*(k + 7)/7
Factor 1/3*n**2 - 1/3 - 1/3*n**3 + 1/3*n.
-(n - 1)**2*(n + 1)/3
Let c(r) be the third derivative of r**5/270 + r**4/27 + 4*r**3/27 - 5*r**2. Factor c(b).
2*(b + 2)**2/9
Let g(y) = -y**2 - 4*y - 5. Let z(p) = 2*p + 2. Let m(h) = 2*g(h) + 5*z(h). Let m(c) = 0. Calculate c.
0, 1
Let d be ((-3)/(-15)*-2)/((-3)/30). Let w(m) be the second derivative of -1/48*m**d + m + 1/12*m**3 + 0 - 1/8*m**2. Factor w(a).
-(a - 1)**2/4
Let c(i) = -i**2 + 11*i + 14. Suppose 5*o - 4*w = -0*o + 72, 0 = 4*w + 12. Let j be c(o). Factor 2/3*d**3 + 0*d**j + 1/3 - 1/3*d**4 - 2/3*d.
-(d - 1)**3*(d + 1)/3
Let g be (-6)/(-12)*(-1)/(-2). Factor 3/4*a - g + 3/4*a**4 - 1/2*a**3 - 1/2*a**2 - 1/4*a**5.
-(a - 1)**4*(a + 1)/4
Let j(x) be the first derivative of x**5/300 - x**3/30 - x**2/2 + 1. Let z(s) be the second derivative of j(s). Determine n, given that z(n) = 0.
-1, 1
Let w(f) be the third derivative of 3*f**2 + 1/60*f**7 + 0*f**4 + 0*f + 3/80*f**6 + 1/60*f**5 + 0 + 0*f**3. Factor w(k).
k**2*(k + 1)*(7*k + 2)/2
Let b(i) be the third derivative of i**8/16800 - i**7/1260 + i**6/225 - i**5/75 + i**4/24 - i**2. Let h(t) be the second derivative of b(t). Factor h(y).
2*(y - 2)**2*(y - 1)/5
Let y be -2*((-20)/12 + (-2)/(-3)). Factor 6/7*z**y - 2/7*z**4 + 4/7*z**3 - 8/7*z - 8/7.
-2*(z - 2)**2*(z + 1)**2/7
Suppose 2*r - 6 = 4*r. Let p be r/(-9) - (-1 - 0). Factor -2/3*u**5 + 0*u**2 + p*u**3 + 0 - 2/3*u + 0*u**4.
-2*u*(u - 1)**2*(u + 1)**2/3
Factor -4/5*m**3 - 1/5 - m - 8/5*m**2.
-(m + 1)*(2*m + 1)**2/5
Let t be ((-6)/(-10) + -1)/((-56)/105). Let k + 1/4*k**2 + t = 0. Calculate k.
-3, -1
Determine c so that 2*c**3 + 0 - 2*c**2 - 2/3*c**4 + 2/3*c = 0.
0, 1
Let r(g) be the first derivative of -g**9/2016 - 3*g**8/1120 + g**6/60 - 2*g**3 + 3. Let v(u) be the third derivative of r(u). Factor v(l).
-3*l**2*(l - 1)*(l + 2)**2/2
Factor -1/2*g**5 - 3/2*g**3 + 0 + 1/2*g**2 + 0*g + 3/2*g**4.
-g**2*(g - 1)**3/2
Find h such that 1/5*h**5 + h**3 + 0 - 4/5*h**4 + 0*h - 2/5*h**2 = 0.
0, 1, 2
Find s, given that 15/4*s**5 + 0 + 9*s**4 + 0*s + 27/4*s**3 + 3/2*s**2 = 0.
-1, -2/5, 0
Suppose -5*n + 2*y - 3 = -8, 14 = -2*n + 4*y. Factor 3*k**2 - 6*k**4 + 1 - 5*k + 5*k**n - 3*k**4 + 5*k**4.
-(k - 1)**2*(k + 1)*(4*k - 1)
Let i(b) be the first derivative of -3*b**5/20 - b**4/2 - b**3/2 + b/4 + 2. Solve i(t) = 0 for t.
-1, 1/3
Suppose 0 = r - 2. Suppose -y + 3*m + 18 = 0, -4*y - 2 + 24 = -2*m. Factor t**y + t**r - t + 4*t**4 + 0*t**3 - 5*t**4.
-t*(t - 1)**2*(t + 1)
Let f = -96 + 96. Factor f*y**2 - 1/2 + 1/2*y**4 + y**3 - y.
(y - 1)*(y + 1)**3/2
Suppose 2*x + 2*h = 10, 3*h - 13 = -14*x + 12*x. Let -4/7 + x*b - 10/7*b**2 = 0. What is b?
2/5, 1
Let p(z) be the second derivative of 0 + 0*z**2 - 9/100*z**5 + 1/50*z**6 + z + 3/20*z**4 - 1/10*z**3. Factor p(f).
3*f*(f - 1)**3/5
Suppose 2*r + 5*a - 21 = 0, -4*a + 3 = -3*r - 0*a. Let w(f) be the second derivative of 0 + 1/24*f**4 + 1/3*f**r + f**2 + f. Factor w(t).
(t + 2)**2/2
Factor -14*z**3 + 19*z**3 + 2*z**4 - 11*z**3 + 4*z**2.
2*z**2*(z - 2)*(z - 1)
Solve 3*m**3 + m - 3 + 0*m + 3 - 3*m**2 - m**4 = 0.
0, 1
Factor -12/5*w - 16/5 + 4/5*w**2.
4*(w - 4)*(w + 1)/5
Let a(z) = -z**2 - 19*z + 125. Let l be a(-24). Factor -g**3 + 1/2*g + 1/2*g**l + 0*g**4 + 0*g**2 + 0.
g*(g - 1)**2*(g + 1)**2/2
Let b(y) be the second derivative of y**8/6720 + y**7/6300 - y**6/720 - y**5/300 - y**4/4 - y. Let q(v) be the third derivative of b(v). Factor q(m).
(m - 1)*(m + 1)*(5*m + 2)/5
Let j(m) be the third derivative of m**8/1680 - m**7/350 + m**6/200 - m**5/300 - 6*m**2. Factor j(r).
r**2*(r - 1)**3/5
Let l(k) = k**3 + 7*k**2 - 9*k - 8. Let h be 1 - (0 - (3 + -12)). Let d be l(h). Factor d*q + 1/2 - 1/2*q**2.
-(q - 1)*(q + 1)/2
Let i(u) be the first derivative of -3*u**2 - 1 + 4*u + 2/3*u**3. Let m(s) = -s**2 + 3*s - 2. Let x(v) = 4*i(v) + 9*m(v). Find n, given that x(n) = 0.
1, 2
Let x(f) be the second derivative of -f**6/33 - 17*f**5/110 - 7*f**4/22 - f**3/3 - 2*f**2/11 - 12*f. Let x(o) = 0. Calculate o.
-1, -2/5
Let t(z) be the third derivative of -z**8/80640 - z**7/20160 - z**5/30 - 2*z**2. Let o(n) be the third derivative of t(n). Factor o(s).
-s*(s + 1)/4
Let m(b) be the third derivative of -b**7/420 + b**6/80 + b**5/60 - b**4/4 + 2*b**3/3 - 4*b**2 + 10*b. Factor m(v).
-(v - 2)**2*(v - 1)*(v + 2)/2
Let s(m) be the first derivative of -m**7/300 + m**6/75 - m**5/100 - m**4/30 + m**3/3 + 2. Let y(r) be the third derivative of s(r). Factor y(n).
-2*(n - 1)**2*(7*n + 2)/5
Factor -96/7*k**3 - 6/7*k**5 + 0*k**2 + 0 + 0*k + 48/7*k**4.
-6*k**3*(k - 4)**2/7
Let c(p) = -p**4 + p**3. Let q(r) be the third derivative of r**7/70 - r**6/40 + r**5/20 - r**4/24 - r**3/3 - r**2. Let i(t) = -4*c(t) - q(t). Factor i(w).
(w - 2)*(w - 1)*(w + 1)**2
Suppose -27*g = -23*g. Factor -3/4*q - 3/2*q**2 + g - 3/4*q**3.
-3*q*(q + 1)**2/4
Let n(f) be the second derivative of 3*f + 0*f**2 + 0 + 1/60*f**6 + 1/84*f**7 - 1/24*f**4 - 1/40*f**5 + 0*f**3. Factor n(l).
l**2*(l - 1)*(l + 1)**2/2
Let j(h) = 3*h**4 + 2*h**2 + 4*h - 1. Let y(c) = -2*c**4 + c**3 - c**2 - 4*c. Let x(s) = -3*j(s) - 4*y(s). Solve x(i) = 0.
-3, -1, 1
Suppose -8*t + 4*t + 44 = 0. Let v(a) = -a**2 + a + 2. Let o(c) = -3*c**2 + 2*c + 5. Let w(z) = t*v(z) - 4*o(z). Find p, given that w(p) = 0.
-2, -1
Let v be 16/28*70/12. Solve 0*d + 0 + 4/3*d**3 - v*d**4 + 0*d**2 - 14/3*d**5 = 0.
-1, 0, 2/7
Let x(l) = 11*l**5 - 12*l**4 + 7*l**3 + 13*l**2 - 9*l + 8. Let d(j) = -j**5 + j**4 - j**3 - j**2 + j - 1. Let b(v) = 18*d(v) + 2*x(v). Factor b(r).
2*(r - 1)**3*(r + 1)*(2*r + 1)
Let n = 14 + -6. Suppose -4 = 3*o + n, p + 3*o = -12. Factor p*s + 0*s**2 + 0*s**3 + 0 - 2/9*s**4.
-2*s**4/9
Let u(q) be the second derivative of -q**5/90 + q**2/2 + q. Let o(z) be the first derivative of u(z). Factor o(v).
-2*v**2/3
Let f = 1 - -2. Let l(r) be the second derivative of -1/3*r**4 + 4/9*r**f + 2/15*r**5 - 1/45*r**6 - 1/3*r**2 + 0 - 2*r. Suppose l(z) = 0. What is z?
1
Factor 6/5 - 21/5*r**2 - 3*r.
-3*(r + 1)*(7*r - 2)/5
Solve 2*a**2 + 25*a + 35*a - 70*a = 0 for a.
0, 5
Let i(o) be the first derivative of -2/5*o**2 - 3 - 1/10*o**4 + 2/5*o**3 + 0*o. Solve i(w) = 0.
0, 1, 2
Factor 4*q + 8 - 13*q**3 + 9*q**3 - 4 + 8 - 12*q**2.
-4*(q - 1)