r 76*g**2 + 28*g + 8 - 24*g**2 - y*g**2.
4*(g + 1)*(5*g + 2)
Let r(v) = v**5 - v**4 - 2*v**3 + v**2 - v + 1. Let g(q) = 8*q**5 + 34*q**4 + 96*q**3 + 110*q**2 + 28*q + 6. Let n(x) = -g(x) + 6*r(x). Factor n(t).
-2*t*(t + 1)**3*(t + 17)
Suppose 2*s - 18 = 16. What is r in 14*r**4 - r + 3*r**5 - s*r**4 + r - 6*r**3 = 0?
-1, 0, 2
Factor 0 + 4/9*r**2 - 2/9*r**5 - 10/9*r**3 + 0*r + 8/9*r**4.
-2*r**2*(r - 2)*(r - 1)**2/9
Let i(g) = -g**2 + 22*g - 114. Let c be i(9). Factor -2*j**2 - 1/2*j + 1/2*j**c + 2.
(j - 4)*(j - 1)*(j + 1)/2
Let i(x) be the second derivative of -5*x**7/42 - x**6/2 - x**5/4 + 5*x**4/4 + 5*x**3/3 + 537*x. Suppose i(r) = 0. What is r?
-2, -1, 0, 1
Let y = -3739/18 - -417/2. Factor 5/9*n**2 - 4/9*n**3 + y*n - 2/9.
-(n - 2)*(n + 1)*(4*n - 1)/9
Let x(l) be the second derivative of -l**7/105 + l**5/15 - l**3/3 - 9*l**2 - 5*l. Let j(b) be the first derivative of x(b). Let j(f) = 0. What is f?
-1, 1
Suppose 3*m + 2*m - 25 = -5*s, -s = -5*m + 31. Suppose 17*x - 44 = m*x. Factor 0 + 0*t - 8/3*t**5 - 2/3*t**2 + 14/3*t**x - 4/3*t**3.
-2*t**2*(t - 1)**2*(4*t + 1)/3
Let h(m) = m - 1. Let r(t) = -5*t**2 + 120*t - 20. Let w(n) = -20*h(n) + r(n). Find p such that w(p) = 0.
0, 20
Let z(s) = 64*s**3 + 508*s**2 + 3158*s + 2638. Let d(f) = 5*f**3 + 39*f**2 + 243*f + 203. Let g(v) = -76*d(v) + 6*z(v). Find b, given that g(b) = 0.
-10, -1
Let z = 1264 + -68255/54. Let q(o) be the second derivative of 0 - 5/54*o**3 + 1/9*o**2 - 2/135*o**6 + 1/45*o**5 + z*o**4 + 1/378*o**7 + 2*o. Factor q(c).
(c - 2)*(c - 1)**3*(c + 1)/9
Let -5*z**4 - 336 - 547 - 808 - 213*z**2 - 327*z**2 + 85*z**3 + 1520*z + 91 = 0. Calculate z.
4, 5
Let q(w) be the first derivative of -w**4/14 + 6*w**3/7 - 20*w**2/7 + 24*w/7 + 78. Determine g so that q(g) = 0.
1, 2, 6
Suppose 234*n - 43*n = -104*n + 590. Find o such that -6/5*o - 1/5*o**n - 9/5 = 0.
-3
Suppose -3*q - 3*c - 11 + 2 = 0, 4*q + 5*c + 12 = 0. Let p be q - (68/(-28) + -2). Solve -p*w**3 - 34/7*w**2 - 32/7*w - 8/7 = 0.
-2, -1, -2/5
Let u(j) be the first derivative of -3*j**7/280 - j**6/18 - j**5/30 + 2*j**3 + 2. Let w(r) be the third derivative of u(r). Factor w(b).
-b*(b + 2)*(9*b + 2)
Let 4/5*y**3 + 2/5*y + 0 - 1/5*y**4 - y**2 = 0. Calculate y.
0, 1, 2
Let m(g) = g**3 + 3*g**2 + 8*g + 4. Let c(a) = -1 + 0 - 39*a + 38*a. Let i(v) = -24*c(v) - 3*m(v). Factor i(o).
-3*(o - 1)*(o + 2)**2
Solve -5*f**5 + 42*f - 1900 + 1930 - 50*f**3 + 13*f - 30*f**4 = 0.
-3, -2, -1, 1
Let f be (-3 - -4)*(-3)/(-6). Let j(w) = -w**2 + 11*w - 18. Let u be j(9). Factor 1/6*y + u - 1/2*y**2 - 1/6*y**4 + f*y**3.
-y*(y - 1)**3/6
Let k be -2 - (-3 - (3 - 3)). Suppose -7 = -3*o - k. Solve -o*n**2 - n**2 - n**3 + 2*n**2 + 2*n**2 = 0.
0, 1
Let l(k) be the second derivative of 0 + 1/18*k**3 + 1/126*k**7 - 1/30*k**5 - 1/18*k**4 + 1/90*k**6 + 10*k + 1/6*k**2. Determine h so that l(h) = 0.
-1, 1
Let l(u) = 5*u - 4. Let p be l(1). Let m(r) = r**2. Let c(d) be the second derivative of -d**5/20 - 5*d**4/12 + d. Let w(b) = p*c(b) + 6*m(b). Factor w(j).
-j**2*(j - 1)
Let m(q) be the first derivative of 12*q + 7/3*q**3 - 27 + 8*q**2 + 1/4*q**4. Determine w so that m(w) = 0.
-3, -2
Suppose -36 = -6*a + 2*a. Let p(r) = -r**2 - 5*r + 2. Let h be p(-5). Factor t**2 + t + 0*t**2 - a*t - 4 - 5*t**h.
-4*(t + 1)**2
Let h = 6861/4 + -1715. Let b(a) be the first derivative of -1/20*a**5 + 0*a + 11 - 1/4*a**4 - h*a**2 - 5/12*a**3. Factor b(v).
-v*(v + 1)**2*(v + 2)/4
Let f(r) be the second derivative of r**7/210 + r**6/15 - 19*r**3/6 + 2*r. Let a(n) be the second derivative of f(n). Solve a(o) = 0 for o.
-6, 0
Let z = -5174/15 - -345. Let r(d) be the second derivative of 8*d - 4/5*d**2 - z*d**6 - 11/10*d**4 - 4/3*d**3 - 11/25*d**5 + 0. Let r(s) = 0. What is s?
-2, -1, -2/5
Factor -2/11*i**2 + 0*i + 0.
-2*i**2/11
Let f(b) be the first derivative of -b**4/28 + b**3 + 45*b**2/14 + 23*b/7 - 63. Let f(j) = 0. What is j?
-1, 23
Let f be ((-24)/20)/((-4)/10). Solve 7*z**2 - 9*z**2 + 4*z - 2*z - 2*z**f + 2 = 0 for z.
-1, 1
Let r(v) = -4*v**2 + 47*v - 58. Let l be r(10). Let m(y) be the second derivative of 5/3*y**3 + 5/12*y**4 + l*y + 5/2*y**2 + 0. Factor m(o).
5*(o + 1)**2
Let k be 3/(-4) - (-474)/(-8). Let d be (-4)/18 - k/27. Determine l so that -2*l**2 + 1 + 3*l**2 - 2*l**d = 0.
-1, 1
Let y(u) be the third derivative of 0*u - 1/28*u**4 + 0 - 1/1260*u**6 + 4/3*u**3 - 2*u**2 - 1/105*u**5. Let c(t) be the first derivative of y(t). Factor c(r).
-2*(r + 1)*(r + 3)/7
Let t(k) = -k**2 - 27*k + 21*k - 21 - 9*k. Let m be t(-13). Suppose 2*z**2 - 2*z**4 + 14/9*z**m - 10/9*z**3 - 4/9*z + 0 = 0. What is z?
-1, 0, 2/7, 1
Suppose 1 = -m - 3. Let w be 1/((-1)/m*4). Let s + w - 2 - s**2 + 3 = 0. Calculate s.
-1, 2
Suppose -114 - 390 = -6*q. Let u be q/70*5/3. Factor -2/13*l**3 + 0*l + 0 - 2/13*l**u.
-2*l**2*(l + 1)/13
Let k(y) = -y**4 - y**3 + 2*y**2 - 2. Let g(p) = 21*p**3 - 6*p**2 - 96*p + 6. Let s(u) = -g(u) - 3*k(u). Find q, given that s(q) = 0.
-2, 0, 4
Let w(l) be the second derivative of 1/135*l**6 + 0 + 4/27*l**4 - 7*l - 1/18*l**5 - 4/27*l**3 + 0*l**2. Factor w(x).
2*x*(x - 2)**2*(x - 1)/9
Let q(t) be the third derivative of t**6/600 - 7*t**5/100 + t**4 - 10*t**3/3 + 9*t**2 - 20*t. Factor q(i).
(i - 10)**2*(i - 1)/5
Suppose 0 = 5*i - 5, 5*l + 2*i - 3*i = 4. Let v be (7 + l)/2 - 0. Solve -4*o**3 + v*o - 13 + 2*o**2 - 2*o**4 + 13 = 0 for o.
-2, -1, 0, 1
Suppose -7*a = -4*a + 3. Let k(x) = x**3 + x**2 - x + 1. Let u(z) = -z**3 + 29*z**2 - 47*z - 73. Let s(v) = a*u(v) + 2*k(v). Factor s(l).
3*(l - 5)**2*(l + 1)
Suppose 28/9*w**4 + 4/9*w**5 - 272/9*w**2 - 128/9*w + 256/3 + 0*w**3 = 0. Calculate w.
-4, -3, 2
Let o(f) = f**3 + 16*f**2 + 4. Let k be o(-16). Factor -48*g**2 + 62*g**3 - k*g**4 - 161*g**3 + 75*g**3 - 32*g.
-4*g*(g + 2)**3
Let i(l) be the first derivative of 4*l**3/9 + 16*l**2/3 - 12*l - 119. Solve i(a) = 0 for a.
-9, 1
Determine n so that 28 + 20*n**2 - 131*n + 15*n**3 - 19*n**3 + 183*n = 0.
-1, 7
Let c(k) be the first derivative of -k**4/8 + 2*k**3/3 + 29*k**2/4 + 12*k + 146. Factor c(v).
-(v - 8)*(v + 1)*(v + 3)/2
Let q(r) be the first derivative of 14 + 1/4*r**3 - 3/4*r**2 + 3/4*r. Factor q(t).
3*(t - 1)**2/4
Let o = 238 + -234. Let t(h) be the first derivative of 1/10*h**o - 1/25*h**5 - 1/10*h**2 + 2/15*h**3 - 1/30*h**6 - 1/5*h - 6. Factor t(f).
-(f - 1)**2*(f + 1)**3/5
Let v(t) be the second derivative of t**7/3780 - t**6/540 + t**5/270 - 8*t**3/3 + 14*t. Let s(u) be the second derivative of v(u). Suppose s(m) = 0. What is m?
0, 1, 2
Let y(i) be the third derivative of i**8/252 + 296*i**7/315 + 7201*i**6/90 + 22030*i**5/9 - 121250*i**4/9 + 250000*i**3/9 - 214*i**2. Solve y(o) = 0 for o.
-50, 1
Factor -1/3*k**3 + 4/3 + 7/3*k + 2/3*k**2.
-(k - 4)*(k + 1)**2/3
Let k(r) = 9*r**2 - 24*r + 101. Let t(h) = -10*h**2 + 20*h - 102. Let x(w) = -6*k(w) - 5*t(w). Factor x(b).
-4*(b - 8)*(b - 3)
Let 4/9*f**3 + 4*f**2 + 0 + 32/9*f = 0. Calculate f.
-8, -1, 0
Let x(w) = -2*w**4 + w**3 - w**2 - w - 2. Let c(o) = -12*o**4 + 7*o**3 - 75*o**2 - 199*o - 140. Let q(k) = -c(k) + 7*x(k). Let q(m) = 0. What is m?
-3, -1, 7
Let n(a) be the second derivative of a**4/78 - 6*a**3/13 + 72*a**2/13 + 325*a. Factor n(t).
2*(t - 12)*(t - 6)/13
Let c(w) be the second derivative of 2*w**6/15 + 7*w**5/5 + 14*w**4/3 + 16*w**3/3 + 3*w - 14. Factor c(p).
4*p*(p + 1)*(p + 2)*(p + 4)
Suppose -76 = -7*r + 3*r. Let p = r + -17. Factor -o**2 + 5*o**2 + 3*o + o**2 - 2*o**p.
3*o*(o + 1)
Suppose 2*d - 3 = -5*x, 0 = d - x - 2*x - 18. Let c be (-3)/(d/(-15)) + -3. Factor -c*b - 1 + 4*b**2 - 15*b + 17 + b.
4*(b - 2)**2
Let h be 3*(-1 + (-54)/(-45)). Factor 0*o**2 + 0*o - h*o**3 + 3/5*o**5 + 0 + 0*o**4.
3*o**3*(o - 1)*(o + 1)/5
Let g(n) be the third derivative of n**8/11200 + n**7/1050 + n**6/400 - n**4/3 + 4*n**2. Let c(j) be the second derivative of g(j). Suppose c(p) = 0. What is p?
-3, -1, 0
Factor 52/7*r - 120/7 - 4/7*r**2.
-4*(r - 10)*(r - 3)/7
Let j(l) be the second derivative of -l**6/360 - l**5/180 + l**4/72 + l**3/18 - 6*l**2 + 12*l. Let h(x) be the first derivative of j(x). Factor h(v).
-(v - 1)*(v + 1)**2/3
Factor -117 - 128 + 2*t**2 + 231 - 6*t - 6*t.
2*(t - 7)*(t + 1)
Let l(b) be the second derivative of -1/420*b**7 + 0 + 1/75*b**6 - 1/60*b**3 - 3/100*b**5 - 10*b + 1/30*b**4 + 0*b**2. Solve l(q) = 0.
0, 1
Supp